**Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids**

P. Gunnasegaran, N.H. Shuaib, H.A. Mohammed, M.F. Abdul Jalal and E. Sandhita *Department of Mechanical Engineering, College of Engineering Universiti Tenaga Nasional, Km7 Jalan Kajang-Puchong, Selangor Malaysia* 

#### **1. Introduction**

286 Fluid Dynamics, Computational Modeling and Applications

Um, S.; Wang, C.Y. & Chen, K.S. (2000). Computational fluid dynamics modeling of proton

Wang, C.Y. (2004). Fundamental models for fuel cell engineering, *Chemical Reviews*, Vol. 104,

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*Hydrogen Energy*, Vol.33, No.6, (2008), pp. 1735-1746, ISSN 0360-3199 Wu, J.; Zi Yuan, X.; Wang, H.; Blanco, M.; Martin, J.J. & Zhang J. (2008) Diagnostic tools in

*Hydrogen Energy*, Vol.33, No.6, (2008), pp. 1747-1757, ISSN 0360-3199 Yao, K.Z.; Koran, K.; McAuley, K.B.; Oosthuizen, P.; Peppley, B. & Xie, T. (2004). A review of

(2000), pp. 4485-4493, ISSN 0013-4651

No.10, (2004), pp. 4727-4765, ISSN 0009-2665

exchange membrane fuel cells. *Journal of the Electrochemical Society.* Vol.147, No.12

PEM fuel cell research: Part I Electrochemical techniques. *International Journal of* 

PEM fuel cell research: Part II: Physical/chemical methods. *International Journal of* 

mathematical models for hydrogen and direct methanol polymer electrolyte membrane fuel cells, *Fuel Cells*, Vol.4, No.1-2, (2004), pp. 3-29, ISSN 1615-6846

#### **1.1 Introduction to microchannel heat sink (MCHS)**

The microchannel heat sink (MCHS) cooling concept is first proposed by Tuckerman and Pease [1] in 1981. MCHSs are the most common and cost-effective hardware employed for the thermal management of MEMS devices. Tuckerman and Pease [1] pointed out that decreasing liquid cooling channel dimensions to the micron scale will lead to increase the heat transfer rate. They demonstrated experimentally a forty-fold improvement in heatsinking capability in Si-base microchannels anodically bonded to Pyrex cover plates. Since then, intense research on MCHS have been conducted to study the heat transfer and fluid flow characteristics of MCHS.

There are two main configurations for the application of microchannel cooling which are direct cooling and indirect cooling. Direct cooling requires a direct contact between the surface to be cooled and the coolant fluid as illustrated in Fig.1.1a. This scheme reduces the thermal resistance between the surface and the coolant and thus, enhances the cooling effectiveness. However, electrical and chemical compatibility between the coolant and device itself needs to be ensured for this system to work [2]. An alternative to the above configuration is the use of a metallic heat sink to conduct the heat away from the device to a coolant which is forced through circular or noncircular grooves in the heat sink. Such an indirect cooling configuration shown in Fig.1.1b allows for a greater flexibility in coolant selection at the cost of increased thermal resistance between the device and the heat sink due to the heat diffusion resistance in the heat sink itself [3].

Microchannels are very fine channels of the width of a normal human hair and are widely used for electronic cooling purposes. In a MCHS, multiple microchannels are stacked together as shown in Fig.1.1 (b) which can increase the total contact surface area for heat transfer enhancement and reduce the total pressure drop by dividing the flow among many channels. Liquid or gas is used as a coolant to flow through these microchannels. The large surface area of MCHS enables the coolant to take away large amounts of energy per unit time per unit area while maintaining a considerably low device temperature. Using these MCHS, heat fluxes can be dissipated at relatively low surface temperatures.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 289

turbulent flows. Tiselj et al. [8] performed experimental and numerical analysis of the effect of axial conduction on the heat transfer in triangular microchannel heat sink. They pointed out that the bulk water and heated wall temperatures did not change linearly

Inspired by the MCHS idea, new designs and modeling approaches of high performance cooling devices have been proposed, including using nanofluids as coolants in the MCHS study. Nanofluids are produced by dispersing nanometer-scale solid particles into base liquids such as water, ethylene glycol (EG), oils, etc. Lee et al. [9] used 38.4 nm of Al2O3 and 23.6 nm of CuO particles to enhance the thermal conductivity of water and EG. They showed that the enhancement percentage in thermal conductivity was not only a function of concentration and conductivities of the particles material and liquid, but it is also function of particle size and shape. Koo and Kleinstreuer [10] considered nanofluid flow in a representative microchannel, and conduction–convection heat transfer for different base fluids such as water and ethylene glycol with 20 nm CuO-nanoparticles. They come out with several suggestions which are a base fluid of high-Prandtl number such as ethylene glycol and oil should be used, using nanoparticles with high thermal conductivity are more

Chein and Huang [11] analyzed silicon microchannel heat sinks performance using nanofluids with a mixture of pure water and nanoscale Cu particles as coolants with various volume fractions. The MCHS with two specific geometries, one with Wch=100 μm and Lch=300 μm, the other with Wch=57 μm and Lch=365 μm, were examined. They found that the performances were greatly improved for these two specific geometries by using nanofluids as the coolants compared with pure water due to the increase in thermal conductivity of coolant and the nanoparticles thermal dispersion effect. The effectiveness of nanofluids for single-phase and two-phase heat transfer in microchannels is analyzed by Lee and Mudawar [12]. They indicated that the higher single-phase heat transfer coefficients are achieved in the entrance region of microchannels with increased nanoparticle concentration. However, the enhancement is weaker in the fully developed region. They suggested that nanoparticles should not be used in two-phase MCHS. This is because once boiling commences, particles begin to deposit into relatively large clusters near the channel exit due to localized evaporation. This clustering phenomenon quickly propagates upstream to fill the entire channel, preventing coolant from entering the heat sink and causing catastrophic failure of the cooling system. Jang and Choi [13] analyzed numerically the cooling performance of MCHS with nanofluids. They showed that the cooling performance of a MCHS with water-base nanofluids containing diamond (1%, 2 nm) at fixed pumping power of 2.25W was enhanced by about 10% compared with that of

There have been relatively few recent studies on nanofluid flow and heat transfer characteristics as comparing with those of pure fluid [14–16]. These studies showed that the heat transfer coefficient was greatly enhanced using nanofluid compared with pure fluid although there is a slight increase in pressure drop due to the presence of nanoparticles in MCHS operation. The enhancement depended on Reynolds number, particle volume fraction, and particle size and shape. It should be noted from the above literature review, however, that limited studies are available on nanofluid flow and heat transfer characteristics of rectangular shaped MCHS performance and this has motivated

advantageous, and a channel with high aspect ratio is desirable.

along the channel.

a MCHS with water.

the present study.

Fig. 1. Schematic diagram of the (a) direct cooling and (b) indirect cooling.

#### **1.2 Cooling performance of MCHS**

In order to drive the development of compact and efficient thermal management technology for advanced electronic devices, cooling devices have to be in light-weight, small in size and of high performance. Steinke and Kandlikar [4] presented a comprehensive review of friction factor data in microchannels with liquid flows. They indicated that entrance and exit losses need to be accounted for while presenting overall friction factors losses in microchannels. Most of the data that accounted for friction factor loss show good agreement with the conventional theory. They also provided a new procedure for correcting measured pressure drop to account for inlet and outlet losses.

Furthermore, three-dimensional fluid flow and heat transfer phenomena inside heated microchannels were investigated by Toh et al. [5]. They solved the steady laminar flow and heat transfer equations using a finite-volume method. It was found that the heat input lowers the frictional losses and viscosity leading to an increase in the temperature of the water, particularly at lower Reynolds numbers. Peng and Peterson [6,7] performed experimental investigations on the pressure drop and convective heat transfer of water flow in rectangular microchannels. They found that the cross sectional aspect ratio had a great influence on the flow friction and convective heat transfer both in laminar and

(a)

Heat dissipating device

> Heat dissipating device

Heat sink

(b)

In order to drive the development of compact and efficient thermal management technology for advanced electronic devices, cooling devices have to be in light-weight, small in size and of high performance. Steinke and Kandlikar [4] presented a comprehensive review of friction factor data in microchannels with liquid flows. They indicated that entrance and exit losses need to be accounted for while presenting overall friction factors losses in microchannels. Most of the data that accounted for friction factor loss show good agreement with the conventional theory. They also provided a new procedure for correcting measured

Furthermore, three-dimensional fluid flow and heat transfer phenomena inside heated microchannels were investigated by Toh et al. [5]. They solved the steady laminar flow and heat transfer equations using a finite-volume method. It was found that the heat input lowers the frictional losses and viscosity leading to an increase in the temperature of the water, particularly at lower Reynolds numbers. Peng and Peterson [6,7] performed experimental investigations on the pressure drop and convective heat transfer of water flow in rectangular microchannels. They found that the cross sectional aspect ratio had a great influence on the flow friction and convective heat transfer both in laminar and

Fig. 1. Schematic diagram of the (a) direct cooling and (b) indirect cooling.

**1.2 Cooling performance of MCHS** 

Insulator

Coolant flow

Coolant flow

Insulator

pressure drop to account for inlet and outlet losses.

turbulent flows. Tiselj et al. [8] performed experimental and numerical analysis of the effect of axial conduction on the heat transfer in triangular microchannel heat sink. They pointed out that the bulk water and heated wall temperatures did not change linearly along the channel.

Inspired by the MCHS idea, new designs and modeling approaches of high performance cooling devices have been proposed, including using nanofluids as coolants in the MCHS study. Nanofluids are produced by dispersing nanometer-scale solid particles into base liquids such as water, ethylene glycol (EG), oils, etc. Lee et al. [9] used 38.4 nm of Al2O3 and 23.6 nm of CuO particles to enhance the thermal conductivity of water and EG. They showed that the enhancement percentage in thermal conductivity was not only a function of concentration and conductivities of the particles material and liquid, but it is also function of particle size and shape. Koo and Kleinstreuer [10] considered nanofluid flow in a representative microchannel, and conduction–convection heat transfer for different base fluids such as water and ethylene glycol with 20 nm CuO-nanoparticles. They come out with several suggestions which are a base fluid of high-Prandtl number such as ethylene glycol and oil should be used, using nanoparticles with high thermal conductivity are more advantageous, and a channel with high aspect ratio is desirable.

Chein and Huang [11] analyzed silicon microchannel heat sinks performance using nanofluids with a mixture of pure water and nanoscale Cu particles as coolants with various volume fractions. The MCHS with two specific geometries, one with Wch=100 μm and Lch=300 μm, the other with Wch=57 μm and Lch=365 μm, were examined. They found that the performances were greatly improved for these two specific geometries by using nanofluids as the coolants compared with pure water due to the increase in thermal conductivity of coolant and the nanoparticles thermal dispersion effect. The effectiveness of nanofluids for single-phase and two-phase heat transfer in microchannels is analyzed by Lee and Mudawar [12]. They indicated that the higher single-phase heat transfer coefficients are achieved in the entrance region of microchannels with increased nanoparticle concentration. However, the enhancement is weaker in the fully developed region. They suggested that nanoparticles should not be used in two-phase MCHS. This is because once boiling commences, particles begin to deposit into relatively large clusters near the channel exit due to localized evaporation. This clustering phenomenon quickly propagates upstream to fill the entire channel, preventing coolant from entering the heat sink and causing catastrophic failure of the cooling system. Jang and Choi [13] analyzed numerically the cooling performance of MCHS with nanofluids. They showed that the cooling performance of a MCHS with water-base nanofluids containing diamond (1%, 2 nm) at fixed pumping power of 2.25W was enhanced by about 10% compared with that of a MCHS with water.

There have been relatively few recent studies on nanofluid flow and heat transfer characteristics as comparing with those of pure fluid [14–16]. These studies showed that the heat transfer coefficient was greatly enhanced using nanofluid compared with pure fluid although there is a slight increase in pressure drop due to the presence of nanoparticles in MCHS operation. The enhancement depended on Reynolds number, particle volume fraction, and particle size and shape. It should be noted from the above literature review, however, that limited studies are available on nanofluid flow and heat transfer characteristics of rectangular shaped MCHS performance and this has motivated the present study.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 291

k (µm) 180 280 380 *l* (µm) 469 452 434 h (µm) 460 430 390 Lc(µm) 10000 10000 10000 S (µm) 596 500 404 Dh (µm) 148 203 238 *β* 22.14<sup>ο</sup> 36.07<sup>ο</sup> 51.95<sup>ο</sup>

Number of channels 25 25 25

microchannels, the governing equations are solved with the following assumptions: 1. Both fluid flow and heat transfer are in steady-state and three-dimensional.

3. Properties of both fluid and heat sink material are temperature-independent.

*U X* + *V Y* + *W Z* 

2. Fluid is in single phase, incompressible and the flow is laminar.

generation from electronic chip, is specified.

*UVW*

heated MCHS can be written as [17]:

Continuity

Momentum

X-Momentum:

Y-Momentum:

Z-Momentum:

Energy:

In the analysis of the entire domain of MCHS, it is necessary to set up the governing equations (continuity, momentum, and energy). For the specific case of heated flow through

4. All the surfaces of MCHS exposed to the surroundings are assumed to be insulated except the top plate where constant heat flux boundary condition, simulating the heat

Thus, the governing equations in dimensionless form which are used in present study for

ˆ 1 Re

ˆ 1 Re

ˆ 1 Re

1 Re.Pr

*XY Z XYZ* 

 

*U U U dP U U U UVW X Y Z dX XYZ* 

*V V V dP V V V UVW X Y Z dY XYZ* 

*W W W dP W W W UVW X Y Z dZ XYZ* 

=0 (2.1)

(2.2a)

(2.2b)

(2.2c)

(2.3)

222 222

222 222

222 222

222 222

Table 2.3. Dimensions for three different sets of triangular cross-section MCHS.

**2.2 Governing equations** 

Case 1 Case 2 Case 3

The current study mainly focuses on 3D computational simulation of heat transfer and laminar liquid flow characteristics in MCHS. Following this introduction section, the governing equations and numerical model is explained, followed by studies on the geometrical parameters with various MCHS shapes (Section 3), effects of different nanoparticle volume fractions (Section 4), effects of different nanofluids types (Section 5), and effects of nanoparticle in different base fluids (Section 6).

#### **2. Problem description and methodology**

#### **2.1 MCHS model**

The physical configuration of the MCHS is schematically shown in Fig.2.1. The heat supplied to the MCHS substrate through a top plate is removed by flowing fluid through a number of 25 microchannels. This article focuses on heat transfer and liquid flow in three different cross sectional shapes of MCHS including rectangular, trapezoidal, and triangular. The dimensions of three different sets for each cross sectional shape of MCHS are given in Table 2.1-2.3.


