Forced Convection Heat Dissipation from Pin Fin Heat Sinks Modified by Rings and Circular Perforation

A set of three-dimensional Computational Fluid Dynamics (CFD) simulations were conducted to study the hydro-thermal efficiency of different pin-fin heat sinks (PFHSs), as illustrated in Figures 1 and 2. These PFHSs consist of a base plate with fins arranged in a staggered manner, placed within a channel as depicted in Fig. 1. The dimensions of the base plate are 75×575×2 mm³ and of the channel are 215×75×20 mm³. Both the base plate and fins were constructed from A8350P aluminum. The staggered cylindrical pin fin (CPFs) heat sink from a previous study was used as a benchmark to validate the methodology employed in this research. Combination between ring and perforation techniques was analyzed parametrically under fully turbulent flow conditions using three-dimensional CFD simulations. This combination was results fives cases named as: case 0, case 1, case 2, case 3, case 4. Simulation was realized for Reynolds number (Re) ranging from 8740 to 22,060. The longitudinal and transversal distances of the pins are set to 15 mm. all dimensions of channel and heat sinks were illustrated in Figs. 1 and 2.

Fig. 1.

General illustration and dimensions (in mm) of air flow channel heat sink

Fig. 2.

Detailed dimensions (in mm) of different heat sink configurations

The fluid flow state is considered to be turbulent flow with single-phase characteristics. In the context of fluid-solid conjugate heat transfer in channel heat sinks, several assumptions are employed to simplify the numerical calculation process as: −

Both air flow and heat transfer are assumed to be in steady states.

These assumptions lead to the formulation of control equations appropriate for the analysis of steady states fluid flow and heat transfer (38) (39), which includes the continuity equation, momentum equation, energy equation, and conduction energy equation (27). (1) ∂ui∂xi=0 {{\partial {u_i}} \over {\partial {x_i}}} = 0 (2) ∂∂xiρuiuj=∂ρ xiμ∂ui∂xj−ρu′iu′j¯−∂p∂xi {\partial \over {\partial {x_i}}}\left( {\rho {u_i}{u_j}} \right) = {\partial \over {\rho \,{x_i}}}\left[ {\left( {\mu {{\partial {u_i}} \over {\partial {x_j}}} - \overline {\rho {{u'}_i}{{u'}_j}} } \right)} \right] - {{\partial p} \over {\partial {x_i}}} (3) ∂(ujT)∂xj=α∇2T+∂∂xj−u′iθ¯ {{\partial ({u_j}T)} \over {\partial {x_j}}} = \alpha {\nabla ^2}T + {\partial \over {\partial {x_j}}}\left( { - \overline {{{u'}_i}\theta } } \right) (4) ∇.λs∇Ts=0 \nabla .\left( {{\lambda _s}\nabla {T_s}} \right) = 0

Where, λ_s is the thermal conductivity of A8350P Aluminum (167 W/m. K), T_s is the temperature field in the Aluminum-solid heat sink.

For closing the equation system, standard k-ε turbulence model was used in this study. This model is largely used to estimate heat transfer and fluid flow in thermal systems(20,33,40,41). Also, this model is better to predict turbulent flow in channels(42).

In order to evaluate heat transfer, performance and fluid flow behaviors of different PFHSs, we used some parameters which are summarized as follows (20).

Nusselt number (Nu): (5) Nu=qDhλair(TW-(Tin+Tout)/2) {\rm{Nu}} = {{qD_h } \over {\lambda _{air} (T_W - (T_{in} + T_{out} )/2)}}

Where, q is the constant heat flux on the base plate of heat sink (5903 W/m²), λ_air is the thermal conductivity of air (0.024 W/m. K). T_in, T_out is the temperatures in the inlet and outlet of channel respectively. T_W is the mean temperature of walls of the base plate and pin fins.

Thermal resistance (R_th): (6) Rth=Tw−Tin/q {R_{th}} = \left( {{T_w} - {T_{in}}} \right)/q

Pressure drops (Δp); (7) Δp=pin−pout \Delta p = {p_{in}} - {p_{out}}

Hydro thermal performance factor (η); (8) η=NuNuCPFHS/ΔpΔpCPFHS13 \eta = \left( {{{Nu} \over {N{u_{CPFHS}}}}} \right)/{\left( {{{\Delta p} \over {\Delta {p_{CPFHS}}}}} \right)^{{1 \over 3}}}

Pumping power (P_P): (9) PP=uin×Ac×Δp {P_P} = {u_{in}} \times {A_c} \times {\Delta _p}

Where, u_in is the speed in the inlet of channel, A_c is the contact solid-fluid surface, Δp is the pressure difference between inlet (p_in) and outlet (p_out) of channel heat sink.

