**1. Introduction**

In present scenario demand of high processing speed from processors and compact size of electronic devices increases the problem of high heat generation because high processing speed of processors increases the power consumption and compactness of electronic devices increases the required number of transistors per chips which ultimately increases the electrical power input. It can be clearly understood from the Moore's law **Figure 1** [1] that how vastly the number of transistors per chip increased after the application of modern compact processors. **Table 1** [2] Clearly indicates that with the development of advanced processors (Intel) having higher processing speed the thermal design power consumption (TDP) of processors increases resulting in higher heat generation. Heat fluxes (heat generated per unit surface area) have

#### **Figure 1.**

*Increase in number of transistors per chip with the development of processors over the year [1].*


#### **Table 1.**

*Thermal design power (TDP) with processing speed of processors [2].*

#### *Application of Semi-Circular Micro-Channel Heat Sink with Phase Change Material… DOI: http://dx.doi.org/10.5772/intechopen.105901*

approached 100 W/cm<sup>2</sup> for advanced microprocessors while the heat fluxes dissipation limited to 37 W/cm<sup>2</sup> for air cooling [3], which ultimately increases the working temperature beyond the safe limit resulting in in-efficient performance and shorter life of the devices. The working temperature of electronic devices should be within 85° C-120°C to ensure the efficient performance of devices [4]. Hence an effective cooling method is needed for dissipating the excess heat flux generated. In this regard Microchannel heat sink has emerged as a latest cooling method for controlling excess heat generated from a compact electronic device. Micro-channel heat sink provides high surface area to volume ratio for a given compact electronic device.

Usually Micro-channel heat sink is constructed from higher thermal conductivity materials such as copper, aluminum, brass etc. consisting channels of micron size (10 to 1000 μm) which acted as a passage of cooling fluid [5]. Only standard cooling technology would not be enough when electronic devices are continuously operated over longer periods due to space limitations and some limitations of thermal conductivity of cooling fluid and materials of heat sink the heat load generated cannot be properly dissipated. Phase change materials (PCM) can be utilized to take up excess heat and dissipate it from the electronic device ultimately improving the performance of an electronic device. PCM generally absorbs heat between the liquid and solid state. So micro-channel heat sink with PCM would be suitable to meet these requirements of heat flux dissipation also when PCM is applied in micro-channel heat sink thermal performance of micro-channel heat sink will enhance. Some literatures are available on the application of PCM in micro-channel heat sink for dissipating heat fluxes from electronic devices. Debich et al. [4] numerically investigated the heat sink based on PCM to find best configuration of heat sink. Analysis is established on the comparison of experimental results of heat sink with and without PCM. Effects of various parameters like geometry, boundary conditions, and materials have been considered for the numerical investigation. Results revealed that heat sink with n- Eicosane have better heat transfer compared with other PCMs based heat sink. Latent heating phase delayed due to increase in the volume fraction of PCM also when input power increases then melting rate of PCM increases ultimately increasing the thermal performance of heat sink. Hasan and Tabena [6] numerically explored the application of PCM in micro-channel heat sink utilizing air as a coolant. Four PCM (paraffin wax, neicosane, p116 and RT41) have been utilized as cooling mediums after using air as cooling fluid in different configurations of micro-channel heat sink at different ambient temperatures. Uniform heat flux is applied at the bottom of heat sink and mixed convection with radiation boundary is applied at the top surfaces. Results show that application of PCM in micro-channel heat sink with different configurations enhances the performance of micro-channel heat sink. The result also indicate that different PCMs cause unusual reduction in micro-channel heat sink surface temperature in the range of ambient temperature because of difference in melting point of different PCMs. Deng et al. [7] analytically investigated thermal performance of a microchannel heat sink using microencapsulated PCM slurry for chip cooling. For analytical investigation of micro-channel heat sink fin and porous media methods have been used under constant heat flux condition. Significant differences in overall Nusselt number (Nu) and fluid temperature distribution have been predicted from the fin and porous media methods. Xu et al. [8] experimentally examined the heat transfer performance of a noble micro-channel heat sink consisted of a cavity with pyramid pin fins and a PCM cavity with square pin fins. Carbon nanotube (CNT) is added to paraffin to increase the thermal conductivity. The thermal performance of heat sink has been improved by using Graphene oxide particles (GOPs) nanofluids pulsating