Table 2.1. Dimensions for three different sets of rectangular cross-section MCHS.


Table 2.2. Dimensions for three different sets of trapezoidal cross-section MCHS.


Table 2.3. Dimensions for three different sets of triangular cross-section MCHS.

#### **2.2 Governing equations**

In the analysis of the entire domain of MCHS, it is necessary to set up the governing equations (continuity, momentum, and energy). For the specific case of heated flow through microchannels, the governing equations are solved with the following assumptions:


Thus, the governing equations in dimensionless form which are used in present study for heated MCHS can be written as [17]:

Continuity

290 Fluid Dynamics, Computational Modeling and Applications

The current study mainly focuses on 3D computational simulation of heat transfer and laminar liquid flow characteristics in MCHS. Following this introduction section, the governing equations and numerical model is explained, followed by studies on the geometrical parameters with various MCHS shapes (Section 3), effects of different nanoparticle volume fractions (Section 4), effects of different nanofluids types (Section 5),

The physical configuration of the MCHS is schematically shown in Fig.2.1. The heat supplied to the MCHS substrate through a top plate is removed by flowing fluid through a number of 25 microchannels. This article focuses on heat transfer and liquid flow in three different cross sectional shapes of MCHS including rectangular, trapezoidal, and triangular. The dimensions of three different sets for each cross sectional shape of MCHS are given in

> Hch (µm) 460 430 390 Wch (µm) 180 280 380 Lc (µm) 10000 10000 10000 S (µm) 596 500 404 Dh (µm) 259 339 385

Number of channels 25 25 25

a (µm) 180 280 380 b (µm) 125 225 325 c (µm) 461 431 391 h (µm) 460 430 390 Lc (µm) 10000 10000 10000 S (µm) 596 500 404 Dh (µm) 229 318 370

Number of channels 25 25 25

Table 2.2. Dimensions for three different sets of trapezoidal cross-section MCHS.

Table 2.1. Dimensions for three different sets of rectangular cross-section MCHS.

Case 1 Case 2 Case 3

Case 1 Case 2 Case 3

and effects of nanoparticle in different base fluids (Section 6).

**2. Problem description and methodology** 

**2.1 MCHS model** 

Table 2.1-2.3.

$$\frac{\partial \mathcal{U}}{\partial X} + \frac{\partial V}{\partial Y} + \frac{\partial W}{\partial Z} = 0 \tag{2.1}$$

Momentum

$$\text{IX-Momentum:} \quad \left( \mathcal{U} \frac{\partial \mathcal{U}}{\partial \mathcal{X}} + V \frac{\partial \mathcal{U}}{\partial \mathcal{Y}} + W \frac{\partial \mathcal{U}}{\partial \mathcal{Z}} \right) = -\frac{d\hat{P}}{d\mathcal{X}} + \frac{1}{\text{Re}} \left( \frac{\hat{\sigma}^2 \mathcal{U}}{\partial \mathcal{X}^2} + \frac{\hat{\sigma}^2 \mathcal{U}}{\partial \mathcal{Y}^2} + \frac{\hat{\sigma}^2 \mathcal{U}}{\hat{\sigma} \mathcal{Z}^2} \right) \tag{2.2a}$$

$$\text{Y-Momentum:} \quad \left( \mathcal{U} \frac{\partial V}{\partial \mathcal{X}} + V \frac{\partial V}{\partial \mathcal{Y}} + W \frac{\partial V}{\partial \mathcal{Z}} \right) = -\frac{d\hat{P}}{d\mathcal{Y}} + \frac{1}{\text{Re}} \left( \frac{\hat{\sigma}^2 V}{\hat{\sigma}\mathcal{X}^2} + \frac{\hat{\sigma}^2 V}{\hat{\sigma}\mathcal{Y}^2} + \frac{\hat{\sigma}^2 V}{\hat{\sigma}\mathcal{Z}^2} \right) \tag{2.2b}$$

$$\text{ZZ-Momentum:} \left( \mathcal{U} \frac{\partial \mathcal{W}}{\partial \mathcal{X}} + V \frac{\partial \mathcal{W}}{\partial \mathcal{Y}} + W \frac{\partial \mathcal{W}}{\partial \mathcal{Z}} \right) = -\frac{d\hat{P}}{d\mathcal{Z}} + \frac{1}{\text{Re}} \left( \frac{\hat{\mathcal{O}}^2 \mathcal{W}}{\partial \mathcal{X}^2} + \frac{\hat{\mathcal{O}}^2 \mathcal{W}}{\partial \mathcal{Y}^2} + \frac{\hat{\mathcal{O}}^2 \mathcal{W}}{\partial \mathcal{Z}^2} \right) \tag{2.2c}$$

Energy:

$$\left(\mathcal{U}\frac{\partial\theta}{\partial\mathbf{X}} + V\frac{\partial\theta}{\partial\mathbf{Y}} + \mathcal{W}\frac{\partial\theta}{\partial\mathbf{Z}}\right) = \frac{1}{\text{Re.Pr}}\left(\frac{\partial^2\theta}{\partial\mathbf{X}^2} + \frac{\partial^2\theta}{\partial\mathbf{Y}^2} + \frac{\partial^2\theta}{\partial\mathbf{Z}^2}\right) \tag{2.3}$$

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 293

(a)

(b)

Aluminum

Liquid

Fig. 2.1. (a) Schematic diagram of the MCHS (b) Section of the MCHS cross sectional shapes

with its dimensions.

Where *X* = � �� , *Y =* � �� , *Z* = � �� , *U =* � ��� , *V* = � ��� , *W* = � ��� , �� <sup>=</sup>�� ���� � is the dimensionless pressure, and *<sup>f</sup> <sup>i</sup> T T* is the dimensionless temperature.

*w i* Given the complexity of these equations, computational methods of solving them are required. The methodology used in the present study to solve these governing equations is described in the following section.

#### **2.3 Boundary conditions**

*T T*

Boundary conditions for all boundaries are specified for this simplified computational domain. Fig.2.1a shows the general MCHS computational model used in this study and Fig.2.1b shows the cross sectional shapes of channel considered in the study. Heat, supplied to the aluminum substrate through a top plate, is removed by flowing fluid through a number of microchannels.

At the entrance of the MCHS assembly (z = 0, from Fig.3.4a), two types of boundaries are encountered which are water flows through the microchannels and removes heat conducted to the surface of the MCHS. The remainder of the entrance is occupied by the aluminum substrate.

At the microchannels sections, the inlet fluid temperature was taken as 293K and the inlet fluid velocity was calculated using

$$
\mu\_{in} = \frac{\text{Re}\,\mu}{\rho D\_h} \tag{2.4}
$$

For rectangular cross-section MCHS,

$$D\_h = \frac{4A}{P} = \frac{2H\_{ch}W\_{ch}}{H\_{ch} + W\_{ch}}\tag{2.5a}$$

where *A* is the channel flow area, *P* is the channel wet perimeter, *Hch* is the channel height, and *Wch* is the channel width.

For trapezoidal cross-section MCHS,

$$D\_h = \frac{4A}{P} = \frac{2(a+b)h}{a+b+2c} \tag{2.5b}$$

where *A* is the channel flow area, *P* is the channel wet perimeter, *a* is the channel top width, *b* is the channel bottom width, *c* is the channel hypotenuse, and *h* is the channel height. For triangular cross-section MCHS,

$$D\_h = \frac{4A}{P} = \frac{2kh}{k+2l} \tag{2.5c}$$

where *A* is the channel flow area, *P* is the channel wet perimeter, *k* is the channel width, *h* is the channel height, and � is the channel hypotenuse.

The Reynolds number in this work was ranged from 100 to 1000. In calculating the velocity, the fluid is assumed to be evenly distributed into all microchannels. The transverse velocities at the inlet are assumed to be zero. On the aluminum substrate, the velocities are zero, and it is assumed to be an adiabatic surface.

Given the complexity of these equations, computational methods of solving them are required. The methodology used in the present study to solve these governing equations is

Boundary conditions for all boundaries are specified for this simplified computational domain. Fig.2.1a shows the general MCHS computational model used in this study and Fig.2.1b shows the cross sectional shapes of channel considered in the study. Heat, supplied to the aluminum substrate through a top plate, is removed by flowing fluid through a

At the entrance of the MCHS assembly (z = 0, from Fig.3.4a), two types of boundaries are encountered which are water flows through the microchannels and removes heat conducted to the surface of the MCHS. The remainder of the entrance is occupied by the aluminum

At the microchannels sections, the inlet fluid temperature was taken as 293K and the inlet

Re

*h*

(2.4)

(2.5b)

(2.5a)

(2.5c)

*D* 

4 2 *ch ch*

*<sup>A</sup> H W <sup>D</sup> PH W*

where *A* is the channel flow area, *P* is the channel wet perimeter, *Hch* is the channel height,

4 2 2 *<sup>h</sup> A a bh*

where *A* is the channel flow area, *P* is the channel wet perimeter, *a* is the channel top width, *b* is the channel bottom width, *c* is the channel hypotenuse, and *h* is the channel height.

> 4 2 2 *<sup>h</sup> A kh <sup>D</sup> Pkl*

where *A* is the channel flow area, *P* is the channel wet perimeter, *k* is the channel width, *h* is

The Reynolds number in this work was ranged from 100 to 1000. In calculating the velocity, the fluid is assumed to be evenly distributed into all microchannels. The transverse velocities at the inlet are assumed to be zero. On the aluminum substrate, the velocities are

*P ab c*

*ch ch*

*in*

*u*

*h*

*D*

, *W* = � ���

 , �� <sup>=</sup>�� ����

� is the dimensionless pressure,

Where *X* = �

and *<sup>f</sup> <sup>i</sup>*

 

substrate.

��

*w i T T T T*

**2.3 Boundary conditions** 

number of microchannels.

fluid velocity was calculated using

For rectangular cross-section MCHS,

and *Wch* is the channel width. For trapezoidal cross-section MCHS,

For triangular cross-section MCHS,

the channel height, and � is the channel hypotenuse.

zero, and it is assumed to be an adiabatic surface.

, *Y =* � ��

described in the following section.

, *Z* = � ��

is the dimensionless temperature.

, *U =* � ���

, *V* = � ���

(a)

Fig. 2.1. (a) Schematic diagram of the MCHS (b) Section of the MCHS cross sectional shapes with its dimensions.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 295

**1.9 10 grids 2.8 10 grids 3.4 10 grids**

Fig. 2.2. Dimensionless temperature profiles for each channel in rectangular cross-section

**1.9 10 grids 2.8 10 grids 3.4 10 grids**

**0 2 4 6 8 10 12 14 16 18 20 22 24 26 Number of channel**

Fig. 2.3**.** Dimensionless pressure drop versus Reynolds number across the rectangular cross-

**0 200 400 600 800 Re**

section MCHS (Dh = 0.259 mm) using three different grids.

**0.0**

**0.4**

**0.8**

**P**

**1.2**

**1.6**

MCHS (Dh = 0.259 mm) using three different grids.

**0.994**

**0.998**

**1.000**

**0.996**

**1.002**

**1.004**

Boundary conditions at the inlet:

$$\text{L\,L = \frac{\text{ll}}{\text{m}\_{\text{in}}}, \,\,\text{L} = \mathbf{1}, \,\,\theta = \mathbf{1} \tag{2.6a}$$

At the outlet:

$$P = P\_{out\,\,\,\prime} \begin{array}{l} \hat{\mathcal{O}}\theta \\ \hat{\mathcal{O}}n \end{array} \tag{2.6b}$$

At the fluid-solid interface:

$$\mathbf{U} = \mathbf{0}, \ \boldsymbol{\theta} = \boldsymbol{\theta}\_{s'} \ -\kappa\_s \frac{\partial \boldsymbol{\theta}\_s}{\partial \mathbf{n}} = -\kappa \frac{\partial \boldsymbol{\theta}}{\partial \mathbf{n}}\tag{2.6c}$$

At the top plate:

$$
\eta\_w = -\kappa\_s \frac{\partial \theta\_s}{\partial n} \tag{2.6d}
$$

In Eq. (2.6), *U* and *θ* are the dimensionless fluid inlet velocity and dimensionless temperature, respectively, *P* is the dimensionless pressure at the outlet, *n* is the direction normal to the wall or the outlet plane, and *qw* is the heat flux applied at the top plate of the heat sink. The heat flux applied at the top plate was ranged from 100-1000 W/m2.

#### **2.4 Numerical solution using FVM**

The governing conservation equations Eqs. (2) – (4) with the corresponding boundary conditions and equations for solid and fluid phases are simultaneously solved as a single domain conjugate problem using the standard finite volume method (FVM) with a hybrid differencing scheme [17]. The standard SIMPLE algorithm is used as the computational algorithm [18]. The iterations are continued until the sum of residuals for all computational cells became negligible (less than 10−7) and velocity magnitudes did not change from iteration to iteration. Because of the assumption of constant fluid properties and negligible buoyancy, the mass and momentum equations are not coupled to the energy equation. Therefore, the temperature field is calculated by solving the energy equation after a converged solution for the flow field is obtained by solving the momentum and continuity equations.

#### **2.5 Numerical implementation, grid testing and code validation**

The distribution of hexahedral cells in the computational domain is determined from a series of tests with different number of cells. For example, for the case of rectangular MCHS, computational cells with 1.9x 105, 2.8 x 105, and 3.4 x 105 grids are used to test the grid independence of the solution. The results are shown in Figs.2.2 and 2.3 which present the dimensionless temperature profiles and dimensionless pressure drop across the heat sink versus Reynolds number, respectively. The dimensionless temperature and dimensionless pressure are defined in Eq.3.1(Section 3) and Eq.5.1(Section 5), respectively. It can be seen that almost identical results obtained when 2.8 x 105 and 3.4 x 105 grids are used. Thus, based on the results shown in these figures, a computational cell with 2.8 x 105 grids is employed for all the numerical computations in this study. Similar study was carried out for other MCHS shapes.