The regime of the air turbulent flow can be determined by using Reynolds number (Re): (10) Re=uin×Dhυ {\mathop{\rm Re}\nolimits} = {{u_{in} \times D_h } \over \upsilon }

Reynolds number (Re) is determined at the hydraulic diameter (D_h) and it ranging from 8740 to 22060 corresponding of inlet velocity interval of 4.14 to 10.45 m/s. Where the temperature in the inlet is set to 300K.

The simulation of conjugate heat transfer and turbulent fluid flow characteristics was conducted using the CFD software COMSOL Multi-Physics v. 5.4. The Reynolds Average Navier Stocks (RANS) and energy equations were discretized through the finite element method (FEM). Convergence criteria of 10⁻⁶ and 10⁻⁹ were set for the RANS and energy equations, respectively.

Grid sensitivity analyzes were performed to ensure the accuracy of the numerical model. Tetrahedral and unstructured grid were generated for each case to determine the most efficient independent grid mesh (Fig. 3).

Fig. 3.

Example of generated tetrahedral mesh, Case 4

A free tetrahedral type mesh was utilized for all numerical domains. Different grid sizes were tested for validation, for example, for CPFHSs arrangement, the grid of 1,367,577 was selected for following simulation.

Because, this case illustrated that Nusselt number (Nu) results showed that its deviation does not less than 1% compared to the refined grid cases. Similar grid independence assessments were carried out for other cases, resulting in the selection of specific grid sizes for each case.

Fig.4 show an example of the test of the grid sensibility for the case 4. The simulations were run on a computing station with a CPU i7 and a frequency of 2.6 GHz and 16 Go of RAM, with each simulation typically taking around 4 hours.

Fig. 4.

Test of grid independence for CPFs

It is crucial to evaluate the accuracy of the current model for realized the following simulations. This evaluation includes confirming the results by comparing them with available data from literature (31). For the validation, we utilized both Nusselt number (Nu) and pressure drop (Δp).

Figs 5(a) and 5(b) depict the variation of Nu and Δp versus Reynolds number (Re), respectively. The examination of Nu results indicated a maximum deviation of 11.51% and 2.60% in comparison to the experimental and numerical results of Chin et al (31). Similarly, the assessment of Δp results displayed a deviation of 15.83% and 8.21%. These deviations due to the utilization of three thermocouples in the inlet of the channel and other three thermo-couples in the outlet by Chin et al (31). Where, in the present study, we used the mean surfaces of the inlet and outlet to evaluate the temperatures.

Fig. 5.

Validation of results for CPFs

One factor that can reduce the effectiveness of CPFs is the creation of air vortices behind the pin at very low speeds (43), resulting in the formation of hot points or lower heat transfer areas (LHTAs)(44,45). Figs. 6 and 7 show the distribution of velocity streamlines and temperature contours for cases 0 and 4 as typical arrangements. In Fig. 6, the airflow splits into two regions as it passes over the sides of the cylindrical pins, with one region having high speeds that are conducive to heat transfer due to the turbulence of air molecules. The second region, located directly behind the pin fins, experiences low-velocity eddies, leading to the formation of hot spots and decreased heat transfer rates.

Fig. 6.

Velocity streamline distribution (m/s) for a) case 0 b) and case 4 at Re=22060

Fig. 7.

Contours of local temperature distribution (K) for a) case 0 b) and case 4 at Re=22060

To address this issue, solutions such as adding rings insert and perforation space have been proposed, as depicted in these figures. By adding rings around CPFs, the area of low-velocity regions can be reduced, decreasing recirculation flow zones and increasing heat transfer areas. Finally, the use of perforation techniques helps to reduce recirculation flow zones with low velocity, thereby decreasing LHTAs behind the pin fins. The flow pattern significantly influences thermal characteristics, with CPFs showing the mean highest temperatures due to the presence of LHTAs. However, by implementing solutions such as increasing perforation number, the occurrence of hot spots and LHTAs can be reduced, leading to improved heat transfer coefficient.

Fig.8 displays the variation of the Nusselt number (Nu) versus Reynolds number (Re) for various PFHS arrangements. The graph demonstrates that Nu augments with increasing Re, attributed to the increased inlet velocity and enhanced inertial shears near the walls. The findings reveal that Nu values increased by of 66.32%, 116.58%, 146.80%, 127.63%, and 180.82% for case 0, case 1, case 2, case 3 and case 4, respectively, compared to cylindrical pin fins at Re = 22,060. Therefore, case 4 ensures better augmentation of heat transfer coefficient of 180.82% due to the perforated space which is helps not only augment heat transfer areas but also significantly reduces the formation of the lower heat transfer areas (LHTAs) behind of the pin fins.

Fig. 8.

