**2. Experimental method**

#### **2.1 Experimental setup**

Three major parts are used in the experimental system: the test section (the microchannel heat exchangers), syringe system, and overall testing loop, as shown in Fig. 2, with four microchannel heat exchangers being tested. The heat transfer process of these devices is carried out between two liquids which are hot water and cold water; the hot and cold fluids are flowing in the opposite directions.

Fig. 3 shows the dimensions of the test sections. The material used for the substrate of heat exchangers is aluminum, with thermal conductivity of 237 W/(mK), density of 2,700 kg/m3, and specific heat at constant pressure of 904 J/(kgK). For each microchannel heat exchanger, the top side for the hot water has 10 microchannels and the bottom side for the cold water also has 10 microchannels. The length of each microchannel is 32 mm. Microchannels have rectangular cross-section with the width and the depth being Wc and Dc, respectively.

Dang and Teng [28, 29] studied the effects of the configuration (such as substrate thickness, cross-sectional area, and inlet/outlet location) on the behaviors of heat transfer and fluid flow of the microchannel heat exchangers. It was found that the actual heat transfer rate was observed to vary insignificantly with the substrate thickness in the range from 1.2 to 2 mm. Moreover, a comparison of the pressure drop and heat transfer behaviors between the microchannel and minichannel heat exchangers was done by Dang et al. [30]. Furthermore, numerical simulations of the microchannel heat exchangers using solver with the capability of dealing with steady-state and time-dependent conditions were carried out [31]. Numerical studies of the behaviors of the microchannel heat exchangers with 3D singlephase fluid flow and heat transfer in [22-26, 28-31] were done by using the COMSOL Multiphysics software, version 3.5. The algorithm of this software was based on the finite element method. The results obtained from the simulation were in good agreement with those obtained from the experiments, with the maximum percentage error being less than

To summarize, Table 1 listed the heat transfer and fluid flow behaviors for single phase microchannel heat exchangers [3, 4]. The heat exchangers were manufactured by different materials with a variety of shapes. Water was the most frequently used working fluid. The heat transfer coefficient and pressure drop were observed to be functions of the mass flow rate. The staggered microcolumn array and the micro-structured surface were found to enhance heat transfer rate in the micro heat exchangers. Because that the substrate thickness (between the hot and the cold channels) of micro heat exchangers was very thin, so the differences between the heat transfer rates obtained from these heat exchangers were

From the above literatures, it is important to better understand the behaviors of heat transfer and pressure drop of the fluid through the microchannel heat exchangers in order to improve their design and optimize their performance. For the present study, single phase heat transfer and uid ow phenomena obtained from experiments and numerical simulations for rectangular-shaped microchannel heat exchangers were investigated. In the following sections, five heat exchangers with different geometrical congurations will be

Three major parts are used in the experimental system: the test section (the microchannel heat exchangers), syringe system, and overall testing loop, as shown in Fig. 2, with four microchannel heat exchangers being tested. The heat transfer process of these devices is carried out between two liquids which are hot water and cold water; the hot and cold fluids

Fig. 3 shows the dimensions of the test sections. The material used for the substrate of heat exchangers is aluminum, with thermal conductivity of 237 W/(mK), density of 2,700 kg/m3, and specific heat at constant pressure of 904 J/(kgK). For each microchannel heat exchanger, the top side for the hot water has 10 microchannels and the bottom side for the cold water also has 10 microchannels. The length of each microchannel is 32 mm. Microchannels have rectangular cross-section with the width and the depth being Wc and Dc, respectively.

negligibly small for several materials used in the studies.

9%.

discussed.

**2. Experimental method 2.1 Experimental setup** 

are flowing in the opposite directions.

Fig. 2. Schematic of the test loop for the heat exchangers [3, 22-31].

In a microchannel heat exchanger, all channels are connected by manifolds for the inlet and outlet of hot water and for those of cold water, respectively. The manifolds of the heat exchangers are of the same cross-sections: having a rectangular shape with a width of 3 mm and a depth of 300 m. Figs. 3a and 3b show the dimensions of the S-types and I-type, respectively, with three S-types and one I-type being designed and manufactured and their dimensions listed in Table 2. Fig. 4 shows the photos of the microchannel heat exchangers with S-type and I-type manifolds. These test sections were manufactured by precision micromachining [20]. Each inlet hole or outlet hole of the heat exchangers has a crosssectional area of 9 mm2. The four sides of the heat exchanger were thermally insulated by the glass wool with a thickness of 5 mm. To seal the microchannels, two layers of PMMA (polymethyl methacrylate) were bonded on the top and bottom sides of the substrate by UV (ultraviolet) light process, as shown in Fig. 4. The physical properties of the PMMA and the glass wool are listed in Table 3 [32].