*<sup>s</sup> <sup>s</sup> <sup>s</sup> n n* 

> *n*

 

1 (2.6a)

(2.6b)

(2.6c)

(2.6d)

, *in <sup>u</sup> <sup>U</sup>*

*<sup>u</sup> <sup>U</sup>* 1,

, *P P out* 0 *n* 

*<sup>s</sup> w s q*

In Eq. (2.6), *U* and *θ* are the dimensionless fluid inlet velocity and dimensionless temperature, respectively, *P* is the dimensionless pressure at the outlet, *n* is the direction normal to the wall or the outlet plane, and *qw* is the heat flux applied at the top plate of the

The governing conservation equations Eqs. (2) – (4) with the corresponding boundary conditions and equations for solid and fluid phases are simultaneously solved as a single domain conjugate problem using the standard finite volume method (FVM) with a hybrid differencing scheme [17]. The standard SIMPLE algorithm is used as the computational algorithm [18]. The iterations are continued until the sum of residuals for all computational cells became negligible (less than 10−7) and velocity magnitudes did not change from iteration to iteration. Because of the assumption of constant fluid properties and negligible buoyancy, the mass and momentum equations are not coupled to the energy equation. Therefore, the temperature field is calculated by solving the energy equation after a converged solution for

The distribution of hexahedral cells in the computational domain is determined from a series of tests with different number of cells. For example, for the case of rectangular MCHS, computational cells with 1.9x 105, 2.8 x 105, and 3.4 x 105 grids are used to test the grid independence of the solution. The results are shown in Figs.2.2 and 2.3 which present the dimensionless temperature profiles and dimensionless pressure drop across the heat sink versus Reynolds number, respectively. The dimensionless temperature and dimensionless pressure are defined in Eq.3.1(Section 3) and Eq.5.1(Section 5), respectively. It can be seen that almost identical results obtained when 2.8 x 105 and 3.4 x 105 grids are used. Thus, based on the results shown in these figures, a computational cell with 2.8 x 105 grids is employed for all the numerical computations in this study. Similar study was carried out for

heat sink. The heat flux applied at the top plate was ranged from 100-1000 W/m2.

the flow field is obtained by solving the momentum and continuity equations.

**2.5 Numerical implementation, grid testing and code validation** 

 

Boundary conditions at the inlet:

At the fluid-solid interface:

 *U* = 0, ,

**2.4 Numerical solution using FVM** 

other MCHS shapes.

At the outlet:

At the top plate:

Fig. 2.2. Dimensionless temperature profiles for each channel in rectangular cross-section MCHS (Dh = 0.259 mm) using three different grids.

Fig. 2.3**.** Dimensionless pressure drop versus Reynolds number across the rectangular crosssection MCHS (Dh = 0.259 mm) using three different grids.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 297

located near the center of the MCHS. The validity of present result shows a similar trend with the result obtained by Chein and Chen [19]. For fluid in channels close to the edge of the MCHS, higher temperature profiles are observed due to the high heat transfer from the

The computed averaged heat transfer coefficient in each channel of the rectangular crosssection MCHS for various hydraulic diameters is illustrated in Fig.3.2. The magnitude of heat transfer coefficient decreases with the increase in hydraulic diameter and the trends are the same for each cross sectional shape of the MCHS. This is due to the fact that lower pressure drop in larger hydraulic diameter corresponds to lower inlet velocity driven into the MCHS. Furthermore, due to the difference of the channel hydraulic diameter which is caused by the difference of channels' area and perimeter, the averaged heat transfer coefficient in each MCHS is also different under a given inlet velocity. For each type of the MCHS, the middle channel (channel number 14) has the highest averaged heat transfer coefficient value as expected. The averaged heat transfer coefficient value for other channels is seen to decrease depending on their distances from the wall. The averaged heat transfer coefficient distribution for all types of MCHS is almost symmetrical with respect to the centerline of the MCHS. It is shown that the heat transfer coefficient of the MCHS is greatly influenced by the hydraulic diameter of the channel, as the hydraulic diameter decreases,

The computed average heat transfer coefficient versus Reynolds number for different cross sectional shapes of the MCHS is presented in Fig.3.3. It is apparent from this figure that the

Fig. 3.2. Averaged heat transfer coefficient in each channel of the MCHS.

**Re = 500 (Rectangular)**

**Dh = 0.259 mm Dh = 0.339 mm Dh = 0.385 mm**

**0 2 4 6 8 10 12 14 16 18 20 22 24 26 Number of channel**

high-temperature edge of the MCHS.

the heat transfer coefficient increases.

**9.43**

**9.44**

**9.45**

**9.46**

**Heat transfer coefficient, h [W/m^2 K]**

**9.47**

**9.48**

**9.49**

**3.2 Heat transfer coefficient** 

#### **3. Effect of geometrical parameters of various MCHS shapes**

This section investigates the effect of geometrical parameters on heat transfer and fluid flow characteristics for different cross sectional shapes of MCHS including rectangular, trapezoidal, and triangular with the dimensions as stated in Table 2.1-2.3, respectively. For this Section, water is used as the working fluid as the main aim is to investigate on the geometrical effects. For Section 4, 5, and 6, various nanofluids are used as the working fluid and only one particular cross sectional shape of MCHS with specified dimensions is considered for each Section. The dimensionless temperature profiles, heat transfer coefficient, friction factor, and thermal resistance which affected by geometrical parameters are discussed and presented.

#### **3.1 Temperature profile**

In the MCHS operation, the high temperature region should occur at the edge of the MCHS since there is no heat dissipation by fluid convection while the low-temperature region should occur in the region where microchannels are placed, especially at the middle regions of the MCHS due to the high heat transfer coefficient. To address this point, the dimensionless average temperature profiles of rectangular cross-section MCHS for different dimensions of the channel area at Re = 500 are presented in Fig.3.1. The dimensionless temperatures for each channel can be defined as:

$$\theta = \frac{T\_f - T\_i}{T\_{w-}T\_i} \tag{3.1}$$

Where *Tf* is the fluid temperature, *Ti* is the inlet temperature, and *Tw* is the wall temperature. It can clearly be seen from Fig.3.1 that the lower temperature profile occurs in the channels

Fig. 3.1. Dimensionless average temperature profiles for each channel in rectangular crosssection MCHS.

located near the center of the MCHS. The validity of present result shows a similar trend with the result obtained by Chein and Chen [19]. For fluid in channels close to the edge of the MCHS, higher temperature profiles are observed due to the high heat transfer from the high-temperature edge of the MCHS.

#### **3.2 Heat transfer coefficient**

296 Fluid Dynamics, Computational Modeling and Applications

This section investigates the effect of geometrical parameters on heat transfer and fluid flow characteristics for different cross sectional shapes of MCHS including rectangular, trapezoidal, and triangular with the dimensions as stated in Table 2.1-2.3, respectively. For this Section, water is used as the working fluid as the main aim is to investigate on the geometrical effects. For Section 4, 5, and 6, various nanofluids are used as the working fluid and only one particular cross sectional shape of MCHS with specified dimensions is considered for each Section. The dimensionless temperature profiles, heat transfer coefficient, friction factor, and thermal resistance which affected by geometrical parameters are discussed and presented.

In the MCHS operation, the high temperature region should occur at the edge of the MCHS since there is no heat dissipation by fluid convection while the low-temperature region should occur in the region where microchannels are placed, especially at the middle regions of the MCHS due to the high heat transfer coefficient. To address this point, the dimensionless average temperature profiles of rectangular cross-section MCHS for different dimensions of the channel area at Re = 500 are presented in Fig.3.1. The dimensionless

> *f i w i T T T T*

**Re = 500 (Rectangular)**

**Hc/Wc = 1.026, L/Dh = 25.98 Hc/Wc = 1.536, L/Dh = 29.49 Hc/Wc = 2.556, L/Dh = 38.65**

Where *Tf* is the fluid temperature, *Ti* is the inlet temperature, and *Tw* is the wall temperature. It can clearly be seen from Fig.3.1 that the lower temperature profile occurs in the channels

Fig. 3.1. Dimensionless average temperature profiles for each channel in rectangular cross-

**0 2 4 6 8 10 12 14 16 18 20 22 24 26 Number of channel**

(3.1)

 

**3. Effect of geometrical parameters of various MCHS shapes** 

**3.1 Temperature profile** 

section MCHS.

**0.996**

**0.997**

**0.998**

**0.999**

**1.000**

temperatures for each channel can be defined as:

The computed averaged heat transfer coefficient in each channel of the rectangular crosssection MCHS for various hydraulic diameters is illustrated in Fig.3.2. The magnitude of heat transfer coefficient decreases with the increase in hydraulic diameter and the trends are the same for each cross sectional shape of the MCHS. This is due to the fact that lower pressure drop in larger hydraulic diameter corresponds to lower inlet velocity driven into the MCHS. Furthermore, due to the difference of the channel hydraulic diameter which is caused by the difference of channels' area and perimeter, the averaged heat transfer coefficient in each MCHS is also different under a given inlet velocity. For each type of the MCHS, the middle channel (channel number 14) has the highest averaged heat transfer coefficient value as expected. The averaged heat transfer coefficient value for other channels is seen to decrease depending on their distances from the wall. The averaged heat transfer coefficient distribution for all types of MCHS is almost symmetrical with respect to the centerline of the MCHS. It is shown that the heat transfer coefficient of the MCHS is greatly influenced by the hydraulic diameter of the channel, as the hydraulic diameter decreases, the heat transfer coefficient increases.

The computed average heat transfer coefficient versus Reynolds number for different cross sectional shapes of the MCHS is presented in Fig.3.3. It is apparent from this figure that the

Fig. 3.2. Averaged heat transfer coefficient in each channel of the MCHS.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 299

Reynolds number, *fRe* from the present numerical simulation for trapezoidal cross-section MCHS with the experimental work done by Wu and Cheng [22]. As noticed, a very good agreement is obtained between the two studies whereby it is shown that *fRe* rises with the increase of Reynolds number. As can be noticed from Fig.3.6, *fRe* increases linearly with the increase of Reynolds number due to the linear dependency of pressure drop on constant inlet velocity for a fixed hydraulic diameter in fully developed laminar region. Thus, *fRe* is

The *f* with different tip angles of triangular cross-section MCHS is illustrated in Fig.3.7. It is clearly observed that *f* increases with the increases of tip angle of the channel. The validity of the present numerical simulation result was also approved by the results of Kandlikar et al. [21]. The results show that the flow behavior is very similar for all types of cross sectional shapes of MCHS where the friction factor decreases with the increase of

In overall, From the Figs.3.4, 3.5, and 3.7, it is also apparent that *f* for rectangular shaped microchannel is most, for trapezoidal shaped microchannel is less, and for triangular shaped microchannel is least. This is due to the triangular shaped microchannel has a smallest area. For trapezoidal shaped microchannels, the flow area is changed suddenly from larger area to smaller area, thus the pressure drop would be large. Therefore, *f* value for trapezoidal shaped microchannels is also larger than the triangular shaped microchannels. For the rectangular shaped microchannels, the flow area is the largest which corresponds to the highest value of *f*. Therefore, *f* of water flowing in MCHS, having the same width and height but with different cross sectional shapes can be very much different due to the difference of

Fig. 3.4. Friction factor at different width-height (Wc/Hc) ratio for rectangular cross-section

**0 200 400 600 800**

**Re**

linearly proportional to Reynolds number for fully developed channel flow.

the cross sectional shape and geometrical dimensions of the channels.

Reynolds number.

MCHS.

**0.00**

**0.04**

**0.08**

**Friction factor, f**

**0.12**

**0.16**

heat transfer coefficient for rectangular cross-section MCHS is the highest. The MCHS of triangular cross-section exhibits the lowest values of heat transfer coefficient. While, the heat transfer coefficient for trapezoidal cross- section MCHS is in between the rectangular and triangular.

Fig. 3.3. Averaged heat transfer coefficient for different cross sectional shapes of the MCHS.

#### **3.3 Friction factor**

The effect of geometrical parameters on the friction factor, *f* for different microchannel shapes is discussed in this section. For the current study, the friction factor is calculated using Darcy equation [20]:

$$f = \frac{{}^{2D\_h}\Delta p}{\rho \, u\_{ln}^2 \, ^{L\_c}}\tag{3.2}$$

Where *Dh* is the hydraulic diameter, �� is the pressure drop, � is the density of water, *uin* is the inlet velocity of water, and *Lc* is the length of channel.

Fig.3.4 shows the friction factor, *f*, at different *Wc/Hc* ratios for rectangular cross-section MCHS. It is clearly observed that *f* increases with the increase of *Wc/Hc* ratio of the channel. Therefore, the flow resistance will increase evidently when the ratio is increased. The reason behind this is that the increase in *Wc/Hc* ratio causes a decrease in the flow area and the pressure drop becomes significant. The validity of the present numerical results was also approved by Kandlikar et al. [21] results, where *f* increases with the increase of *Wc/Hc* ratio for rectangular cross-section MCHS.

Fig.3.5 shows *f* with three geometrical parameters including bottom-to-top width ratio *(b/a)*, height-to-top width ratio *(h/a)*, and length-to-hydraulic diameter ratio *(L/Dh)*, which affect the friction and heat transfer in the trapezoidal cross-section MCHS. Fig.3.6 shows a comparison of predicted Poiseuille number which is the product of friction factor, *f* and

heat transfer coefficient for rectangular cross-section MCHS is the highest. The MCHS of triangular cross-section exhibits the lowest values of heat transfer coefficient. While, the heat transfer coefficient for trapezoidal cross- section MCHS is in between the rectangular and

> **Rectangular, Dh = 0.259 mm Trapezoidal, Dh = 0.229 mm Triangular, Dh = 0.238 mm**

Fig. 3.3. Averaged heat transfer coefficient for different cross sectional shapes of the MCHS.

**0 200 400 600 800 Re**

The effect of geometrical parameters on the friction factor, *f* for different microchannel shapes is discussed in this section. For the current study, the friction factor is calculated

> � � ��� �� � ��� � ��

Where *Dh* is the hydraulic diameter, �� is the pressure drop, � is the density of water, *uin* is

Fig.3.4 shows the friction factor, *f*, at different *Wc/Hc* ratios for rectangular cross-section MCHS. It is clearly observed that *f* increases with the increase of *Wc/Hc* ratio of the channel. Therefore, the flow resistance will increase evidently when the ratio is increased. The reason behind this is that the increase in *Wc/Hc* ratio causes a decrease in the flow area and the pressure drop becomes significant. The validity of the present numerical results was also approved by Kandlikar et al. [21] results, where *f* increases with the increase of *Wc/Hc* ratio

Fig.3.5 shows *f* with three geometrical parameters including bottom-to-top width ratio *(b/a)*, height-to-top width ratio *(h/a)*, and length-to-hydraulic diameter ratio *(L/Dh)*, which affect the friction and heat transfer in the trapezoidal cross-section MCHS. Fig.3.6 shows a comparison of predicted Poiseuille number which is the product of friction factor, *f* and

(3.2)

triangular.