flow. Their results demonstrated that performance of heat sink improved significantly by utilizing PCM composite and GOPs nanofluids. The thermal resistance reduces significantly and the Nu surged up to 34.9% when the proportion of CNT was approximately 20%. The heat transfer performance has maximum increment under pulsating flow. The increased effect of exciting flow and PCM composite are also exaggerated by heating load and pump power. The higher heating load gives augmentation effect while pump power gives the decrement effect. Chang et al. [9] explored the performance of a modified heat sink with cavity on top portion of the heat sink for the purpose of storing composite PCM. The cavity was crammed with PCM composite having CNTs of concentration (9% and 15%). Their outcomes revealed that the thermal conductivities of composite PCM's were increased by 291.6% and 537.5% for the mass fraction 9% and 15% of graphite particles. It has been also found that the application of composite PCM decreases the system's maximum temperature significantly compared to pure paraffin. Karaipekli et al. [10] investigated the heat transfer performance of expanded CNTs composite/perlite/paraffine PCM. Results showed that the thermal conductivity increases by 26, 60 and 113.3% respectively for the mass fraction of CNTs 0.3%, 0.5%, and 1%. Rostamian et al. [11] experimentally examined the performance of electronic board heat sink utilizing pure and microencapsulated PCMs. Different geometries of heat sink like Square with three fins and seven fins, circular with 12 fins have been used for investigation over a range of electrical power 5 to 18 W in two cases preset and pulsed power based on the board critical temperature of 80°C. Experimental findings indicated that square seven fins heat sink to be the best among all configurations. Operating time increases when volume fraction of PX52 increases and it has been found that the critical temperature for PX52 was less than the critical temperature for pure PCM under the same conditions because of higher rate of heat transfer. Siyabi et al. [12] experimentally studied the consequences of PCM combination, adjustment of PCMs in multiple heat sink, PCM thickness, melting point and magnitude of heat source on conduct of three different heat sink. It has been found that (i) PCM combination RT50–RT55 enhances the temperature regulation period and also decreases the temperature of at the end point of the operation, (ii) the arrangement of RT58–RT47 decreases slightly the peak temperature compared to RT47–RT58 arrangement (iii) when thickness of PCM increased from 30 mm to 60 mm, the temperature regulation period increased by 50 min, (iv) when the melting point of PCM increases then the temperature regulation period and the heat sink temperature increases and (v) As the power rating increases from 1 to 2 W the temperature regulation period decreases. Kothari et al. [13] experimentally studied the competent thermal management system based on PCM to cool portable electronic devices. Paraffin wax was used as PCM for four different configurations of heat sink made of aluminum (unfinned heat sink with pure PCM, two finned heat sink with pure PCM, unfinned heat sink with MF-PCM composite and two finned heat sink with MF-PCM composite) in the present study to boost the operating time of heat sink to attain a critical set point temperature. Results showed that higher enhancement ratio and effective thermal control obtained with two finned heat sink with MF-PCM as compared to other configurations of heat sink. Thomas et al. [14] numerically investigate the heat transfer performance of a transferable electronic device by application of PCM in heat sink. n-eicosane with a melting point of 36.5°C has been used as PCM. Results indicated that for the increase in ambient temperature and decrease in latent heat PCM was melting as noted by increase in the power consumption. Gaikwad and More [15] experimentally investigated the potential of application of PCM slurry flowing through rectangular micro-channel heat sink for cooling of computer

#### *Application of Semi-Circular Micro-Channel Heat Sink with Phase Change Material… DOI: http://dx.doi.org/10.5772/intechopen.105901*