Table 2. Geometric parameters of the microchannel heat exchangers [3, 25].

Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 257

Glass wool PMMA

a) S-typeb) I-type

Experimental data for the microchannel heat exchanger were obtained under the constant room temperature of 25 – 26 ºC. DI water (deionized water) was used as the working fluid. Each inlet or outlet of the heat exchanger has a set of two thermocouples to record the temperature values, and there are eight thermocouples in total. At each side, a differential pressure transducer was used to measure the pressure drop. To assess the accuracy of measurements presented in this work, the uncertainty values for measured parameters are listed in Table 4. In addition, the uncertainties on the dimensions of microchannel evaluated by using a scanning laser made by Mitaka/Ryokosha model NH-3. The uncertainties of the scanning laser were estimated to be ± 0.03 µm. Equipments used for the experiments are

> **Parameter Uncertainty**  Temperature 0.1 C Pressure 0.025% FS Mass flow rate 0.0015 g Channel height 7 m Channel width 10 m Channel length 70 m

**Material Density kg/m3 Thermal conductivity W/(mK)** 

PMMA 1420 0.19 Glass wool 154 0.051

Fig. 4. Photos of the microchannel heat exchangers being tests.

Table 3. Physical properties of the PMMA and the glass wool [32].

5. Differential pressure transducer, Model PMP4110, made by Duck 6. Micro electronic balance, Model TE-214S, made by Sartorious.

listed as follows [3, 22-31]: 1. Thermocouples, T-type

2. Pump, Model PU-2087, made by Jasco 3. Pump, VSP-1200, made by Tokyo Rikakikai 4. Heater, Model AXW-8, made by Medilab

Table 4. Uncertainty data for measured parameters.

b) I-type

Fig. 3. Dimensions of the test samples.

Fig. 4. Photos of the microchannel heat exchangers being tests.


Table 3. Physical properties of the PMMA and the glass wool [32].

Experimental data for the microchannel heat exchanger were obtained under the constant room temperature of 25 – 26 ºC. DI water (deionized water) was used as the working fluid. Each inlet or outlet of the heat exchanger has a set of two thermocouples to record the temperature values, and there are eight thermocouples in total. At each side, a differential pressure transducer was used to measure the pressure drop. To assess the accuracy of measurements presented in this work, the uncertainty values for measured parameters are listed in Table 4. In addition, the uncertainties on the dimensions of microchannel evaluated by using a scanning laser made by Mitaka/Ryokosha model NH-3. The uncertainties of the scanning laser were estimated to be ± 0.03 µm. Equipments used for the experiments are listed as follows [3, 22-31]:

1. Thermocouples, T-type

256 Heat Exchangers – Basics Design Applications

a) S-type

Manifold

Channel

b) I-type

Fig. 3. Dimensions of the test samples.



Table 4. Uncertainty data for measured parameters.

Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 259

and outlet temperatures of the hot and cold side, respectively, *q* is heat flux, *A* is heat

resistance, *R hh conv h c* 1/ 1/ is convective thermal resistance, *hh* and *hc* are the convective

is thermal conductivity, and *Tlm* is the log mean temperature difference.

*wD m*

 

<sup>2</sup> Re *<sup>h</sup>*

2 <sup>2</sup> 2 2 Re *h h*

 

where *D AP h c* 4 / is the hydraulic diameter, *w* is velocity in the z-direction,

where *<sup>h</sup> p* and *<sup>c</sup> p* are pressure drops of hot and cold sides, respectively.

[35]; the final expressions for uncertainties were given as follows:

, is determined by [19, 25]

*Q*

*L L p f <sup>w</sup> <sup>f</sup> <sup>w</sup> <sup>D</sup> <sup>D</sup>*

*W D*

is density, *Ac* is cross-sectional area, *P* is wetted perimeter, *L* is channel length,

*<sup>c</sup>* m c (T -T ) c c c,o c,i *t hc*

1/2 2 2 <sup>2</sup> 2 2 , , , , *q c c co ci c c c c co ci c c*

1/2 2 2 <sup>2</sup> 2 2

1/2 <sup>2</sup> 2 2 2 2

*c c c c*

*p pp*

The experimental uncertainties were estimated, following the method described by Holman

, , , , 2 22 2 ,, ,, ,, ,,

*m W D*

 

 

*m c T T W L*

*c c co ci c c*

*U m c T T W L q m c TT W L* 

*c c co ci c c k hi ho ci co hi ho ci co*

*U m W D*

*U m c TT W L*

*<sup>k</sup> TT TT TT TT*

*c c*

*thc ppp* (10)

(11)

 /

is conductive thermal

is thickness of heat

(8)

(9)

is dynamic

(12)

(13)

(14)

transfer area, *k* is overall heat transfer coefficient, *Rcond*

The pressure drop due to friction is determined by [33,34] :

The total pressure drop of the heat exchanger is given by

Re Re

transfer,

viscosity,

The performance index,

and *f* is Fanning friction factor.