**3.3 Friction factor** 

using Darcy equation [20]:

**9.30**

**9.40**

**9.50**

**Heat transfer coefficient, h [W/m^2 K]**

**9.60**

**9.70**

for rectangular cross-section MCHS.

the inlet velocity of water, and *Lc* is the length of channel.

Reynolds number, *fRe* from the present numerical simulation for trapezoidal cross-section MCHS with the experimental work done by Wu and Cheng [22]. As noticed, a very good agreement is obtained between the two studies whereby it is shown that *fRe* rises with the increase of Reynolds number. As can be noticed from Fig.3.6, *fRe* increases linearly with the increase of Reynolds number due to the linear dependency of pressure drop on constant inlet velocity for a fixed hydraulic diameter in fully developed laminar region. Thus, *fRe* is linearly proportional to Reynolds number for fully developed channel flow.

The *f* with different tip angles of triangular cross-section MCHS is illustrated in Fig.3.7. It is clearly observed that *f* increases with the increases of tip angle of the channel. The validity of the present numerical simulation result was also approved by the results of Kandlikar et al. [21]. The results show that the flow behavior is very similar for all types of cross sectional shapes of MCHS where the friction factor decreases with the increase of Reynolds number.

In overall, From the Figs.3.4, 3.5, and 3.7, it is also apparent that *f* for rectangular shaped microchannel is most, for trapezoidal shaped microchannel is less, and for triangular shaped microchannel is least. This is due to the triangular shaped microchannel has a smallest area. For trapezoidal shaped microchannels, the flow area is changed suddenly from larger area to smaller area, thus the pressure drop would be large. Therefore, *f* value for trapezoidal shaped microchannels is also larger than the triangular shaped microchannels. For the rectangular shaped microchannels, the flow area is the largest which corresponds to the highest value of *f*. Therefore, *f* of water flowing in MCHS, having the same width and height but with different cross sectional shapes can be very much different due to the difference of the cross sectional shape and geometrical dimensions of the channels.

Fig. 3.4. Friction factor at different width-height (Wc/Hc) ratio for rectangular cross-section MCHS.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 301

Fig. 3.7. Friction factor with different tip angles of triangular cross-section MCHS.

 *Rth* = *w in* ,max

The performance of the MCHS is commonly presented by the thermal resistance (Rth) which

Another important parameter in MCHS operation is the pressure drop across the MCHS which relates to the coolant pumping power required. The pumping power is used to drive the coolant in MCHS operation. It is the product of the pressure drop across the heat

 *Q* = *N W*ch *H*ch *uin* (3.5) where *N* is the number of microchannels, *W*ch is the width of channel, *H*ch is the height of

 *Q* = 0.5 *N (a + b) uin* (3.6) where *N* is the number of microchannels, *k* is the width of channel, *h* is the height of

*in T T Q*

(3.3)

Pumping power = *Q*οܲ (3.4)

**3.4 Thermal resistance** 

sinkǡ οܲ and volume flow rate, *Q*:

For rectangular cross-section MCHS,

For trapezoidal cross-section MCHS,

channel, and *uin* is the inlet velocity of water.

channel, and *u*in,nf is the inlet velocity of water.

where *Q* is defined as:

is defined as:

Fig. 3.5. Friction factor with three different geometrical parameters of trapezoidal crosssection MCHS.

Fig. 3.6. Comparison of Poiseuille number of trapezoidal cross-section MCHS with [22].

Fig. 3.7. Friction factor with different tip angles of triangular cross-section MCHS.

#### **3.4 Thermal resistance**

300 Fluid Dynamics, Computational Modeling and Applications

Fig. 3.5. Friction factor with three different geometrical parameters of trapezoidal cross-

**Trapezoidal b/a = 0.694, h/a = 2.556, L/Dh = 43.71 b/a = 0.804, h/a = 1.536, L/Dh = 31.47 b/a = 0.855, h/a = 1.0263, L/Dh = 27.04**

**Wu & Cheng [22]**

**0 200 400 600 800 1000**

**Re**

Fig. 3.6. Comparison of Poiseuille number of trapezoidal cross-section MCHS with [22].

**0 200 400 600 800 1000 Re**

section MCHS.

**0.00**

**4**

**8**

**12**

**16**

**f Re**

**20**

**24**

**28**

**0.02**

**0.04**

**0.06**

**0.08**

**Friction factor, f**

**0.10**

**0.12**

**0.14**

The performance of the MCHS is commonly presented by the thermal resistance (Rth) which is defined as:

$$R\_{\text{fl}} = \frac{T\_{w,\text{max}} - T\_{\text{int}}}{Q\_{\text{in}}} \tag{3.3}$$

Another important parameter in MCHS operation is the pressure drop across the MCHS which relates to the coolant pumping power required. The pumping power is used to drive the coolant in MCHS operation. It is the product of the pressure drop across the heat sinkǡ οܲ and volume flow rate, *Q*:

$$\text{Pumpping power} = Q \Delta P \tag{3.4}$$

where *Q* is defined as: For rectangular cross-section MCHS,

$$Q = N \,\mathcal{W}\_{\rm ch} \, H\_{\rm ch} \, \mu\_{\rm in} \tag{3.5}$$

where *N* is the number of microchannels, *W*ch is the width of channel, *H*ch is the height of channel, and *uin* is the inlet velocity of water. For trapezoidal cross-section MCHS,

$$Q = 0.5 \text{ N } (a + b) \, u\_{in} \tag{3.6}$$

where *N* is the number of microchannels, *k* is the width of channel, *h* is the height of channel, and *u*in,nf is the inlet velocity of water.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 303

cooled MCHS. In the current study, the effect of using three different particle volume fractions on heat transfer and liquid flow characteristics in MCHS will be discussed. Since the cooling performance of MCHS with various cross sectional shapes is investigated in previous chapter, now a rectangular cross-section MCHS with specific dimensions as shown in Table 4.1 is considered. Results of interest such as temperature, heat transfer coefficient,

The forgoing thermophysical properties for the nanoparticle (alumina), base fluid (water), and the alumina-water nanofluid of three different volume fractions formulated are listed in Table 4.2. The density, thermal conductivity, and dynamic viscosity of the nanofluid appear significantly increased while the specific heat of nanofluid decreased with the increase of its particle volume fraction compared to pure water. The nanofluid of φ = 5% alumina, for instance, has a relative increase of 14.88%, 15.17%, and 12.46% in the density, thermal conductivity, and dynamic viscosity and has a relative decrease of 14.14% in specific heat,

Dh (µm) Hch (µm) Wch (µm) Lch (µm) S (µm)

339.15 43 280 10000 500

Properties Nanoparticle Base fluid Nanofluid (alumina-water)

ρ (kg/m3) 3970 998.2 1027.92 1072.5 114 .79

Cp (J/kg.K) 765 4182 4050.03 3865.79 3590.55

k (W/m.K) 40 0.613 0.631 0.658 0.706

µ (Ns/m2) 0.001003 0.001028 0.001066 0.001128

In this study, aluminum oxide with different particle volume fractions is used as the working fluid. The thermophysical properties required for flow as listed in Table 4.2 are

Density: ߩ*nf* = (1−߮) ߩ*bf* ߮ߩ*p* (4.1)

Heat capacity: (ߩܿ*p*) *nf* = (1−߮) (ߩܿ*p*) *bf* ߮(ߩܿ*p*) *p* (4.2)

Table 4.2. Thermophysical properties of alumina nanoparticles, water, and nanofluid at

(alumina) (water) *φ*= 1% *φ*= 2.5% *φ*= 5%

Table 4.1. Dimensions of the rectangular cross-section MCHS.

**4.1 Thermophysical properties of nanofluid** 

calculated using the following equations [24, 25, 26, 27]:

friction factor, wall shear stress, and thermal resistance are reported in this section.

respectively, compared to pure water.

293K.

For triangular cross-section MCHS,

$$Q = 0.5 \text{ N} \, k \, h \, \text{u}\_{\text{in}} \tag{3.7}$$

where *N* is the number of microchannels, *k* is the width of channel, *h* is the height of channel, and *u*in is the inlet velocity of water.

Fig. 3.8. Thermal resistance of MCHS with different cross-section shapes as function of pumping power.

The effect of using different cross sectional shapes of MCHS on thermal resistance, *R*th versus pumping power is shown in Fig.3.8. The pumping power is determined from the calculated volume flow rate for rectangular, trapezoidal, and triangular cross-section shape using Eq.3.5-Eq.3.7, respectively, and computed pressure drop using Eq.3.4. It is evident from this figure that the *R*th for rectangular cross-section MCHS is the lowest followed by trapezoidal and triangular cross-section MCHS. Thus, a MCHS with rectangular crosssection is capable for removing high heat flux due to its small difference between maximum wall temperature and inlet temperature at particular pumping power compared with that for MCHS with trapezoidal and triangular cross-sections.

#### **4. Effect of nanoparticle volume fractions on MCHS performance**

Nanofluids are produced from a suspension of nanoparticles with specified volume fraction in a conventional base fluid such as water, have been gaining interest recently due to its potential to greatly outperform traditional thermal transport liquids in MCHS [23]. However, the cooling effectiveness of using nanofluid as well as addressing other technical problems, such as agglomeration of the nanoparticles which yield to MCHS clogging due to the high particle volume fraction are vital to practical implementation of the nanofluid-

 *Q* = 0.5 *N k h u*in (3.7) where *N* is the number of microchannels, *k* is the width of channel, *h* is the height of

Fig. 3.8. Thermal resistance of MCHS with different cross-section shapes as function of

for MCHS with trapezoidal and triangular cross-sections.

**4. Effect of nanoparticle volume fractions on MCHS performance** 

The effect of using different cross sectional shapes of MCHS on thermal resistance, *R*th versus pumping power is shown in Fig.3.8. The pumping power is determined from the calculated volume flow rate for rectangular, trapezoidal, and triangular cross-section shape using Eq.3.5-Eq.3.7, respectively, and computed pressure drop using Eq.3.4. It is evident from this figure that the *R*th for rectangular cross-section MCHS is the lowest followed by trapezoidal and triangular cross-section MCHS. Thus, a MCHS with rectangular crosssection is capable for removing high heat flux due to its small difference between maximum wall temperature and inlet temperature at particular pumping power compared with that

Nanofluids are produced from a suspension of nanoparticles with specified volume fraction in a conventional base fluid such as water, have been gaining interest recently due to its potential to greatly outperform traditional thermal transport liquids in MCHS [23]. However, the cooling effectiveness of using nanofluid as well as addressing other technical problems, such as agglomeration of the nanoparticles which yield to MCHS clogging due to the high particle volume fraction are vital to practical implementation of the nanofluid-

For triangular cross-section MCHS,

pumping power.

channel, and *u*in is the inlet velocity of water.

cooled MCHS. In the current study, the effect of using three different particle volume fractions on heat transfer and liquid flow characteristics in MCHS will be discussed. Since the cooling performance of MCHS with various cross sectional shapes is investigated in previous chapter, now a rectangular cross-section MCHS with specific dimensions as shown in Table 4.1 is considered. Results of interest such as temperature, heat transfer coefficient, friction factor, wall shear stress, and thermal resistance are reported in this section.

The forgoing thermophysical properties for the nanoparticle (alumina), base fluid (water), and the alumina-water nanofluid of three different volume fractions formulated are listed in Table 4.2. The density, thermal conductivity, and dynamic viscosity of the nanofluid appear significantly increased while the specific heat of nanofluid decreased with the increase of its particle volume fraction compared to pure water. The nanofluid of φ = 5% alumina, for instance, has a relative increase of 14.88%, 15.17%, and 12.46% in the density, thermal conductivity, and dynamic viscosity and has a relative decrease of 14.14% in specific heat, respectively, compared to pure water.


Table 4.1. Dimensions of the rectangular cross-section MCHS.


Table 4.2. Thermophysical properties of alumina nanoparticles, water, and nanofluid at 293K.

#### **4.1 Thermophysical properties of nanofluid**

In this study, aluminum oxide with different particle volume fractions is used as the working fluid. The thermophysical properties required for flow as listed in Table 4.2 are calculated using the following equations [24, 25, 26, 27]:

Density: ߩ*nf* = (1−߮) ߩ*bf* ߮ߩ*p* (4.1)

Heat capacity: (ߩܿ*p*) *nf* = (1−߮) (ߩܿ*p*) *bf* ߮(ߩܿ*p*) *p* (4.2)

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 305

**Re = 900, q = 500 W/m**

 **= 1% = 2.5%**

 **= 0% (pure water)**

Fig. 4.2. Dimensionless temperature versus number of channels for 500 W/m2.

**1.000005 Re = 900, q = 1000 W/m** 

**0.997**

**0.999945**

**0.999965**

**0.999985**

**0.998**

**0.999**

**0 2 4 6 8 10 12 14 16 18 20 22 24 26 Channel Number**

 **= 0% (pure water)**

 **= 1% = 2.5%**

Fig. 4.3. Dimensionless temperature versus number of channels for 1000 W/m2.

**0 2 4 6 8 10 12 14 16 18 20 22 24 26 Channel Number**

$$\text{Thermal conductivity:} \qquad k\_{nf} = \frac{k\_p + 2k\_{bf} + 2(k\_p - k\_{bf})\rho}{k\_p + 2k\_{bf} - (k\_p - k\_{bf})\rho} \; k\_{bf} \tag{4.3}$$

$$\text{Viscosity:} \tag{4.4} \tag{4.5} \mu\_{nf} = \mu\_{bf} \left( 1 + 2.5\varphi \right) \tag{4.4}$$

Where ߮ is particle volume fraction, the subscript "*nf*" refers to nanofluid, "*bf*" refers to base fluid, and "*p*" refers to particle.

#### **4.2 Temperature profile**

The dimensionless temperature distribution at each channel of MCHS at Re = 900 for various particle volume fractions and different heat fluxes is shown in Figs.4.1–4.3. The dimensionless temperature is calculated using Eq.3.1 (Section 3). The presence of nanoparticles has an effect of reducing the temperature as the particle volume fraction of nanofluids increasing due to its higher dynamic viscosity and lower heat capacity compared to pure water. However, these conditions only can be greatly achieved for the case of heat flux = 1000 W/m2 compared to 100 W/m2 and 500 W/m2. For case 100 W/m2 and 500 W/m2, there is no significant differences between nanofluids and pure water, and the results are inconsistent for temperature distributions. Therefore, the presence of nanoparticles could enhance cooling of MCHS under the extreme heat flux conditions, the same trend was reported by Tsai and Chein [15] and Murshed et al. [28].

Fig. 4.1. Dimensionless temperature versus number of channels for 100 W/m2.