processor. Comparative analysis has been done for two working fluids water and PCM slurry with two different aspect ratios of 2 and 3 at flow rates ranging from 75 ml/min to 300 ml/min. The results show that cooling systems using PCM are advantageous not only over the conventional air cooling system but also on the water cooling system. Experimental results showed that lower maximum temperature of processor can be achieved at the same mass flow rate and pumping power by using PCM slurry over the water. Hence micro-channel heat sink with PCM slurries found to be more effective fluid in comparison to water as a cooling fluid. Kondle et al. [16] numerically investigated the thermal performance of PCM fluid for laminar flow conditions in rectangular and circular microchannel. Investigation has been performed under different aspect ratios and boundary conditions. Results showed that Nusselt number (Nu) increases when PCM slurry has been used as cooling fluid as compared to only water as cooling fluid for all aspect ratios. Kuravi et al. [17] numerically studied the performance of nano-encapsulated PCM slurry in manifold microchannel heat sink. Effect of different parameters has been considered for the study such as inlet temperature of fluid, concentration of PCM, and heat flux. Results showed that Nu increased for PCM slurry and bulk mean temperature of fluid reduces for PCM slurry as compared to pure single phase fluid. After studying above literatures it can be clearly concluded that thermal performance of a micro-channel heat sink can be enhanced by using PCM as slurry to flow in micro-channels or to adhere PCM in the heat sink. From the literatures it has been inferred that application of PCMs in a semi-circular micro-channel heat sink is yet to be studied. In this paper application of PCM as slurry has been studied using water as a base fluid in a micro-channel heat sink consisting of micro-channels with semi-circular shape at the end i.e. semi-circular micro-channels. Semi-circular micro-channels have been used because semi-circular shape of microchannels can be easily created by wire EDM machining also this wire EDM is most economical among other methods of machining.

### **2. Selection of PCM for the study**

PCM is a substance which has high latent heat of fusion i.e. melting and solidified at a certain temperature. It has ability to store and release large quantities of heat. PCM continues to absorb heat till all the materials are melted without significant rise in temperature. Hence PCM has been selected based on its melting temperature and accordingly maximum temperature rise of the heat sink. PCM can be classified as Organic, Inorganic and biomaterial etc. The cost of PCM increases with it's purity. Pure paraffin wax is more costly than technical grade paraffin. The cost of PCM is not the criteria for the selection of PCM in this study as the volume of the micro-channel heat sink is very low so very less amount of PCM will be required. In the present study PCM slurry of RT41 with water as base fluid has been used to flow through the semi-circular micro-channels.

#### **3. Methodology**

The model of micro-channel heat sink considered for analytical study is square cross-section of dimension 25 mm 25 mm. The micro-channel heat sink consists of semi-circular micro-channels of 350 μm (0.35 mm) diameter with 0.20 mm of space between two channels as shown in **Figure 2**. The model has been studied for uniform

**Figure 2.**

*Schematic diagram of semi-circular micro-channel heat sink.*


**Table 2.**

*Properties of fluid materials considered for the study [6].*

power supply of 95 W from a heater attached to the bottom of the heat sink. In order to study the model of heat sink some assumptions have been considered.


### **3.1 Properties of working fluid**

Properties of working fluid (PCM slurry) have been calculated from the relations available in the literature [18]. The calculated properties of PCM slurry used as working fluid summarized below in **Table 3**.

Density (ρf)

$$
\rho\_{\text{slurry}} = \text{q}\rho\_{\text{w}} + (\mathbf{1} - \mathbf{q})\rho\_{\text{PCM}} \tag{1}
$$

where φ is volumetric concentration of working fluid, ρw is density of water and ρPCM is the density of phase change material.

Viscosity (μf)

$$
\mu\_{\text{shury}} = \left(\mathbf{1} - \mathbf{q} - \mathbf{1}.\mathbf{1}6\mathbf{q}^2\right)^{-2.5} \tag{2}
$$


*Application of Semi-Circular Micro-Channel Heat Sink with Phase Change Material… DOI: http://dx.doi.org/10.5772/intechopen.105901*

**Table 3.**

*Calculated properties of working fluid.*

Thermal conductivity (kf)

$$\mathbf{k}\_{\text{slury}} = \mathbf{k}\_{\text{w}} \frac{2 + \left(\mathbf{k}\_{\text{PCM}} \boldsymbol{\zeta}\_{\text{k}\_{\text{w}}}\right) + 2\mathbf{q}\left\{\left(\mathbf{k}\_{\text{PCM}} \boldsymbol{\zeta}\_{\text{k}\_{\text{w}}}\right) - \mathbf{1}\right\}}{2 + \left(\mathbf{k}\_{\text{PCM}} \boldsymbol{\zeta}\_{\text{k}\_{\text{w}}}\right) - \mathbf{q}\left\{\left(\mathbf{k}\_{\text{PCM}} \boldsymbol{\zeta}\_{\text{k}\_{\text{w}}}\right) - \mathbf{1}\right\}} \tag{3}$$

where kw is the thermal conductivity of water and kPCM is the thermal conductivity of phase change material.

