# Enhancement of the thermal and hydraulic performance of PCPFHS and PSPFHS through improving the splitter plate shape.

1. IntroductionDue to rapid advancements in micro-electro-mechanical-systems in recent decades, the size of electronic components has decreased and also the thermal power produced by the devices has increased dramatically. This has increased the operating temperature of the electronic devices which can greatly reduce their reliability and service life. Therefore, many recent studies focus on the thermal management of electronic chips in order to find effective ways to remove excess heat and maintain the operating temperature in acceptable range. Devices such as heat pipes (Zhao and Avedisian 1997; Kim et al. 2003) and impinging jet cooling (Nishino et al. 1996; Chung and Luo 2002) have been studied so far. Among different types of cooling systems, the heat sink has attracted interest due to the effective function and reasonable cost. Although air is commonly used coolant fluid for cooling but boiling liquid can also be applied (Tso, Xu, and Tou 1999; Tso, Tou, and Xu 2000). Tuckerman and Peace in 1981, proposed the concept of micro-channel heat sink cooling (MCHS). They fabricated the micro-channel heat sinks on silicon wafers and proved that water is an effective coolant for MCHS which can be used for cooling devices such as high performance microprocessors, laser diode arrays, radars and high energy laser mirrors (Tuckerman and Pease 1981; Qu and Mudawar 2002). In addition to this, Osanloo et al. studied the performance of a water-cooled double-layered micro-channel heat sink having tapered channels (TDL-MCHS) for different convergence angles (0, 2, 4 and 6). They reported that by increasing the channels convergence angle, the thermal performance was improved. Whereas, due to increased pressure drop, the required pumping power was increased. They investigated the distribution of temperature and the ratio of thermal resistance to pumping power and suggested the convergence angle of 4[degrees] as the optimum angle for channels (Osanloo et al. 2016). Two popular types of heat sinks which are widely used in industry are: pin fin heat sinks and plate fin heat sink. Pin fin heat sinks have a simple design and are easier to manufacture, while the plate fin heat sinks have higher manufacturing cost however the heat transfer coefficient is higher in this type (Yu et al. 2005). In-line and staggered arrangement of pin fin was studied in 1980 by Sparrow et al. (Sparrow, Ramsey, and Altemani 1980) and proved that not only the heat transfer coefficient is higher in staggered arrangement compared to the in-line arrangement, but also the pressure drop is higher for staggered arrangement. In-line arrangement exhibits higher heat transfer with the same pumping power and heat transfer area, while the staggered arrangement requires lower surface temperature load and mass flow rate. Kordyban compared the performance of pin fin and plate fin heat sinks with identical dimensions. The temperature difference between the bottom plate of the heat sink and the ambient air was 50[degrees] for pin fin heat sink and 44 [degrees]C for plate fin heat sinks, respectively. Although, the pin fin had a surface area of 194 [cm.sup.2] which was larger than that of plate fin surface area (58 [cm.sup.2]) which shows that the plate fin leads to better heat transfer due to less temperature difference (Kordyban 1998). Forghan et al. performed an experimental investigation on the fin pin, plate fin and flared fin heat sinks. They found that for low air velocities, the heat rejection performance in plate fin heat sink is at least 20% better than other heat sink types (Forghan et al. 2001). For effective heat sink design, several criteria including high heat transfer rate, low pressure drop, ease of manufacture, simple structure, reasonable cost and etc. should be considered. Tao et al. proposed three mechanisms to increase single-phase heat transfer in micro-channels. These mechanisms include: (1) reducing of the thermal boundary layer; (2) increasing the flow interruption and (3) increasing the velocity gradient in the vicinity of the heated surfaces (Tao et al. 2002). However, parallel plate fins make the airflow smooth while passing through the heat sink which is undesirable for heat transfer performance of the heat sinks. Sometimes existing PFHS's cannot meet cooling requirements of electronic components in small scale. In this case, it is necessary to modify the structure of the heat sink to improve heat transfer performance. Based on the above reasons, the idea of how to make the flow inside the PFHS more turbulent and improve heat transfer performance, plate pin fin heat sink (PPFHS) was obtained from existing PFHS (Yu et al. 2005). Yu et al. studied the PPFHS numerically and experimentally and found that PPFHS benefit from better heat transfer performance compared to PFHS, while the former have much greater pressure drop and generally the PPFHS is more efficient (Yu, Feng, and Liu 2003; Yu, Feng, and Jianmei 2004). Yang and Peng performed an investigation on the effect of combined height of pin fin in PPFHS and showed that circular plate pin fin heat sink have better overall performance in comparison to the plate fin heat sink (Yang and Peng 2009). Yuan et al. performed a numerical study on thermal performance of PPFHS and the results showed that the height of the pin and air velocity have a significant effect on the hydrodynamic performance of PPFHS, but the linear arrangement and distance of the pins along the flow has little effect. Also the temperature of PPFHS for heat flux of 2.2 w/[m.sup.2] for air velocity of 6.5 m/s remains under 358 K (Yuan et al. 2012). Tiwari et al. conducted a 3D numerical simulation to study the effect of using splitter plate in circular tube on the thermal and hydraulic behaviour of the fluid. They reported that using a splitter plate spreads the streamline and decreases the vortex length. They investigated the flow and heat transfer for various Reynolds numbers, and compared the heat transfer for both with and without splitter plate in the tubes (Tiwari et al. 2005).