2( ) *p bf p bf p bf p bf k k kk k k kk*

 (4.4) (2.5߮ + 1) ߤ= ߤ :Viscosity Where ߮ is particle volume fraction, the subscript "*nf*" refers to nanofluid, "*bf*" refers to base

The dimensionless temperature distribution at each channel of MCHS at Re = 900 for various particle volume fractions and different heat fluxes is shown in Figs.4.1–4.3. The dimensionless temperature is calculated using Eq.3.1 (Section 3). The presence of nanoparticles has an effect of reducing the temperature as the particle volume fraction of nanofluids increasing due to its higher dynamic viscosity and lower heat capacity compared to pure water. However, these conditions only can be greatly achieved for the case of heat flux = 1000 W/m2 compared to 100 W/m2 and 500 W/m2. For case 100 W/m2 and 500 W/m2, there is no significant differences between nanofluids and pure water, and the results are inconsistent for temperature distributions. Therefore, the presence of nanoparticles could enhance cooling of MCHS under the extreme heat flux conditions, the

same trend was reported by Tsai and Chein [15] and Murshed et al. [28].

Fig. 4.1. Dimensionless temperature versus number of channels for 100 W/m2.

**1.00**

**1.20**

**1.40**

**1.60**

**1.80**

**0 2 4 6 8 10 12 14 16 18 20 22 24 26 Channel Number**

**Re = 900, q = 100 W/m**

 **= 1% = 2.5%**

 **= 0% (pure water)**

*bf k* (4.3)

Thermal conductivity: *nf <sup>k</sup>* 2 2( )

fluid, and "*p*" refers to particle.

**4.2 Temperature profile** 

Fig. 4.2. Dimensionless temperature versus number of channels for 500 W/m2.

Fig. 4.3. Dimensionless temperature versus number of channels for 1000 W/m2.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 307

The variation of the friction factor for various particle volume fractions is shown in Figs.4.5 and 4.6 for Reynolds number ranged from100-500 and 500-1000, respectively. The friction

> *f* = 2 , 2 *<sup>h</sup> nf in nf c D p*

Where *Dh* is the hydraulic diameter, *p* is the pressure drop, ߩis the density of nanofluid,

The results show that the friction factor is similar for all particle volume fractions where the friction factor decreases with the increase of Reynolds number. Based on Figs.4.5 and 4.6, it can be stated that the increment of dynamic viscosity due to the presence of the nanoparticles in water, only appears to give a slight rise in friction factor especially for low Reynolds number range (Fig.4.5). For high Reynolds number range (Fig.4.6), the nanofluid

Fig.4.7 shows a comparison of the predicted friction factor from the present numerical simulation against previous experimental studies [12, 30]. A very good agreement was obtained for φ = 0% (pure) and φ = 1% alumina, which shows that the friction factor

(4.6)

 **= 0% (pure water)**

 **= 1% = 2.5% = 5%**

*u L*

*uin,nf* is the inlet velocity of nanofluid, and *Lc* is the length of channel.

Fig. 4.5. Friction factor of MCHS for Reynolds number ranged from 100-500.

**100 200 300 400 500 Re**

**4.4 Friction factor** 

factor is calculated using Darcy equation [20]:

flow yields significant effect on friction factor.

decreases with the increase of Reynolds number.

**0.04**

**0.05**

**0.06**

**0.07**

**Friction factor, f**

**0.08**

**0.09**

**0.10**

**0.11**

#### **4.3 Heat transfer coefficient**

The effect of increasing nanoparticle percentage volume fraction on the dimensionless heat transfer coefficient of the nanofluid in each channel of MCHS is shown in Fig.4.4. The dimensionless heat transfer coefficient is calculated using:

$$
\hat{H} = \frac{h\_{nf}}{h\_{avg,water}}\tag{4.5}
$$

Where *hnf* is the nanofluids heat transfer coefficient value and *havg,water* is the average heat transfer coefficient of pure water. It is inferred that the nanofluids can enhance the heat transfer of MCHS as its volume fraction increases from 0% to 2.5%. However, nanofluid with 5% volume fraction is not able to enhance the heat transfer or performing almost the same result as pure water. This may due to agglomeration of the nanoparticles. The validity of the present results is confirmed with Murshed et al. [28] results. From Fig.4.4, it is also observed that the middle channel (channel 14) has the highest averaged heat transfer coefficient value as expected. The averaged heat transfer coefficient value for other channels is seen to decrease depending on their distance from the wall. The present results as illustrated in Fig.5.6 show similar trend with the results obtained by Liu and Garimella [29] and Chein and Chen [19]. Since higher temperatures are observed due to the heat transfer from the high-temperature edge of the heat sink, the averaged heat transfer coefficient is lower in channels close to the edge of the heat sink.

Fig. 4.4. Dimensionless averaged heat transfer coefficient versus number of channels for various particle volume fractions.

#### **4.4 Friction factor**

306 Fluid Dynamics, Computational Modeling and Applications

The effect of increasing nanoparticle percentage volume fraction on the dimensionless heat transfer coefficient of the nanofluid in each channel of MCHS is shown in Fig.4.4. The

> ��� ����������

Where *hnf* is the nanofluids heat transfer coefficient value and *havg,water* is the average heat transfer coefficient of pure water. It is inferred that the nanofluids can enhance the heat transfer of MCHS as its volume fraction increases from 0% to 2.5%. However, nanofluid with 5% volume fraction is not able to enhance the heat transfer or performing almost the same result as pure water. This may due to agglomeration of the nanoparticles. The validity of the present results is confirmed with Murshed et al. [28] results. From Fig.4.4, it is also observed that the middle channel (channel 14) has the highest averaged heat transfer coefficient value as expected. The averaged heat transfer coefficient value for other channels is seen to decrease depending on their distance from the wall. The present results as illustrated in Fig.5.6 show similar trend with the results obtained by Liu and Garimella [29] and Chein and Chen [19]. Since higher temperatures are observed due to the heat transfer from the high-temperature edge of the heat sink, the averaged heat transfer coefficient is

Fig. 4.4. Dimensionless averaged heat transfer coefficient versus number of channels for

(4.5)

ℎ� =

**4.3 Heat transfer coefficient** 

dimensionless heat transfer coefficient is calculated using:

lower in channels close to the edge of the heat sink.

various particle volume fractions.

The variation of the friction factor for various particle volume fractions is shown in Figs.4.5 and 4.6 for Reynolds number ranged from100-500 and 500-1000, respectively. The friction factor is calculated using Darcy equation [20]:

$$f = \frac{2D\_h \Delta p}{\rho\_{\text{nf}} u\_{\text{in.nf}} \text{\$^2\text{L}\_c}}\tag{4.6}$$

Where *Dh* is the hydraulic diameter, *p* is the pressure drop, ߩis the density of nanofluid, *uin,nf* is the inlet velocity of nanofluid, and *Lc* is the length of channel.

The results show that the friction factor is similar for all particle volume fractions where the friction factor decreases with the increase of Reynolds number. Based on Figs.4.5 and 4.6, it can be stated that the increment of dynamic viscosity due to the presence of the nanoparticles in water, only appears to give a slight rise in friction factor especially for low Reynolds number range (Fig.4.5). For high Reynolds number range (Fig.4.6), the nanofluid flow yields significant effect on friction factor.

Fig.4.7 shows a comparison of the predicted friction factor from the present numerical simulation against previous experimental studies [12, 30]. A very good agreement was obtained for φ = 0% (pure) and φ = 1% alumina, which shows that the friction factor decreases with the increase of Reynolds number.

Fig. 4.5. Friction factor of MCHS for Reynolds number ranged from 100-500.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 309

The effect of different volume fractions of nanoparticles on the local dimensionless wall shear stress is also investigated in the current study and the results are shown in Fig.4.8. The

> ߬ ෝ= ఛ ఛೌೡǡೢೌ

Where *τnf* is the nanofluid wall shear stress and *τavg, water* is the average value of pure water

As depicted in Fig.4.8, the wall shear stress increases with increasing Reynolds number for a specified percentage of volume fractions. It is clearly seen that for all cases investigated, the presence of nanoparticles substantially increases the wall shear-stress as compared with pure water. In general, for all cases examined, the least wall shear stress occurs at lower

Since the maximum wall temperature (Tw, max) of nanofluid-cooled MCHS is lower than pure water-cooled MCHS, reduction of thermal resistance in nanofluid-cooled MCHS is then expected. If the presence of nanoparticles in coolant did not produce extra pressure drop which relates to the coolant pumping power required, it can then be considered as another benefit of using nanofluid as the coolant in MCHS operation. The volume flow rate, *Q* for

 *Q* = *N W*ch *H*ch *uin,*nf (4.8) Where *N* is the number of microchannels, *W*ch is the width of channel, *H*ch is the height of

The cooling performance of the MCHS using nanofluid is assessed by exploring the results for the thermal resistance, *R*th as defined in Eq.3.3. The variation of thermal resistance versus pumping power is presented in Fig.4.9. The pumping power is determined from the calculated volume flow rate as defined in Eq.4.8 and computed pressure drop using Eq.3.4 (Section 3). As depicted in Fig.4.9, the nanofluid is shown to have significantly lower value of *R*th as its particle volume fraction increases than pure water. For the current geometry

be achieved is about 57.6% for nanofluid with particle volume fraction of 5% at 0.0145 W. This great improvement in *R*th is mainly due to the increase in thermal conductivity and decrease in temperature difference between inlet and maximum wall temperature as the particle volume fraction increases. The additional reduction in *R*th is clearly due to the thermal dispersion. Since water has the highest *R*th value, it is not preferable for removing high heat flux. The percent enhancement of MCHS's cooling performance is actually

> , , ,

*R R*

*R*

100% *th nf th water th water*

Where *Rth,nf* corresponds to thermal resistance of particular nanofluid and *Rth,water*

*x*

(4.9)

(4.7)

**4.5 Wall shear stress** 

wall shear stress.

**4.6 Thermal resistance** 

calculated by using:

dimensionless wall shear stress is calculated using:

value of φ = 1 % while highest value occurs at φ = 5 %.

rectangular shaped microchannel is defined as:

channel, and *uin,*nf is the inlet velocity of nanofluid.

under study, the maximum reduction in *R*th that can

corresponds to thermal resistance of pure water.

Fig. 4.6. Friction factor of MCHS for Reynolds number ranged from 500-1000.

Fig. 4.7. A comparison of predicted friction factor with [12] and [30].

#### **4.5 Wall shear stress**

308 Fluid Dynamics, Computational Modeling and Applications

 **= 0% (pure water)**

 **= 1% = 2.5% = 5%**

Fig. 4.6. Friction factor of MCHS for Reynolds number ranged from 500-1000.

**0.018**

**0.00**

**0.04**

**0.08**

**Friction factor, f**

**0.12**

**0.020**

**0.022**

**0.024**

**0.026**

**Friction factor, f**

**0.028**

**0.030**

**0.032**

**0.034**

**0.036**

**500 600 700 800 900 1000**

**Re**

 **= 0% Present work = 1% Present work = 0% Lee & Mudawar [12] = 1% Lee & Mudawar [12] = 1% Ho et al. [30] = 0% Ho et al. [30]**

**0 200 400 600 800 1000 Re**

Fig. 4.7. A comparison of predicted friction factor with [12] and [30].

The effect of different volume fractions of nanoparticles on the local dimensionless wall shear stress is also investigated in the current study and the results are shown in Fig.4.8. The dimensionless wall shear stress is calculated using:

$$
\widehat{\mathbf{r}} = \frac{\mathbf{r}\_{nf}}{\mathbf{r}\_{avg,water}} \tag{4.7}
$$

Where *τnf* is the nanofluid wall shear stress and *τavg, water* is the average value of pure water wall shear stress.

As depicted in Fig.4.8, the wall shear stress increases with increasing Reynolds number for a specified percentage of volume fractions. It is clearly seen that for all cases investigated, the presence of nanoparticles substantially increases the wall shear-stress as compared with pure water. In general, for all cases examined, the least wall shear stress occurs at lower value of φ = 1 % while highest value occurs at φ = 5 %.

#### **4.6 Thermal resistance**

Since the maximum wall temperature (Tw, max) of nanofluid-cooled MCHS is lower than pure water-cooled MCHS, reduction of thermal resistance in nanofluid-cooled MCHS is then expected. If the presence of nanoparticles in coolant did not produce extra pressure drop which relates to the coolant pumping power required, it can then be considered as another benefit of using nanofluid as the coolant in MCHS operation. The volume flow rate, *Q* for rectangular shaped microchannel is defined as:

$$Q = \mathcal{N} \, \mathcal{W}\_{\rm ch} \, H\_{\rm ch} \, \mathcal{U}\_{\rm inv, mf} \tag{4.8}$$

Where *N* is the number of microchannels, *W*ch is the width of channel, *H*ch is the height of channel, and *uin,*nf is the inlet velocity of nanofluid.