Specific heat (cf)

$$\mathbf{c}\_{\text{slury}} = \frac{\boldsymbol{\varrho} \left( \mathbf{c}\_{\text{sp}} + \mathbf{c}\_{\text{Lp}} \right)}{\mathbf{2}} + \frac{\boldsymbol{\varrho} \mathbf{L} \mathbf{A} \mathbf{t} \mathbf{n} \mathbf{t} \text{ heat}}{\mathbf{T}\_{\text{L}} - \mathbf{T}\_{\text{s}}} + \frac{(\mathbf{1} - \boldsymbol{\varrho}) \boldsymbol{\rho}\_{\text{w}} \mathbf{c}\_{\text{w}}}{\boldsymbol{\varrho}\_{\text{f}}} \tag{4}$$

where cPCM is the specific heat of phase change material and cw is the specific heat of water.

#### **3.2 Data interpretation**

The working fluid used to flow as coolant through the semicircular micro-channels of 0.35 mm over the entire compact micro-channel heat sink of 25 mm<sup>2</sup> considered for the present work. The calculated properties of working fluid (PCM slurry) have been used for the analysis of the heat sink. Data assumed for the analysis of present work is summarized below in **Table 4**.

Power supply to the heat sink (P) in Watt

$$\mathbf{P} = \mathbf{Q} \times \rho\_{\text{slurry}} \times \mathbf{c\_{slurry}} (\mathbf{T\_{out}} - \mathbf{T\_{in}})$$

$$\mathbf{T\_{out}} = \mathbf{T\_{in}} + \frac{\mathbf{P}}{\mathbf{Q} \times \rho\_{\text{slurry}} \times \mathbf{c\_{slurry}}} \tag{5}$$


**Table 4.**

*Data assumption for the analytical analysis.*

where Q is the flow rate of slurry in m3/s, Tout and Tin are outlet and inlet temperature of working fluid at the inlet and outlet of heat sink.

Reynolds Number (Re)

$$\text{Re} = \frac{\rho\_{\text{slury}} \mathbf{v} \mathbf{D}\_{\text{h}}}{\mu\_{\text{slurry}}} \tag{6}$$

Hydraulic diameter (Dh) can be calculated from

$$\mathbf{D}\_{\mathbf{h}} = \frac{\mathbf{A}}{\mathbf{P}\_{\mathbf{w}}} \tag{7}$$

where A is the cross-sectional area of micro-channel and Pw is the wetted perimeter. For semi-circular cross-section

$$\mathbf{A} = \frac{\pi \mathbf{D}^2}{8} = \mathbf{0}.0481 \mathbf{0}. \text{mm}^2 \tag{8}$$

So Dh for semi-circular micro-channels can be formulated as

$$\mathbf{D}\_{\mathrm{h}} = \frac{\pi \mathbf{D}}{\pi + 2} = \mathbf{0}.2138 \text{ mm} \tag{9}$$

Prandtl number (Pr)

$$\mathbf{Pr} = \frac{\mathbf{c}\_{\text{slurry}} \mu\_{\text{slurry}}}{\mathbf{k}\_{\text{slurry}}} \tag{10}$$

Nusselt Number (Nu) correlations with Re and Pr [19]. If 100 <sup>&</sup>lt; Re <sup>&</sup>lt; 1500 then *Nu* <sup>¼</sup> <sup>0</sup>*:*<sup>253</sup> *Re* <sup>0</sup>*:*<sup>597</sup> *Pr*<sup>0</sup>*:*<sup>349</sup> and if 1500 <sup>&</sup>lt; Re <sup>&</sup>lt; 15,000 then

$$\text{Nu} = \text{0.253 } \text{Re}^{0.62} \text{Pr}^{0.340} \tag{11}$$

As we know that

$$\mathbf{Nu} = \frac{\mathbf{h\_{slury}} \mathbf{D\_h}}{\mathbf{k\_{slury}}} ; \quad \mathbf{h\_{slury}} = \frac{\mathbf{Nu} \times \mathbf{k\_{slury}}}{\mathbf{D\_h}} \tag{12}$$

Also heat absorbed (H) in Watt to the micro-channels is given by the relation

$$\mathbf{H} = \mathbf{h}\_{\text{slurry}} \mathbf{A}\_{\text{surface}} (\mathbf{T}\_{\text{w}} - \mathbf{T}\_{\text{in}}) \tag{13}$$

where Asurface is the surface area of the micro-channels and Tw is the wall temperature of the micro-channels.