The Reynolds number is calculated by:

heat transfer coefficients of the hot side and the cold side, respectively,

#### **2.2 Analysis of data**

In the following analyses, five assumptions were made:


For the experiments carried out in this study, the effects of various parameters on the heat transfer and fluid flow – such as heat flux, effectiveness, pressure drop, and performance index – of the heat exchangers are discussed as follows.

The maximum heat transfer rate, *Qmax*, is evaluated by

$$Q\_{\text{max}} = \left(mc\right)\_{\text{min}} \left(T\_{h,i} - T\_{c,i}\right) \tag{1}$$

The heat transfer rate of the heat exchanger, *Q*, is calculated by

$$Q\_c = m\_c c\_c \left( T\_{c,o} - T\_{c,i} \right) \tag{2}$$

The effectiveness (NTU method) is determined by

$$\mathcal{L} = \frac{Q\_c}{Q\_{\text{max}}} \tag{3}$$

Heat flux is calculated by

$$q = \frac{Q\_c}{A} = \frac{\text{m}\_c \text{c}\_c \text{ (T}\_{c,o} \text{-T}\_{c,l})}{\text{nL}\_c \text{W}\_c} \tag{4}$$

or

$$q = k \, \Delta T\_{lm} = \frac{\Delta T\_{lm}}{\Sigma R} \tag{5}$$

The overall thermal resistance *R* is determined by

$$
\sum \mathcal{R} = \mathcal{R}\_{cond} + \mathcal{R}\_{conv} \tag{6}
$$

The log mean temperature difference is calculated by

$$
\Delta T\_{lm} = \frac{\Delta T\_{\text{max}} - \Delta T\_{\text{min}}}{\ln \frac{\Delta T\_{\text{max}}}{\Delta T\_{\text{min}}}} \tag{7}
$$

where *m* is mass flow rate (subscripts *h* and *c* stand for the hot side and cold side, respectively), n is number of microchannels, *c* is specific heat, *Th,i*, *Th,o, Tc,i* and *Tc,o* are inlet and outlet temperatures of the hot and cold side, respectively, *q* is heat flux, *A* is heat transfer area, *k* is overall heat transfer coefficient, *Rcond* / is conductive thermal resistance, *R hh conv h c* 1/ 1/ is convective thermal resistance, *hh* and *hc* are the convective heat transfer coefficients of the hot side and the cold side, respectively, is thickness of heat transfer, is thermal conductivity, and *Tlm* is the log mean temperature difference.

The Reynolds number is calculated by:

258 Heat Exchangers – Basics Design Applications


For the experiments carried out in this study, the effects of various parameters on the heat transfer and fluid flow – such as heat flux, effectiveness, pressure drop, and performance

> max *Qc Q*

*c*

*R* is determined by

*lm*

c c c,o c,i c m c (T -T ) nL

*c*

*R* 

max min max min

*T*

ln

where *m* is mass flow rate (subscripts *h* and *c* stand for the hot side and cold side, respectively), n is number of microchannels, *c* is specific heat, *Th,i*, *Th,o, Tc,i* and *Tc,o* are inlet

*T T <sup>T</sup> <sup>T</sup>*

*Q mc T T* max min *hi ci* , , (1)

*Q mc T T c c c co ci* , , (2)

*<sup>Q</sup> <sup>q</sup> A W* (4)

*RR R cond conv* (6)

(3)

(5)

(7)

**2.2 Analysis of data** 




the same order.

Heat flux is calculated by

The overall thermal resistance

or

In the following analyses, five assumptions were made:


index – of the heat exchangers are discussed as follows. The maximum heat transfer rate, *Qmax*, is evaluated by

The effectiveness (NTU method) is determined by

*q = kTlm* <sup>=</sup>*Tlm*

The log mean temperature difference is calculated by

The heat transfer rate of the heat exchanger, *Q*, is calculated by

$$\text{Re} = \frac{\rho w D\_h}{\mu} = \frac{2m}{\mu \left(\mathcal{W}\_c + D\_c\right)}\tag{8}$$

The pressure drop due to friction is determined by [33,34] :

$$
\Delta p = 2f\rho w^2 \frac{L}{D\_h} = 2f \operatorname{Re} \frac{L}{D\_h^2} w\mu \tag{9}
$$

where *D AP h c* 4 / is the hydraulic diameter, *w* is velocity in the z-direction, is dynamic viscosity, is density, *Ac* is cross-sectional area, *P* is wetted perimeter, *L* is channel length, and *f* is Fanning friction factor.