The cooling performance of the MCHS using nanofluid is assessed by exploring the results for the thermal resistance, *R*th as defined in Eq.3.3. The variation of thermal resistance versus pumping power is presented in Fig.4.9. The pumping power is determined from the calculated volume flow rate as defined in Eq.4.8 and computed pressure drop using Eq.3.4 (Section 3). As depicted in Fig.4.9, the nanofluid is shown to have significantly lower value of *R*th as its particle volume fraction increases than pure water. For the current geometry under study, the maximum reduction in *R*th that can

be achieved is about 57.6% for nanofluid with particle volume fraction of 5% at 0.0145 W. This great improvement in *R*th is mainly due to the increase in thermal conductivity and decrease in temperature difference between inlet and maximum wall temperature as the particle volume fraction increases. The additional reduction in *R*th is clearly due to the thermal dispersion. Since water has the highest *R*th value, it is not preferable for removing high heat flux. The percent enhancement of MCHS's cooling performance is actually calculated by using:

$$\frac{R\_{th,uf} - R\_{th,water}}{R\_{th,water}} \ge 100\,\%\tag{4.9}$$

Where *Rth,nf* corresponds to thermal resistance of particular nanofluid and *Rth,water* corresponds to thermal resistance of pure water.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 311

Based on the results that obtained in Section 4 which focused on the effect of using different particle volume fractions of Al2O3-H2O on heat transfer and liquid flow characteristics in MCHS, it is known that nanofluids have the capability to enhance the heat transfer performance of MCHS with smaller pressure drop penalty. However, due to production of various nanofluids in market, further investigations on using different types of nanofluids in MCHS are necessary because the heat transfer enhancement of MCHS is strongly depend on thermophysical properties of dispersed nanoparticles in base fluid [31]. Thus, in this chapter, the effect of using six types of nanofluids on heat transfer and liquid flow characteristics in triangular cross-section MCHS with specified dimensions is

The specific dimensions of the triangular MCHS used in this section are given in Table 5.1. A constant particle volume fraction value of 2% is considered for all types of nanofluids studied in this chapter. The thermophysical properties for all types of nanoparticles, base fluid (water), and the nanofluids with particle volume fraction of 2% are listed in Table 5.2. For all types of nanofluids studied, the density, thermal conductivity, and dynamic viscosity appear significantly higher while the specific heat of nanofluids is lower than pure water. For instance, diamond-H2O nanofluid has a relative increase of 5.03%, 6.11%, and 5% in the density, thermal conductivity, and dynamic viscosity and has a relative decrease of 5.90% in

In this section, different types of nanofluids which are Al2O3-H2O, Ag-H2O, CuO-H2O, diamond-H2O, SiO2-H2O, and TiO2-H2O are used as working fluids. The thermophysical properties as listed in Table 5.2 including density, heat capacity, thermal conductivity, and viscosity for all types of nanofluids which are involved in the governing equations are

The thermal performance of using different types of nanofluids in MCHS is examined by presenting the results of the dimensionless heat transfer coefficient along the length of channel number 1 in Fig.5.1. It is observed that all types of nanofluids-cooled MCHS could be able to enhance the heat transfer compared with pure water-cooled MCHS. The waterbase nanofluid containing diamond has the highest heat transfer coefficient value followed by SiO2, CuO, TiO2, Ag and Al2O3. However, there is no significant difference that can be detected between TiO2 and CuO due to their small difference in thermal diffusivity. However, there is a very small increment in CuO-H2O-cooled MCHS especially at the outlet

Dh (µm) k (µm) h (µm) l (µm) Lch (µm) S (µm) β

230 280 430 452 10000 500 36.07ο

**5. Effect of using different nanofluids on MCHS performance** 

comprehensively investigated.

**5.1 Heat transfer coefficient** 

specific heat, respectively, compared with pure water.

calculated using Eqs.4.1-4.4 (Section 4), respectively.

of the channel compared with that for TiO2-H2O-cooled MCHS.

Table 5.1. Dimensions of the triangular cross-section MCHS.

Fig. 4.8. Dimensionless wall shear stress versus Reynolds number for various particle volume fractions.

Fig. 4.9. Thermal resistance of MCHS as function of pumping power.

#### **5. Effect of using different nanofluids on MCHS performance**

Based on the results that obtained in Section 4 which focused on the effect of using different particle volume fractions of Al2O3-H2O on heat transfer and liquid flow characteristics in MCHS, it is known that nanofluids have the capability to enhance the heat transfer performance of MCHS with smaller pressure drop penalty. However, due to production of various nanofluids in market, further investigations on using different types of nanofluids in MCHS are necessary because the heat transfer enhancement of MCHS is strongly depend on thermophysical properties of dispersed nanoparticles in base fluid [31]. Thus, in this chapter, the effect of using six types of nanofluids on heat transfer and liquid flow characteristics in triangular cross-section MCHS with specified dimensions is comprehensively investigated.

The specific dimensions of the triangular MCHS used in this section are given in Table 5.1. A constant particle volume fraction value of 2% is considered for all types of nanofluids studied in this chapter. The thermophysical properties for all types of nanoparticles, base fluid (water), and the nanofluids with particle volume fraction of 2% are listed in Table 5.2. For all types of nanofluids studied, the density, thermal conductivity, and dynamic viscosity appear significantly higher while the specific heat of nanofluids is lower than pure water. For instance, diamond-H2O nanofluid has a relative increase of 5.03%, 6.11%, and 5% in the density, thermal conductivity, and dynamic viscosity and has a relative decrease of 5.90% in specific heat, respectively, compared with pure water.

In this section, different types of nanofluids which are Al2O3-H2O, Ag-H2O, CuO-H2O, diamond-H2O, SiO2-H2O, and TiO2-H2O are used as working fluids. The thermophysical properties as listed in Table 5.2 including density, heat capacity, thermal conductivity, and viscosity for all types of nanofluids which are involved in the governing equations are calculated using Eqs.4.1-4.4 (Section 4), respectively.

#### **5.1 Heat transfer coefficient**

310 Fluid Dynamics, Computational Modeling and Applications

 **= 0% (pure water)**

 **= 1% = 2.5% = 5%**

Fig. 4.8. Dimensionless wall shear stress versus Reynolds number for various particle

**0 200 400 600 800 1000 Re**

**= 0% (pure water)**

**= 1% = 2.5% = 5%**

**0.008 0.012 0.016 0.020 Pumping power (W)**

Fig. 4.9. Thermal resistance of MCHS as function of pumping power.

volume fractions.

**0.00**

**0.000**

**0.005**

**0.010**

**Thermal resistance (K/W)**

**0.015**

**0.020**

**0.50**

**1.00**

**1.50**

**2.00**

**2.50**

The thermal performance of using different types of nanofluids in MCHS is examined by presenting the results of the dimensionless heat transfer coefficient along the length of channel number 1 in Fig.5.1. It is observed that all types of nanofluids-cooled MCHS could be able to enhance the heat transfer compared with pure water-cooled MCHS. The waterbase nanofluid containing diamond has the highest heat transfer coefficient value followed by SiO2, CuO, TiO2, Ag and Al2O3. However, there is no significant difference that can be detected between TiO2 and CuO due to their small difference in thermal diffusivity. However, there is a very small increment in CuO-H2O-cooled MCHS especially at the outlet of the channel compared with that for TiO2-H2O-cooled MCHS.


Table 5.1. Dimensions of the triangular cross-section MCHS.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 313

Since the velocity at the entrance of the channel was kept constant at Re = 600, it can be noticed that the heat transfer coefficient decreases linearly along the length of channel because of the development of thermal boundary layer for all cases. The highest value of heat transfer coefficient occurs near the entrance. The present results show a similar trend with the results obtained by Lee and Mudawar [12]. It is also depicted from Fig.5.1 that the difference in dimensionless heat transfer coefficient between various nanofluids is too small but it follows trend and not too far from reported values. From the results obtained,

thermal resistance is expected with diamond-H2O nanofluid cooled MCHS due to its lowest temperature distribution. Therefore, the presence of diamond nanoparticle in water could greatly enhance the cooling of MCHS compared with other types of nanofluids. This is due to the highest thermal transport capacity of diamond in nature and diamond particles are often used as filler in mixtures for upgrading the performance of a matrix (composition of mixtures) as reported by Xie et al. [32]. Thus, it is reasonable to expect that the addition of diamond nanoparticles in water would lead to heat transfer

Fig. 5.1. Dimensionless heat transfer coefficient along the length of channel No.1.

**0.9999**

**1.0000**

**1.0001**

**h**

**1.0002**

**1.0003**

**0 10 20 30 40 50 Z**

**DM SiO CuO TiO Ag Al O pure water**

lowest

enhancement.


Table 5.2. Thermophysical properties of nanoparticles, water and nanofluids at 293K.

Properties Nanoparticle Base fluid Nanofluid (diamond-H2O)

 Cp (J/kg.K) 497.26 4182 3935.28 κ (W/m.K) 1000 0.613 0.65046

 Cp (J/kg.K) 703 4182 4032.25 κ (W/m.K) 1.2 0.613 0.62194

 Cp (J/kg.K) 535.6 4182 3754.26 κ (W/m.K) 20 0.613 0.64722

 Cp (J/kg.K) 686.2 4182 3902.53 κ (W/m.K)) 8.9538 0.613 0.64364

 Cp (J/kg.K) 235 4182 3484.44 κ (W/m.K) 429 0.613 0.65037

 Cp (J/kg.K) 765 4182 3925.47526 κ (W/m.K) 40 0.613 0.64882

Table 5.2. Thermophysical properties of nanoparticles, water and nanofluids at 293K.

) 3510 998.2 1048.436

) 0.001003 0.00105315

) 2200 998.2 1022.236

) 0.001003 0.00105315

) 6500 998.2 1108.236

) 0.001003 0.00105315

) 4250 998.2 1063.236

) 0.001003 0.00105315

) 10500 998.2 1188.236

) 0.001003 0.00105315

) 3970 998.2 1057.636

) 0.001003 0.00105315

(aluminum oxide) (water) *φ* = 2%

Properties Nanoparticle Base fluid Nanofluid (SiO2-H2O)

Properties Nanoparticle Base fluid Nanofluid (CuO-H2O)

Properties Nanoparticle Base fluid Nanofluid (TiO2-H2O)

Properties Nanoparticle Base fluid Nanofluid (Ag-H2O)

Properties Nanoparticle Base fluid Nanofluid (Al2O3-H2O)

(diamond) (water) *φ* = 2%

(silicon dioxide) (water) *φ* = 2%

(copper oxide) (water) *φ* = 2%

(titanium dioxide) (water) *φ* = 2%

(silver) (water) *φ* = 2%

py p p p

ρ (kg/m3

µ (Ns/m2

ρ (kg/m3

µ (Ns/m2

ρ (kg/m3

µ (Ns/m2

ρ (kg/m3

µ (Ns/m2

ρ (kg/m3

µ (Ns/m2

ρ (kg/m3

µ (Ns/m2

Since the velocity at the entrance of the channel was kept constant at Re = 600, it can be noticed that the heat transfer coefficient decreases linearly along the length of channel because of the development of thermal boundary layer for all cases. The highest value of heat transfer coefficient occurs near the entrance. The present results show a similar trend with the results obtained by Lee and Mudawar [12]. It is also depicted from Fig.5.1 that the difference in dimensionless heat transfer coefficient between various nanofluids is too small but it follows trend and not too far from reported values. From the results obtained, lowest

thermal resistance is expected with diamond-H2O nanofluid cooled MCHS due to its lowest temperature distribution. Therefore, the presence of diamond nanoparticle in water could greatly enhance the cooling of MCHS compared with other types of nanofluids. This is due to the highest thermal transport capacity of diamond in nature and diamond particles are often used as filler in mixtures for upgrading the performance of a matrix (composition of mixtures) as reported by Xie et al. [32]. Thus, it is reasonable to expect that the addition of diamond nanoparticles in water would lead to heat transfer enhancement.

Fig. 5.1. Dimensionless heat transfer coefficient along the length of channel No.1.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 315

roughness [28]. However, Ag-H2O-cooled MCHS still has lower value of pressure drop than pure water-cooled MCHS and there is no extra pressure drop in CuO-H2O-cooled MCHS as compared with pure water-cooled MCHS. The reason for this result is Ag-H2O has the lowest Prandtl number (Pr = 5.6 and followed by CuO-H2O (Pr = 6.1). The small difference in pressure drop between other types of nanofluids which can be seen in Fig.5.2 is due to small differences in their Prandtl numbers and SiO2-H2O yields the highest pressure drop across the MCHS due to its highest Prandtl number (Pr = 6.8). Therefore, the pressure drop penalty is not only affected by the viscosity of nanofluids but also the Prandtl number of nanofluids which need to be considered in nanofluids selection as a coolant for MCHS. Apart from that, slight increment in pressure drop particularly for Ag-H2O and CuO-H2O-cooled MCHS which can be considered as one of the benefits of using nanofluid in MCHS operations in order to achieve

The pumping power which is the product of the pressure drop across the heat sinkǡ οܲ and volume flow rate, *Q*, is calculated using Eq.3.4. The volume flow rate, *Q* for triangular

 *Q* = 0.5 *N k h u*in,nf (5.1) Where *N* is the number of microchannels, *k* is the width of channel, *h* is the height of

The thermal resistance for all types of nanofluids as function of pumping power is shown in Fig.5.3. It is observed that all types of nanofluids reduce the thermal resistance of MCHS

overall heat transfer enhancement with small pressure drop penalty.

Fig. 5.3. Thermal resistance of MCHS as function of pumping power.

**5.3 Thermal resistance** 

shaped microchannel is defined as:

channel, and *u*in,nf is the inlet velocity of nanofluid.

#### **5.2 Pressure drop**

The dimensionless pressure distribution of the MCHS for various nanofluids and pure water along the length of channel number 1 is shown in Fig.5.2. The dimensionless pressure distribution is calculated using:

Fig. 5.2. Dimensionless pressure drop variation along the length of channel No.1.

$$
\hat{P} = \frac{\Delta P}{\rho u\_{\text{tn}}^2} \tag{5.1}
$$

where �� is the pressure drop of particular microchannel configuration, *ρ* is the water density, and ��� is the inlet water velocity.

It can obviously be seen that the high pressure region occurs at the entrance and the low pressure region occurs at the outlet of the heat sink. This is due to the needs of high pressure to push the fluid flow along the direction of the microchannels out from the outlet plenum of heat sink. Thus, the pressure decreases linearly along the length of channel for all types of nanofluids studied including pure water. Because of that, there is no apparent difference observed between pure water and nanofluids flows particularly at the outlet region of MCHS. However, compared with pure water cooled case, slightly larger pressure drops for nanofluid-cooled MCHS were found except for Ag-H2O nanofluid which has the lowest value of pressure drop among nanofluids types. The water-base nanofluids containing SiO2 has the highest value of pressure drop and followed by diamond-H2O respectively. The pressure drop in water-base nanofluids-cooled MCHS containing Al2O3 and TiO2 are slightly lower than diamond-H2O-cooled MCHS.

Since the viscosity of nanofluids is larger than pure water as indicated in Table 5.2, larger pressure drop is expected in nanofluid-cooled MCHS. Another reason that contributes to increase the pressure drop is the deposition of nanoparticle in water is increasing the wall roughness [28]. However, Ag-H2O-cooled MCHS still has lower value of pressure drop than pure water-cooled MCHS and there is no extra pressure drop in CuO-H2O-cooled MCHS as compared with pure water-cooled MCHS. The reason for this result is Ag-H2O has the lowest Prandtl number (Pr = 5.6 and followed by CuO-H2O (Pr = 6.1). The small difference in pressure drop between other types of nanofluids which can be seen in Fig.5.2 is due to small differences in their Prandtl numbers and SiO2-H2O yields the highest pressure drop across the MCHS due to its highest Prandtl number (Pr = 6.8). Therefore, the pressure drop penalty is not only affected by the viscosity of nanofluids but also the Prandtl number of nanofluids which need to be considered in nanofluids selection as a coolant for MCHS. Apart from that, slight increment in pressure drop particularly for Ag-H2O and CuO-H2O-cooled MCHS which can be considered as one of the benefits of using nanofluid in MCHS operations in order to achieve overall heat transfer enhancement with small pressure drop penalty.