Surface area of semi-circular micro-channels can be calculated as

$$\mathbf{A}\_{\text{surface}} = \frac{\boldsymbol{\pi} \times \mathbf{D} \times \mathbf{L}}{2} \tag{14}$$

where L is total length of micro-channels equal to 675 mm = 0.675 m.

From energy balance power supply (P) to the heat sink is equal to the heat

absorbed (H) by the micro-channels assuming there are no any heat losses.

Wall temperature (Tw) can be formulated as

$$\mathbf{T\_w} = \mathbf{T\_{in}} + \frac{\mathbf{P}}{\mathbf{h\_{surry}} \mathbf{A\_{surface}}} \tag{15}$$

#### **4. Validation of result**

Validation of result has been done according to Gaikwad and More [15] for Nusselt number (Nu) and flow rate of PCM slurry in the range of 75 ml/min to 300 ml/min at concentration of φ = 0.25 (**Table 5**). Present result at φ = 0.25 compared with Gaikwad and More [15] as shown in **Figure 3**. The results of present work shows similar pattern of variation in Nu with increasing flow rate.


**Table 5.** *Calculated values on the variation of flow rate.*

**Figure 3.** *comparison of Nu vs. flow rate with the results of Gaikwad and More [15].*

#### **5. Results and discussion**

In present analysis analytical study of square chip of heat sink (25 mm 25 mm) consisting of semi-circular micro-channels has been carried out using PCM slurry as working fluid with inlet temperature of 303 K. Analytical study is based on the general equations and correlations based on the available literatures. Results obtained for varying mass flow rate from 75 ml/min to 300 ml/min [15]. Effect of flow rate on slurry outlet temperature of heat sink can be seen from **Figure 4** where slurry temperature at the outlet of micro-channel heat sink decreases with mass flow rate, as the specific heat of PCM slurry increases with increasing concentration of PCM particles. Hence at concentration of φ = 0.5 has lower outlet temperature than φ = 0.25 with increasing flow rate and maximum decrement in outlet temperature of slurry is found to be about 0.63% in φ = 0.25 and 0.45% in φ = 0.5. In **Figure 5**. Reynolds number for φ = 0.5 is far below than φ = 0.25. The graph of Reynolds number is almost flat for φ = 0.5 as Reynolds increases marginally with increasing flow rate while for φ = 0.25 the Reynolds number increases linearly with increasing flow rate. This trend signifies that with increasing concentration the viscosity of slurry also increases resulting in decreasing Reynolds number.

**Figure 4.** *Effect of flow rate on slurry outlet temperature of the heat sink.*

*Application of Semi-Circular Micro-Channel Heat Sink with Phase Change Material… DOI: http://dx.doi.org/10.5772/intechopen.105901*

**Figure 5** *Effect of mass flow rate on Reynolds number.*

**Figure 6.** *Effect of mass flow rate on Nusselt number (nu).*

**Figure 7.** *Effect of mass flow rate on heat transfer coefficient of slurry.*

In **Figure 6** Nusselt number (Nu) increases significantly with increase in mass flow rate for both concentrations due to increase in specific heat accordingly. Increase in specific heat of PCM slurry observed because of increase in latent heat of the slurry as

**Figure 8.** *Effect of mass flow rate on wall temperature of micro-channel heat sink.*

it approaches the melting temperature. Higher Nu has been observed for φ = 0.25 while lower value of Nu observed for φ = 0.50 due to high viscous flow at higher concentration of PCM slurry in micro-channels. In **Figure 7** similar trend of graph has been observed for heat transfer coefficient of slurry when flow rate increases as Nu is a function of heat transfer coefficient and maximum increment in heat transfer coefficient of slurry found to be 19.9 for φ = 0.25 and 18.8% for φ = 0.50. In **Figure 8** with increase of the flow rate the wall temperature of the micro-channel heat sink decreases for both concentrations of PCM slurry. Wall temperature decreases significantly for φ = 0.50 than φ = 0.25 due to higher latent heat absorption capacity at higher concentration of PCM particles.