In this paper, the effect of employing V-shaped splitter plates behind the circular pins (V-shaped Splitter Plate Circular Pin Fin Heat Sink) (Hereinafter VSPCPFHS) and square pins (V-shaped Splitter Plate Square Pin Fin Heat Sink) (Hereinafter VSPSPFHS) inside the heat sink is studied numerically for the first time. The most significant feature of this new type of V-shaped splitter plates is reducing pressure drop and thermal resistance as well as increasing the effectiveness and reliability, simultaneously. In order to demonstrate the influence of using V-shape splitter plates on the velocity field and temperature, the results for pressure drop, heat resistance, the average temperature of the bottom plate, the profit factor (J) and reliability were compared for VSPCPFHS, VSPSPFHS and PFHS.

2. Problem definition

Plate Fin Heat Sinks (PFHSs) were developed to enhance the heat transfer from the electronic devices. Yu et al. introduced a new type of PFHSs having cylindrical pins between the plates and called it Plate Pin Fin Heat Sinks (PPFHSs). It is confirmed that placing cylindrical pins between the plates causes a decrease in thermal resistance by 30% in comparison to normal PFHSs (Yu et al. 2005). Employing pins oriented along the streamline would increase the pressure drop which in turn affects the function of the heat sink (Yu et al. 2005). In order to eliminate this problem and enhance the performance of PPFHS, a V-shaped splitter is located behind the circular and square cylindrical pins which lessen the turbulence and thus pressure drop around the pins. Moreover, the enlargement of surface due to employing V-shaped splitter enhances the heat transfer which acts favourable to heat sink performance. VSCPPFHS and VSSPPFHS with all geometrical parameters are shown in Figure 1(a) and (b), respectively, along with detailed information in Table 1.

Because of iterative structure of the heat sink, in order to reduce the computational costs, only one flow passage is simulated the heat sink is considered as a single duct. Figure 2 illustrates the computational domain with extruded pins and corresponding splitters. Aluminium was considered for the structural material of the heat sink with conductivity of 202.5 W/m K. For verification of numerical simulation, the heating power of the surface is set to 3665 W/[m.sup.2].

3. Numerical approach and validation

3.1. Governing equations

Governing equations (momentum, energy conservation and continuity) should be solved to study the coupled heat transfer between fins and fluid flow. The flow was considered incompressible and the viscous dissipations were omitted. There is vortex gathering inside the SPPFHS as mentioned in literature (Yu et al. 2005) thus the air flow was considered to be turbulent between the plate fins. Separating the velocity to mean velocity and fluctuating velocity, and taking the mean velocity from governing equations leads to:

Continuity:

[[partial derivative][bar.u.sub.i]/[partial derivative][bar.x.sub.i]] = 0 (1)

Momentum:

[rho][bar.u.sub.i][[partial derivative][bar.u.sub.i]/[partial derivative][x.sub.j]] = - [[partial derivative][bar.p]/[partial derivative][x.sub.i]] + [[partial derivative]/[partial derivative][x.sub.j]] [[[mu].sub.l]([[partial derivative][bar.u.sub.i]/[partial derivative][x.sub.j]] + [[partial derivative][bar.u.sub.j]/[partial derivative][x.sub.i]]) - [rho][bar.u.sub.i][bar.u.sub.j]] (2)

Energy:

[rho][bar.u.sub.i][[partial derivative][bar.T]/[partial derivative][x.sub.j]] = [[partial derivative]/[partial derivative][x.sub.j]] [([[[mu].sub.l]/[[sigma].sub.l]] + [[[mu].sub.t]/[[sigma].sub.t]]) [[partial derivative][bar.T]/[partial derivative][x.sub.j]]] (3)

where, u is the velocity, [[mu].sub.l] is kinematic viscosity and superscript--is to show mean values. For solid parts, we have:

[[partial derivative]/[partial derivative][x.sub.i]] ([k.sub.s][[partial derivative]T/[partial derivative][x.sub.i]]) = 0 (4)

where [k.sub.s] is solid conductivity. For aluminium fin [k.sub.s] = 202.4 W/m K.