#### **5.3 Thermal resistance**

314 Fluid Dynamics, Computational Modeling and Applications

The dimensionless pressure distribution of the MCHS for various nanofluids and pure water along the length of channel number 1 is shown in Fig.5.2. The dimensionless pressure

Fig. 5.2. Dimensionless pressure drop variation along the length of channel No.1.

�� = �� ����

where �� is the pressure drop of particular microchannel configuration, *ρ* is the water

It can obviously be seen that the high pressure region occurs at the entrance and the low pressure region occurs at the outlet of the heat sink. This is due to the needs of high pressure to push the fluid flow along the direction of the microchannels out from the outlet plenum of heat sink. Thus, the pressure decreases linearly along the length of channel for all types of nanofluids studied including pure water. Because of that, there is no apparent difference observed between pure water and nanofluids flows particularly at the outlet region of MCHS. However, compared with pure water cooled case, slightly larger pressure drops for nanofluid-cooled MCHS were found except for Ag-H2O nanofluid which has the lowest value of pressure drop among nanofluids types. The water-base nanofluids containing SiO2 has the highest value of pressure drop and followed by diamond-H2O respectively. The pressure drop in water-base nanofluids-cooled MCHS containing Al2O3 and TiO2 are

Since the viscosity of nanofluids is larger than pure water as indicated in Table 5.2, larger pressure drop is expected in nanofluid-cooled MCHS. Another reason that contributes to increase the pressure drop is the deposition of nanoparticle in water is increasing the wall

� (5.1)

**5.2 Pressure drop** 

distribution is calculated using:

density, and ��� is the inlet water velocity.

slightly lower than diamond-H2O-cooled MCHS.

The pumping power which is the product of the pressure drop across the heat sinkǡ οܲ and volume flow rate, *Q*, is calculated using Eq.3.4. The volume flow rate, *Q* for triangular shaped microchannel is defined as:

$$Q = 0.5 \text{ N } k \text{ } h \text{ } u\_{\text{in,rd}} \tag{5.1}$$

Where *N* is the number of microchannels, *k* is the width of channel, *h* is the height of channel, and *u*in,nf is the inlet velocity of nanofluid.

The thermal resistance for all types of nanofluids as function of pumping power is shown in Fig.5.3. It is observed that all types of nanofluids reduce the thermal resistance of MCHS

Fig. 5.3. Thermal resistance of MCHS as function of pumping power.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 317

Properties Nanoparticle Base fluid Nanofluid (H2O-Diamond)

 Cp (J/kg.K) 497.26 4182 3935.28 κ (W/m.K) 1000 0.613 0.65046

 Cp (J/kg.K) 497.26 2382.1 2268.56 κ (W/m.K) 1000 0.2492 0.26445

 Cp (J/kg.K) 497.26 1880.3 1777.09 κ (W/m.K) 1000 0.145 0.15387

 Cp (J/kg.K) 497.26 2385 2283.76 κ (W/m.K)) 1000 0.286 0.30349

contribute to increase the thermal transport capacity of the mixture.

) 3510 998.2 1048.436

) 0.001003 0.00105315 Properties Nanoparticle Base fluid Nanofluid (EG-Diamond)

) 3510 1117.48 1165.33

) 0.022 0.0231 Properties Nanoparticle Base fluid Nanofluid (Oil-Diamond)

) 3510 888.23 940.665

) 0.8451 0.88736 Properties Nanoparticle Base fluid Nanofluid (Glycerin-Diamond)

) 3510 1264.03 1308.95

) 1.5347 1.61144

Table 6.2. Thermophysical properties of diamond nanoparticels, base fluids and nanofluids

The effect of different types of base fluids on dimensionless temperature variation is presented in Fig.6.1. It can clearly be seen that the temperature of pure water is always highest among all types of base fluids. By comparing dimensionless temperature distributions between different types of base fluids, glycerin-diamond has the lowest value of temperature while water-diamond has the highest value of temperature and followed by EG-diamond and oil-diamond. Based on results shown in Fig.6.1, it can be stated that the lowest thermal resistance is expected in the glycerin-diamond fluid cooled MCHS due to its lowest temperature distribution. Therefore, the presence of diamond nanoparticle in glycerin could greatly enhance the cooling of MCHS compared with other types of base fluids studied. This is because of glycerin has the highest dynamic viscosity in nature compared to other base fluids and diamond particle mixed properly in glycerin which

ρ (kg/m3

µ (Ns/m2

ρ (kg/m3

µ (Ns/m2

ρ (kg/m3

µ (Ns/m2

ρ (kg/m3

µ (Ns/m2

**6.1 Temperature profile** 

at 293K.

(Diamond) (Water) *φ* = 2%

(Diamond) (Ethylene Glycol) *φ* = 2%

(Diamond) (Oil) *φ* = 2%

(Diamond) (Glycerin) *φ* = 2%

than pure water. The maximum reduction in *R*th is achieved in diamond-H2O MCHS is 3.1292 K/W when pumping power is 0.0097207 W. The results indicate that the cooling performance of a MCHS at pumping power = 0.005 W is enhanced by about 2 % for waterbase nanofluids containing diamond, SiO2, CuO, and TiO2, 1.13% for water-base nanofluids containing Al2O3, and 1.04% for water-base nanofluids containing Ag respectively, compared with that of the MCHS with pure water. The percent enhancement of MCHS cooling performance is also calculated using Eq.4.9. The great improvement in *R*th is mainly due to the increase in thermal conductivity and decrease in temperature difference between inlet and maximum wall temperature. The additional reduction in *R*th is also due to the thermal dispersion of particle volume fractions.

### **6. Effect of using different base fluids on MCHS performance**

Since base fluid for all types of nanofluids studied in Section 5 was water, it is important and necessary to know the heat transfer and liquid flow characteristics in MCHS using other types of conventional base fluids such as ethylene glycol (EG), glycerin, and oil. By using other types of conventional base fluids instead of using water, the MCHS cooling performance could be enhanced or may not. Thus, considering nanofluid flow in a microchannel, the effect of using different types of base fluids including water, EG, engine oil, and glycerin on heat transfer and liquid flow characteristics in trapezoidal shaped MCHS which was selected for this chapter with specified dimensions is extensively discussed in this chapter. The specified dimensions are given in Table 6.1.

Since the best uniformities in heat transfer coefficient and temperature can be achieved in MCHS using diamond nanoparticle as obtained in Section 5, the diamond nanoparticle is selected and considered for all types of base fluids studied in this chapter. The thermophysical properties for diamond nanoparticle, for all types of base fluids, and the nanofluids with particle volume fraction of 2% formulated are listed in Table 6.2. For all types of nanofluids, the density, thermal conductivity, and dynamic viscosity appear significantly higher while the specific heat of nanofluids is lower than the base fluids. For instance, the EG-diamond nanofluid has a relative increase of 4.28%, 6.12%, and 5% in the density, thermal conductivity, and dynamic viscosity and has a relative decrease of 4.77% in specific heat, respectively, compared with EG base fluid.

The thermophysical properties as listed in Table 6.2 including density, heat capacity, thermal conductivity, and viscosity for all types of base fluids for nanoparticles are calculated using Eqs.4.1-4.4 (Section 4), respectively.


Table 6.1. Dimensions of the trapezoidal cross-section MCHS.

than pure water. The maximum reduction in *R*th is achieved in diamond-H2O MCHS is 3.1292 K/W when pumping power is 0.0097207 W. The results indicate that the cooling performance of a MCHS at pumping power = 0.005 W is enhanced by about 2 % for waterbase nanofluids containing diamond, SiO2, CuO, and TiO2, 1.13% for water-base nanofluids containing Al2O3, and 1.04% for water-base nanofluids containing Ag respectively, compared with that of the MCHS with pure water. The percent enhancement of MCHS cooling performance is also calculated using Eq.4.9. The great improvement in *R*th is mainly due to the increase in thermal conductivity and decrease in temperature difference between inlet and maximum wall temperature. The additional reduction in *R*th is also due to the

Since base fluid for all types of nanofluids studied in Section 5 was water, it is important and necessary to know the heat transfer and liquid flow characteristics in MCHS using other types of conventional base fluids such as ethylene glycol (EG), glycerin, and oil. By using other types of conventional base fluids instead of using water, the MCHS cooling performance could be enhanced or may not. Thus, considering nanofluid flow in a microchannel, the effect of using different types of base fluids including water, EG, engine oil, and glycerin on heat transfer and liquid flow characteristics in trapezoidal shaped MCHS which was selected for this chapter with specified dimensions is extensively

Since the best uniformities in heat transfer coefficient and temperature can be achieved in MCHS using diamond nanoparticle as obtained in Section 5, the diamond nanoparticle is selected and considered for all types of base fluids studied in this chapter. The thermophysical properties for diamond nanoparticle, for all types of base fluids, and the nanofluids with particle volume fraction of 2% formulated are listed in Table 6.2. For all types of nanofluids, the density, thermal conductivity, and dynamic viscosity appear significantly higher while the specific heat of nanofluids is lower than the base fluids. For instance, the EG-diamond nanofluid has a relative increase of 4.28%, 6.12%, and 5% in the density, thermal conductivity, and dynamic viscosity and has a relative decrease of 4.77% in

The thermophysical properties as listed in Table 6.2 including density, heat capacity, thermal conductivity, and viscosity for all types of base fluids for nanoparticles are

Dh (µm) a (µm) b (µm) c (µm) Lch (µm) h (µm)

318 280 225 431 10000 430

thermal dispersion of particle volume fractions.

**6. Effect of using different base fluids on MCHS performance** 

discussed in this chapter. The specified dimensions are given in Table 6.1.

specific heat, respectively, compared with EG base fluid.

Table 6.1. Dimensions of the trapezoidal cross-section MCHS.

calculated using Eqs.4.1-4.4 (Section 4), respectively.


Table 6.2. Thermophysical properties of diamond nanoparticels, base fluids and nanofluids at 293K.

#### **6.1 Temperature profile**

The effect of different types of base fluids on dimensionless temperature variation is presented in Fig.6.1. It can clearly be seen that the temperature of pure water is always highest among all types of base fluids. By comparing dimensionless temperature distributions between different types of base fluids, glycerin-diamond has the lowest value of temperature while water-diamond has the highest value of temperature and followed by EG-diamond and oil-diamond. Based on results shown in Fig.6.1, it can be stated that the lowest thermal resistance is expected in the glycerin-diamond fluid cooled MCHS due to its lowest temperature distribution. Therefore, the presence of diamond nanoparticle in glycerin could greatly enhance the cooling of MCHS compared with other types of base fluids studied. This is because of glycerin has the highest dynamic viscosity in nature compared to other base fluids and diamond particle mixed properly in glycerin which contribute to increase the thermal transport capacity of the mixture.

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 319

Fig. 6.2. Dimensionless heat transfer coefficient along the length of channel No.20 for

Fig. 6.3. Dimensionless averaged heat transfer coefficient versus number of channels for

Fig.6.4 shows the dimensionless heat transfer coefficient in each channel of various substrate materials for EG-base fluid. The highest ℎ� is achieved in copper made microchannels, which has the lowest thermal diffusivity followed by aluminium, steel, and titanium. The increase in ℎ� could be attributed to the decreased conduction resistance along the microchannel wall due to much lower thermal diffusivity in copper made microchannels. The averaged heat transfer coefficient of oil and glycerine base-cooled MCHS shows a similar trend as for EG base-cooled MCHS. However, the condition becomes different for low Prandtl number base

various base fluids.

various base fluids.

#### **6.2 Heat transfer coefficient**

The thermal performance of using different types of base fluids in MCHS is examined by plotting results of the dimensionless heat transfer coefficient along the length of channel number 20 as shown in Fig.6.2. Koo and Kleinstreuer [10] reported that higher Prandtl number base fluids-cooled MCHS could be able to enhance the heat transfer performance of MCHS as compared with water base-cooled MCHS. This was proven by the present results where the glycerin base-cooled MCHS has the highest ℎ� value due to the highest Prandtl number value followed by oil, and EG.

Fig. 6.1. Dimensionless temperature profile versus number of channels for pure water and various base fluids.

Fig.6.3 shows the dimensionless heat transfer coefficient in each channel of the heat sinks for various base fluids-cooled MCHS. The ℎ� for high Prandtl number base fluids is always higher than that for water base fluid. This is due to the fact that high Prandtl number base fluids are experiencing stronger thermal flow development effects as reported by Koo and Kleinstreuer [10]. However, there is no significant differences in ℎ� for EG, oil, and glycerine but when the plot is zoomed in, there are slight differences in ℎ� where glycerin base-cooled MCHS has the highest ℎ� value, oil is in between, and EG is the least. For each type of the heat sinks, the middle channel (channel number 14) has the highest ℎ� value as expected. The averaged heat transfer coefficient value for other channels is seen to decrease depending on their distances from the wall. The averaged heat transfer coefficient distribution for all types of MCHS is almost symmetrical with respect to the centreline of the heat sink.

The thermal performance of using different types of base fluids in MCHS is examined by plotting results of the dimensionless heat transfer coefficient along the length of channel number 20 as shown in Fig.6.2. Koo and Kleinstreuer [10] reported that higher Prandtl number base fluids-cooled MCHS could be able to enhance the heat transfer performance of MCHS as compared with water base-cooled MCHS. This was proven by the present results where the glycerin base-cooled MCHS has the highest ℎ� value due to the highest Prandtl

Fig. 6.1. Dimensionless temperature profile versus number of channels for pure water and

Fig.6.3 shows the dimensionless heat transfer coefficient in each channel of the heat sinks for various base fluids-cooled MCHS. The ℎ� for high Prandtl number base fluids is always higher than that for water base fluid. This is due to the fact that high Prandtl number base fluids are experiencing stronger thermal flow development effects as reported by Koo and Kleinstreuer [10]. However, there is no significant differences in ℎ� for EG, oil, and glycerine but when the plot is zoomed in, there are slight differences in ℎ� where glycerin base-cooled MCHS has the highest ℎ� value, oil is in between, and EG is the least. For each type of the heat sinks, the middle channel (channel number 14) has the highest ℎ� value as expected. The averaged heat transfer coefficient value for other channels is seen to decrease depending on their distances from the wall. The averaged heat transfer coefficient distribution for all types of MCHS is almost symmetrical with respect to the

**6.2 Heat transfer coefficient** 

various base fluids.

centreline of the heat sink.

number value followed by oil, and EG.

Fig. 6.2. Dimensionless heat transfer coefficient along the length of channel No.20 for various base fluids.

Fig. 6.3. Dimensionless averaged heat transfer coefficient versus number of channels for various base fluids.