The total pressure drop of the heat exchanger is given by

$$
\Delta p\_t = \Delta p\_h + \Delta p\_c \tag{10}
$$

where *<sup>h</sup> p* and *<sup>c</sup> p* are pressure drops of hot and cold sides, respectively.

The performance index, , is determined by [19, 25]

$$\mathbf{c}' \mathbf{s} = \frac{\mathbf{Q}\_{\mathbf{c}}}{\Delta p\_{\mathbf{t}}} = \frac{\mathbf{m}\_{\mathbf{c}} \mathbf{c}\_{\mathbf{c}} \text{ (T}\_{\mathbf{c},o} \text{ -T}\_{\mathbf{c},i} \text{)}}{\Delta p\_{\mathbf{t}} + \Delta p\_{\mathbf{c}}} \tag{11}$$

The experimental uncertainties were estimated, following the method described by Holman [35]; the final expressions for uncertainties were given as follows:

$$\frac{\mathbf{U}\_{q}}{q} = \left[ \left( \frac{\partial m\_{c}}{m\_{c}} \right)^{2} + \left( \frac{\partial c\_{c}}{c\_{c}} \right)^{2} + \left( \frac{\partial T\_{c,o} + \partial T\_{c,i}}{T\_{c,o} + T\_{c,i}} \right)^{2} + \left( \frac{\partial \mathcal{W}\_{c}}{\mathcal{W}\_{c}} \right)^{2} + \left( \frac{\partial L\_{c}}{L\_{c}} \right)^{2} \right]^{1/2} \tag{12}$$

$$\frac{\mathcal{U}I\_k}{k} = \begin{bmatrix} \left(\frac{\partial m\_c}{m\_c}\right)^2 + \left(\frac{\partial c\_c}{c\_c}\right)^2 + \left(\frac{\partial T\_{c,o} + \partial T\_{c,i}}{T\_{c,o} + T\_{c,i}}\right)^2 + \left(\frac{\partial \mathcal{W}\_c}{\mathcal{W}\_c}\right)^2 + \left(\frac{\partial L\_c}{L\_c}\right)^2 + \begin{bmatrix} \frac{\partial L\_c}{\partial s} \\ \frac{\partial L\_c}{\partial s} \end{bmatrix} + \begin{bmatrix} \frac{\partial L\_c}{\partial s} \end{bmatrix} + \begin{bmatrix} \frac{\partial L\_c}{\partial s} \\ \frac{\partial L\_c}{\partial s} \end{bmatrix} + \begin{bmatrix} \frac{\partial L\_c}{\partial s} \end{bmatrix} \tag{13}$$
 
$$\left[\left(\frac{\partial T\_{h,i}}{T\_{h,i}}\right)^2 + \left(\frac{\partial T\_{h,o}}{T\_{h,o}}\right)^2 + \left(\frac{\partial T\_{c,i}}{T\_{c,i}}\right)^2 + \left(\frac{\partial T\_{c,o}}{T\_{c,o}}\right)^2\right] \tag{14}$$

$$\frac{\partial L\_{\rm Re}}{\partial \mathbf{e}} = \left[ \left( \frac{\partial m}{m} \right)^2 + \left( \frac{\partial \rho}{\rho} \right)^2 + \left( \frac{\partial \mu}{\mu} \right)^2 + \left( \frac{\partial \mathcal{W}\_c}{\mathcal{W}\_c} \right)^2 + \left( \frac{\partial \mathcal{D}\_c}{\mathcal{D}\_c} \right)^2 \right]^{1/2} \tag{14}$$

Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 261

For the effects of fluid properties on heat transfer and fluid flow behaviors, the microchannel heat exchanger T1 was tested; the results were shown more in detail by Dang

For experiments carried out in the study, the inlet temperature and mass flow rate of the cold side were fixed at 26.5 ºC and 0.1773 g/s, respectively. For the hot side, an inlet temperature was fixed at 52 ºC and the mass flow rates were varying from 0.1841 to 0.3239 g/s. The thermal boundary conditions of the top and bottom walls of the heat exchanger were assumed to be constant heat flux. The convective heat transfer coefficient between the wall and the ambient used for this solver was 10 W/(m2K), with the ambient temperature and air velocity of 26 C and 0.2 m/s, respectively. The temperature profile of the microchannel heat exchanger is shown in Fig. 6 for a mass flow rate of 0.2556 g/s at the hot