Variation of Nusselt number (Nu) versus Reynolds number (Re)

The variation of thermal resistance (R_th) against Re for different PFHS configurations was depicted in Fig.9. It is evident from this illustration that an increase in Re results in a decline in R_th, consistent with the trends observed for Nu in Fig. 8. A remarkable reduction in thermal resistance is achieved at the highest Reynolds number (i.e., Re = 22,060).

Fig. 9.

Variation of thermal resistance (R_th) versus Reynolds number (Re)

The percentage reductions in R_th for case 0, case 1, case 2, case 3, and case 4 are 58.49%, 102.41%, 69.56%, 108.95%, and 154.54% compared to the cylindrical pin fins (CPFs), respectively.

As a consequence, the location of rings around CPFs augment heat transfer areas which are participate to reduce the thermal resistance of PFHSs, where the perforation space obviously enhances conjugate heat transfer by augmenting heat transfer surfaces and diminishing hot spots behind the pin fins. From these results, case 4 ensures a significant reduction in the thermal resistance by 154.54% compared to CPFs at Re = 22,060.

Fig. 10 illustrates the variation of the pressure drop (Δp) and Reynolds number (Re) across different PFHS arrangements. These configurations present prominent advantages over conventional or cylindrical pin fin heat sinks (CPF), resulting in a significant reduction in pressure losses despite the enhanced heat transfer coefficients except case 0. The graph indicates that with an increase in Reynolds number (Re), there is a corresponding increase in pressure drop due to the emergence of flow blocking phenomena and heightened inertial shears near the wall of pin fins (PFs) and the base plate. The findings reveal that in comparison to CPFs at Re = 22,060, there is a remarkable reduction in Δp by 14.46 %, 34.46 %, 61.04%, and 62.19% for case 1, case 2, case 3, and case 4, respectively. Except, case 0 creates a pressure drop penalty of 29.22% for the same comparison. These results demonstrate that the perforation space helps to reduce pressure drop due to the diminution in blockage flow before the pin fins.

Fig. 10.

Variation of pressure difference (Δp) versus Reynolds number

The integration of rings around of the CPFs and perforation methods has partially removed recirculation zones behind the pin fins, which are responsible for reducing pressure drop. The pumping power (P_P) is directly related to the pressure drop (Δp), inlet velocity (u_in), and frontal area (A_c) as depicted in equation 9. Fig. 11 shows the linking between P_P and Re for various PFHS configurations. It is obvious that an increase in Re leads to an evolution in P_P due to the amplified inlet velocity. Nevertheless, a substantial increase in P_P is observed in the proposed configurations compared to CPFs, attributed to the augmentation in frontal area (A_c). For the highest Reynolds number (Re = 22,060), P_P augments by 39.56%, 31.67%, 32.43%, 26.91%, and 41.29% for case 0, case 1, case 2, case 3, and case 4, respectively, compared to CPFs at Re = 22,060.

Fig. 11.

Variation of pumping power (P_P) versus Reynolds number (Re)

Fig. 12 illustrates the change in hydro thermal performance factor (η) with Reynolds number for pin fin heat sinks (PFHSs) featuring different perforation and rings arrangements. The figure indicates that η values are consistently above 1 for all configurations of PFHS, suggesting that these configurations exhibit superior performance compared to the reference case (CPFs). This underscores the effectiveness of the perforation technique and rings insert in enhancing the thermal performance of the PFHSs, at least within the scope of this study. Furthermore, in the presence of rings insert, the results reveal that rings increases both with higher Reynolds number and an increased number of perforations. Specifically, for Cases 0 to 4 at Reynolds number of 22,060, the corresponding η values are approximately 1.57, 2.26, 2.72, 2.67 and 3.29, respectively. Based on these findings, it is determined that case 4 demonstrates the highest performance, achieving an η of 3.29 at Reynolds number of 22,060, and is thus identified as the optimal configuration. Compared with the reference case (31), the optimal configuration (case 4) ensures an reduction of 77.5% and 77.65% for the volume and mass of heat sink, respectively, leading to space and cost savings in addition to improved hydrothermal performance.

Fig. 12.

Variation of thermal resistance (η) versus Reynolds number (Re)

Fig. 13 depicts the variation of the hydrothermal performance factor versus contact surface. The first observation from this figure is insertions of ring and perforation augment the surface of contact. Usually, the increase in the surface of contact between air flow and the solid let to an augmentation in the performance of heat sink. In addition, the perforation in external rings leads to slight diminution in the thermal performance as shown in case 2 to case 3. But, the perforation in the rings and grooves helps to augment the hydro-thermal performance factor.

Fig. 13.

Variation of the hydrothermal performance factor (η) versus contact surface (A_C)