k-[epsilon] turbulence model has been employed to continue and close the above equations, and the results were obtained based on this model. The transport equations for k and [epsilon] are given as follows:

Transport equation for k

[mathematical expression not reproducible] (5)

Transport equation for [epsilon]

[mathematical expression not reproducible] (6)

where [[mu].sub.t] = [rho][C.sub.[mu]] [[k.sup.2]/[epsilon]] and closures coefficients were set to: [C.sub.1] = 1.44, [C.sub.2] = 1.92, [C.sub.[mu]] = 0.09, [[sigma].sub.k] = 1, [[sigma].sub.[epsilon]] = 1.3.

In order to separate pressure-velocity coupled equations, the SIMPLE algorithm was employed. The face values of momentum k, [epsilon] were interpolated using the power-law discretisation scheme and for pressure values second order discretisation scheme was applied. Pressure drop ([DELTA]p) and thermal resistance Rth were measured to evaluate the flow and temperature characteristics according to Equations (7) and (8).

[DELTA]p = [p.sub.in] - [p.sub.out] (7)

[R.sub.th] = [[DELTA]T/Q] (8)

where [p.sub.in] and [p.sub.out] stand for the inlet and outlet pressures of the air in a single duct, [DELTA]T demonstrates the difference between the ambient air temperature and the highest temperature on the fin base, and Q stands for the constant heating power applied on the base plate of the heat sink.

3.2. Boundary conditions

Taking into account accurate boundary conditions, the Equations (1-3) shall be solved. Figure 2 illustrates the boundary conditions in the computational domain, containing a single duct of the heat sink and the outlet computational section. It is noteworthy to mention that the outlet section is considered such that to avoid the back flow at the outlet. Also, according to this Figure, one single flow passage is taken into account in order to reduce the computational domain. This assumption simplifies the problem by considering the symmetric boundary conditions at the outlet section of the computational domain. Also, adiabatic walls and no-slip BC are imposed on the fin's wall to cover the energy equation and velocity field. Moreover, uniform inlet velocity and outlet pressure along with specified inlet temperature are considered as shown in Figure 2.

3.3. Numerical validation

Numerical simulation was carried out with five different inlet velocities of 4.5, 6.5, 8, 10 and 12.2 m/s which correspond to Reynolds numbers of 2053, 2967, 3651, 4563 and 5567, respectively, and the Reynolds numbers are obtained based on the hydraulic diameter. Yu et al. experimental data (Yu et al. 2005) were used to validate the numerical simulations, then the pressure drop and thermal resistance were compared. Figure 3(a) shows the pressure drop variations as per inlet velocity. From this Figure, it could be observed that pressure drop increases almost linearly with increasing inlet velocity; and current numerical results are in good agreement with experimental data. Similarly Figure 3(b) shows the linear reduction of thermal resistance with increasing inlet velocity.

Hexagonal type of meshes was constructed in the fluid and solid zones. The grid Independency checked for average transfer coefficient of the heat sink, have for different number of grids in VSPCPFHS and VSPSPHFS for different L/D ratios. The appropriate number of grids for VSPCPFHS and VSPSPHFS having L/D = 1 was found out to be 541,921 and 495,725, respectively; For L/D = 2, optimum number of grids were obtained 562,381 and 508,735, respectively and finally for L/D = 3, the proper number of grids were obtained 580,850 and 513,244, respectively.

4. Results and discussion

Figures 4-7 illustrate the changes in pressure drop, thermal resistance, profit factor and average temperature on the base plate as a function of inlet fluid velocity for different heat fluxes. In all these Figures results for PFHS, PPFHS and VSPPFHS (V-shaped splitter plate pin fin heat sink) with circular and square cylindrical pins for three splitter lengths are presented.

Figure 4(a) and (b) show results of pressure drop in both square and circular cylindrical pins in the PPFHSs with and without V-shaped splitters for Q = 50 W and 100 W, respectively. It could be seen that by increasing the flow rate, the pressure drop increases in all configurations. As it is obvious, the lowest pressure drop corresponds to PFHS, which acts as a single duct. Placing a pin fin inside the PFHS causes resistance against the flow resulting higher pressure drop. As it is expected, pressure drop in circular cylindrical pin PPFHSs are considerably less than square ones. This is mostly due to sharp edges in square cylindrical PPFHSs and larger wake zones. The resistance occurred via pin fin inside the PFHS can be nullified to some extent by employing V-shaped splitters behind the cylindrical pins. This is highly arises from existence of sharp interfaces in square cylinder and bigger wake zone. Employing the V-shaped splitter plates attached to the cylindrical pins would reduce the resistance increment. Moreover, Figure 4 expresses that the V-shaped splitter with longer length of L, has fewer pressure drop. Also note should be given that two sources contribute to the pressure drop viscosity effects and separation. Hence, increasing the splitter's length may increase the viscosity pressure drops, but weakening of the vortex behind the pin, will reduce the total pressure drop.