At a constant inlet temperature of 52 ºC at the hot side, for the case with both mass flow rate and temperature constant at the inlet of cold side, a relationship between the outlet temperatures (for both the hot side and cold side) and the mass flow rate of the hot side is shown in Fig. 7a. The outlet temperatures increase as the mass flow rate of the hot side increases. Because that the heat exchanger under study is the one with counter-flow, the outlet temperature of the cold side is higher than that obtained at the hot side [22-24]. A comparison between the numerical and experimental results is also shown in Fig. 7a. Fig 7a shows the outlet temperatures as a function of the mass flow rate of the hot side, and the results obtained from the simulation are in good agreement with those obtained from the experiments. The maximum difference of the outlet temperatures is 0.8 C and the

et al. [26]. The parameters of heat exchangers are listed in Table 2. **Flow rate and inlet temperature being constant for the cold side** 

Fig. 6. The temperature profile of the microchannel heat exchanger.

**4. Results** 

side.

**4.1 Effects of fluid properties** 

maximum percentage error is 2%.

$$\frac{\partial L\_c}{\partial \mathbf{c}} = \left[ \left( \frac{\hat{\mathbf{c}} \mathbf{m}\_c}{\mathbf{m}\_c} \right)^2 + \left( \frac{\hat{\mathbf{c}} \mathbf{c}\_c}{\mathbf{c}\_c} \right)^2 + \left( \frac{\hat{\mathbf{c}} \mathbf{m}}{\mathbf{m}} \right)^2 + \left( \frac{\hat{\mathbf{c}} \mathbf{c}}{\mathbf{c}} \right)^2 + \left( \frac{\hat{\mathbf{c}} \mathbf{T}\_{c,o} + \hat{\sigma} \mathbf{T}\_{c,i}}{\mathbf{T}\_{c,o} + \mathbf{T}\_{c,i}} \right)^2 + \left( \frac{\hat{\sigma} \mathbf{T}\_{h,i} + \hat{\sigma} \mathbf{T}\_{c,i}}{\mathbf{T}\_{h,i} + \mathbf{T}\_{c,i}} \right)^2 \right]^{1/2} \tag{15}$$

$$\frac{\partial L\_{\xi}}{\xi} = \left[ \left( \frac{\partial m\_{c}}{m\_{c}} \right)^{2} + \left( \frac{\partial c\_{c}}{c\_{c}} \right)^{2} + \left( \frac{\partial T\_{c,o} + \partial T\_{c,i}}{T\_{c,o} + T\_{c,i}} \right)^{2} + \left( \frac{\partial \Delta p\_{h}}{\Delta p\_{h}} \right)^{2} + \left( \frac{\partial \Delta p\_{c}}{\Delta p\_{c}} \right)^{2} \right]^{1/2} \tag{16}$$

By using the estimated errors of parameters listed in Table 3, the maximum experimental uncertainties in determining q, k, Re, , and were 2.1%, 2.2%, 3.1%, 0.9%, and 3.3%, respectively, for all cases being studied.

## **3. Numerical simulation**

Numerical study of the behavior of the microchannel heat exchanger with 3D single-phase fluid flow and heat transfer was done by using the COMSOL Multiphysics software, version 3.5. The algorithm of this software was based on the finite element method. For the COMSOL package, the generalized minimal residual (GMRES) method was used to solve for the model used in this study; the GMRES method was an iterative method for general linear systems. At every step, the method performed minimization of the residual vector in a Krylov subspace [32], and the Arnoldi iteration was used to find this residual vector. To improve the convergence of the iterative solver used by the GMRES method, the Incomplete LU (lower-upper) pre-conditioner was selected for nonsymmetric systems, where LU is a matrix which was the product of a lower triangular matrix and an upper triangular matrix. For the study, water was used as the working fluid. With the mass flow rate of water from 0.1667 to 0.8540 g/s, the Reynolds number was lower than 400 and the working fluid in the microchannels of the heat exchanger was under laminar flow condition [2]. No internal heat generation was specified, resulting in *Qi* = 0. The finite elements in the grid meshes were partitioned to be triangular, as shown in Fig. 5. The maximum element size scaling factor was 1.9, with element growth rate of 1.7, mesh curvature factor of 0.8, and mesh curvature cut-off of 0.05. In Fig. 4, the schematic meshing of the heat exchanger consists of 26,151 mesh elements, the number of degrees of freedom is 76,411, and a relative tolerance is 10-6.

Fig. 5. Grid mesh diagram of the microchannel heat exchanger.