Fig.6.4 shows the dimensionless heat transfer coefficient in each channel of various substrate materials for EG-base fluid. The highest ℎ� is achieved in copper made microchannels, which has the lowest thermal diffusivity followed by aluminium, steel, and titanium. The increase in ℎ� could be attributed to the decreased conduction resistance along the microchannel wall due to much lower thermal diffusivity in copper made microchannels. The averaged heat transfer coefficient of oil and glycerine base-cooled MCHS shows a similar trend as for EG base-cooled MCHS. However, the condition becomes different for low Prandtl number base

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 321

The variation of dimensionless pressure of the MCHS for various base fluids along the length of channel number 20 is presented in Fig.6.6. It can obviously be seen that the high pressure region occurs at the entrance and the low pressure region occurs at the outlet of MCHS. This is due to the needs of high pressure to push the fluid flow along the direction of the microchannels out from the outlet plenum of heat sink. Thus, the pressure decreases

The higher ܲ for nanofluid-cooled MCHS is found in high Prandtl number base fluids due to the highest dynamic viscosity as stated in Table 6.2 as reported by Koo and Kleinstreuer [10]. The water base-cooled MCHS has the lowest value of pressure drop due to its lowest dynamic viscosity among other base fluids. There is no apparent difference in ܲ between EG, oil and glycerin as can be seen in Fig.6.6 although glycerin has the highest value of ܲ followed by oil and EG, respectively. Since the dynamic viscosity of EG, oil and glycerin base fluids is larger than water, larger pressure drop is expected in the high Prandtl number base fluids than the low Prandtl number base fluids. Thus, selection of high Prandtl number base fluids as coolant in MCHS should be considered in balancing heat transfer

Fig. 6.6. Dimensionless pressure drop variation along the length of channel No.20.

conclusions can be drawn from all the simulation results.

For the effects of MCHS geometrical parameters:

**0.00**

**0.20**

**^ P** **0.40**

The cooling efficiency of MCHS is numerically investigated using the FVM in this study. A three-dimensional model, fully developed laminar flow and heat transfer governing equations are solved using the finite volume method. Based on these effects, several

**0 10 20 30 40 Z**

**Water-diamond Ethylene glycol-diamond**

**Oil-diamond Glycerin-diamond**

linearly along the length of channel for all types of base fluids studied.

**6.3 Pressure drop** 

**7. Conclusions** 

enhancement and pressure drop penalty.

**0.60**

fluid (water) where the highest ℎ� is present in steel made microchannels as depicted in Fig.6.5. This proves that the thermal diffusivity of substrate material on the heat transfer in micro domains has significant effect for low and high Prandtl number base fluids. Thus, based on the results presented in Fig.6.5, it can be stated that the heat transfer performance of a low Prandtl number base fluid such as water can be greatly enhanced by using it as a coolant in MCHS of a high thermal diffusivity made substrate material such as steel.

Fig. 6.4. Dimensionless averaged heat transfer coefficient versus number of channels for ethylene glycol-base nanofluid with different substrate materials.

Fig. 6.5. Dimensionless averaged heat transfer coefficient versus number of channels for water-base nanofluid with different substrate materials.

#### **6.3 Pressure drop**

320 Fluid Dynamics, Computational Modeling and Applications

fluid (water) where the highest ℎ� is present in steel made microchannels as depicted in Fig.6.5. This proves that the thermal diffusivity of substrate material on the heat transfer in micro domains has significant effect for low and high Prandtl number base fluids. Thus, based on the results presented in Fig.6.5, it can be stated that the heat transfer performance of a low Prandtl number base fluid such as water can be greatly enhanced by using it as a

coolant in MCHS of a high thermal diffusivity made substrate material such as steel.

Fig. 6.4. Dimensionless averaged heat transfer coefficient versus number of channels for

Fig. 6.5. Dimensionless averaged heat transfer coefficient versus number of channels for

water-base nanofluid with different substrate materials.

ethylene glycol-base nanofluid with different substrate materials.

The variation of dimensionless pressure of the MCHS for various base fluids along the length of channel number 20 is presented in Fig.6.6. It can obviously be seen that the high pressure region occurs at the entrance and the low pressure region occurs at the outlet of MCHS. This is due to the needs of high pressure to push the fluid flow along the direction of the microchannels out from the outlet plenum of heat sink. Thus, the pressure decreases linearly along the length of channel for all types of base fluids studied.

The higher ܲ for nanofluid-cooled MCHS is found in high Prandtl number base fluids due to the highest dynamic viscosity as stated in Table 6.2 as reported by Koo and Kleinstreuer [10]. The water base-cooled MCHS has the lowest value of pressure drop due to its lowest dynamic viscosity among other base fluids. There is no apparent difference in ܲ between EG, oil and glycerin as can be seen in Fig.6.6 although glycerin has the highest value of ܲ followed by oil and EG, respectively. Since the dynamic viscosity of EG, oil and glycerin base fluids is larger than water, larger pressure drop is expected in the high Prandtl number base fluids than the low Prandtl number base fluids. Thus, selection of high Prandtl number base fluids as coolant in MCHS should be considered in balancing heat transfer enhancement and pressure drop penalty.

Fig. 6.6. Dimensionless pressure drop variation along the length of channel No.20.

#### **7. Conclusions**

The cooling efficiency of MCHS is numerically investigated using the FVM in this study. A three-dimensional model, fully developed laminar flow and heat transfer governing equations are solved using the finite volume method. Based on these effects, several conclusions can be drawn from all the simulation results.

For the effects of MCHS geometrical parameters:

Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 323

Cu copper CuO copper oxide

DM diamond EG Ethylene Glycol f friction factor fRe Poiseuille number FV Finite Volume

MCHS, µm

H2O water

Dh hydraulic diameter, µm

FVM Finite Volume Method

h heat transfer coefficient, W/m2.K

κ thermal conductivity, W/m.K κ� solid thermal conductivity, W/m.K

Lch channel length, µm MCHS Microchannel Heat Sink n direction normal to the wall

Nu Nusselt number

Pow pumping power, W Q volume flow rate, m3/s

Re Reynolds number Rth thermal resistance, K/W

SiO2 silicon dioxide

TiO2 titanium dioxide

u fluid velocity, m/s uin inlet fluid velocity, m/s

Ti titanium

t substrate thickness, µm T fluid phase temperature, K

Tin fluid inlet temperature, K

P channel wet perimeter, µm P� dimensionless pressure Pin inlet pressure, Pa Pout outlet pressure, Pa Pr Prandtl number PW pure water

h� dimensionless heat transfer coefficient

**n** direction normal to the surface element

*h* channel height for trapezoidal and triangular cross-section

Hch channel height for rectangular cross-section MCHS, µm

k channel width for triangular cross-section MCHS, µm

qw heat flux at microchannel heat sink top plate, W/m2

S distance between two microchannels, µm

Ts microchannel heat sink solid temperature, K

U dimensionless velocity in x-coordinate V dimensionless velocity in y-coordinate

*l* channel hypotenuse for triangular cross-section MCHS, µm


For nanofluids in MCHS:


#### **8. Nomenclature**


 The width to height ratio (*Wc/Hc*) has a significant effect on the Poiseuille number for the rectangular cross-section microchannels. Poiseuille number increases linearly with

 For the trapezoidal cross-section MCHS, the height-to-top width ratio (*H/a*), the bottomto-top width ratio (*b/a*), and length-to-hydraulic diameter ratio (*L/Dh*) are the important design parameters for trapezoidal microchannels. Poiseuille number increases linearly

 The tip angle (*β*) has a remarkable effect on the Poiseuille number for the triangular cross-section MCHS. Poiseuille number increases linearly with the increase of *β*. In order to achieve overall heat transfer enhancement in MCHS, it is envision that rectangular cross-section MCHS with a small hydraulic diameter was of greater benefit to the heat transfer coefficient with a lower penalty in pressure drop and friction factor

 The cooling performance of MCHS improved well when the particle volume fraction increases. However, the heat transfer becomes poor in larger amount of particle volume fraction of nanofluid flow as the heat transfer could not be enhanced compared with

The presence of nanoparticles substantially increases the friction factor and wall shear

 The nanofluid-cooled MCHS has lower thermal resistance than pure water-cooled MCHS. The thermal resistance decreases as the particle volume fraction increases. Diamond nanoparticles dispersed in water is preferable since diamond-H2O-cooled

Ag nanoparticles dispersed in water is recommended as it has lowest pressure drop and

 In order to achieve overall heat transfer enhancement, a base fluid of high Prandtl number (210-12800) such as glycerin, oil, and ethylene should be used to maximize the

 Different types of base fluids do not have a significant influence on the friction factor. The heat transfer for low Prandtl number fluid flow such as water is greatly enhanced in high thermal diffusivity made material such as steel compared with low thermal diffusivity materials. These findings suggest that for low Prandtl number base fluids, the substrate material of high thermal diffusivity is desirable and vice versa in order to

the increase of *Wc/Hc*.

For nanofluids in MCHS:

pure water.

**8. Nomenclature** 

Ag silver Al aluminum Al2O3 aluminum oxide

when *H/a* and *L/Dh* decreases while b/a increases.

compared with trapezoidal and triangular cross section MCHS.

stress. Both are rises with the increase of particle volume fractions.

MCHS has highest heat transfer coefficient value among the others.

a channel top width for trapezoidal cross-section MCHS, µm

b channel bottom width for trapezoidal cross-section MCHS, µm c channel hypotenuse for trapezoidal cross-section MCHS, µm

wall shear stress among the other nanofluids studied.

merits of adding nanoparticles for fluid flow in MCHS.

achieve a better heat transfer in MCHS.

A channel flow area, m2

cp specific heat, J/kg.K


Heat Transfer Enhancement in Microchannel Heat Sink Using Nanofluids 325

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#### **Greek Symbols**


#### **Subscripts**


#### **9. Acknowledgements**

The authors would like to sincerely thank the Ministry of Higher Education (MOHE) of Malaysia for the provision of a grant with code no FRGS01090010 to support this work. In addition, the supports and helps provided by all members of the Centre for Advanced Computational Engineering (CACE) at Department of Mechanical Engineering, UNITEN to carry out the research in this paper are deeply appreciated.

## **10. References**


The authors would like to sincerely thank the Ministry of Higher Education (MOHE) of Malaysia for the provision of a grant with code no FRGS01090010 to support this work. In addition, the supports and helps provided by all members of the Centre for Advanced Computational Engineering (CACE) at Department of Mechanical Engineering, UNITEN to

[1] D.B. Tuckerman, R.F.W Pease, "*High Performance Heat Sinking for VLSI*", IEEE Elect. Dev.

[2] P.R. Parida, "*Experimental Investigation of Heat Transfer Rate in Micro-Channels*'', Master

[3] I. Mudawar, "*Assessment of High Heat Flux Thermal Management Schemes*", IEEE Trans.

[4] S.G. Kandlikar, M.E. Steinke, "*Examples of Microchannel Mass Transfer Processes in* 

*Biological Systems"*, in Proc. 1st Int. Conf. Minichannels and Microchannels, ASME,

Thesis, Indian Institute of Technology Guwahati, India, 2007.

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W dimensionless velocity in z-coordinate

*β* tip angle for triangular cross-section MCHS

carry out the research in this paper are deeply appreciated.

Lett., vol. 2, 1981, pp 126-129.

vol. 11, April 24-25, 2003, pp 933-943.

X, Y, Z dimensionless cartesian coordinates

*α* thermal diffusivity, m2/s

�̂ dimensionless wall shear stress *φ* particle volume fraction, % *θ* dimensionless temperature

� viscosity, kg/m.s � density, kg/m3 *τ* wall shear stress

**Greek Symbols** 

**Subscripts** 

*avg* average *bf* base fluid *ch* channel *f* pure fluid *nf* nanofluid *h* hydraulic *i* inlet *o* outlet *s* solid *th* thermal *w* wall

**9. Acknowledgements** 

**10. References** 

Wch channel width for rectangular cross-section MCHS, µm


**14** 

*Poland* 

Stanisław Łopata and Paweł Ocłoń *Cracow University of Technology, Cracow* 

**Modelling and Optimizing Operating Conditions** 

**of Heat Exchanger with Finned Elliptical Tubes** 

High performance heat exchangers are widely used in many industries such as petrochemical industry, automotive industry, energetic industry and many others. The name of this kind of heat exchangers is in consistency with their structure. Large heat transfer area leads to high thermal efficiency of the device. Its working principle is to cool rapidly large amount of gaseous or liquid medium. Because of its compact size, it is possible to use it for easy installation in various systems, like the heating, drying, air

High thermal performance of this type of heat exchangers (Nagatha, 2004; Ibrahim & Gomaa, 2009) is achieved due to large packed rectangular fins on tube surface, as well as the shape of the tubes. The elliptical shape ensures better distribution of velocity along the tube circumference during the flow, as well as lower pressure drop in comparison to the circular shape (Matos et al, 2004; Jang & Yang, 1998; Li et al, 2006; Nishiyama et al, 1988; Khan et al, 2004; Saboya & Saboya, 1981; Saboya & Sparrow, 1974; Bordallo & Saboya, 1999). Consequently, the coefficient of heat transfer in the elliptical shape is larger when compared to the circular shape (Idem et al, 1990; Rocha et al, 1997; Taler, 2009). It brings about that the

To use all the aforementioned advantages, it is necessary to ensure uniform distribution of velocity in all the tubes. Failing that, it leads to large differences in mean temperature in the tubes. Consequently, excessive thermal stress occurs, that may cause the heat exchanger to break down. Small volume of collectors of the heat exchangers implicates possibility of improper flow condition inside the tubes, causing unsuitable inner distribution of thermal and mechanical loads. Damages to a tube, Fig. 1, as well as a tube bundle prone to buckling, Fig. 2, prove, that such a failure is possible (Łopata & Ocłon,

Compressible stresses are undesirable (Łopata & Ocłon, 2010; Łopata & Ocłon, 2011) in this type of construction, because the allowable compressible load (allowable buckling stress) for

The simplified method to assess failure of a high performance heat exchanger with finned elliptical tubes is presented in the paper. The diagram, shown on Fig. 3, presents the method. The geometrical representation of construction – a CAD model is prepared at first. Next, on the basis of prepared geometry, numerical representation of the model is created. Afterwards, the flow computation - CFD (Ferziger & Peric 1999; Anderson, 1995; Gresho &

heat exchange process is more efficient in elliptical than in circular tubes.

a slender tube is significantly lower than the safe tensile load.

**1. Introduction** 

conditioning and the other systems.

2010; Ocłon & Łopata, 2011).