Variation of thermal resistance in terms of velocity is shown in Figure 5. In the PFHS the fluid has regular layer motion and therefore boundary-layer resistance is high. This causes the PFHS to have higher thermal resistance compare to square and circular cylindrical pins in the PPFHSs with and without splitters. By placing pin-fin inside the heat sink, the regular motion of layers becomes disarranged, and the boundary-layer resistance weakens causing the thermal resistance to reduce.

Also it could be understood that the thermal resistance in square cylindrical pin in the PPFHSs is significantly less than circular cylindrical pin. The splitter plates behind the circular and square cylindrical pin fins stabilises the flow around the pins resulting in reduced of heat transfer coefficient, however due to the larger surface of heat exchange, the thermal resistance decreases in both the heat sinks altogether. The numerical results acknowledge the claim as well. Also, by increasing the ratio of splitter plate's length to the diameter of pins, for both types of heat sinks, the thermal resistance decreases.

To define the non-dimensional parameter of profit factor the thermal resistance and pressure drop is combined in a single parameter and the results are compared in various heat sinks, according to Equation (9):

J = [Q/E] (9)

E = UA[DELTA]p. (10)

where E represents the pumping power, U is the free stream velocity and A is for the cross section area. Figure 6 compares the Profit Factor (J) square and circular pins in the PPFHSs with and without V-shaped splitter plates. In general, for all the cases, by increasing the velocity, the values of J are reduced, which are due to pressure drop inside the channel. The results show that for a constant speed, the values of J for circular PCPHFS are higher than PSPHFS, which is caused by elevated pressure drop. In addition, Figure 6 shows that at a constant velocity, by increasing the ratio of V-shaped splitter plate length to pin diameter in both square and circular pins in the PPHFS, the parameter J increases; but the greater increase can be observed in the case of PCPHFS.

As it is clear from the definition of profit factor, higher values of J factor results in more heat loss with lower pumping power, which is desirable in terms of operation costs and energy consumption level.

Average temperature of the base plate of the heat sinks with different Pin Fin shapes is shown in Figure 8. According to the numerical results, the heat sink temperature with square cylindrical pin-fins is less than a circular cylindrical pin-fin heat sink. As shown in Figure 8 with increasing the velocity, the heat transfer coefficient is enhanced, which increases the convection heat transfer of the fluid and ultimately the temperature is reduced. For the same heat flux, the temperature drop in square PSPHFS is more than circular one, which is due to more flow turbulence in this case. The minimum temperature in each case is located on the base plate on the heat sink and corresponds to the PPHFS with V-shaped splitter plates; and by increasing the length of splitter plates, the average temperature of the heat sinks will further decrease.

4.3. Estimation of lifetime improvement

In this section, the lifetime improvement is predicted for a given power transistor. In this regard, according to (Military, U. S. 1992) number of failures for low-frequency and bipolar transistor per million hours is calculated from the following equation:

[[lambda].sub.p] = [[lambda].sub.b] [[PI].sub.T] [[PI].sub.A][[PI].sub.R][[PI].sub.S][[PI].sub.Q][[PI].sub.E] (13)

where [[lambda].sub.b] represents the base failure rate, [[PI].sub.T] is temperature factor, [[PI].sub.A] is application factor, [[PI].sub.R] is power rating factor, [[PI].sub.S] is voltage stress factor, [[PI].sub.Q] is quality factor, and [[PI].sub.E] stands for environment factor. All of the above parameters were considered constant except for temperature factor [[PI].sub.T], which varies with temperature as follows:

[[PI].sub.T] = exp(-2114([1/[T.sub.J] + 273] - [1/298])) (14)

where worst case junction temperature [T.sub.J] can be evaluated by:

[T.sub.J] = [T.sub.C] + [[THETA].sub.JC]P (15)

In Equation (15) [T.sub.c] is case temperature, and [[theta].sub.JC] expresses junction-to-case thermal resistance ([degrees]C/watt) for a device soldered to a PCB. It can be demonstrated that for a power transistor the value of [[theta].sub.JC]P equals 25.

Thus, Equation (15) for power transistor can be rewritten as:

[T.sub.J] = [T.sub.C] + 25([degrees]C) (16)

According to the Equations (13)-(16) and Figure 8, Failure Number Reduction Percentage for transistors, per million hours can be obtained from Equation (17).

FNRP = [FN[R.sub.VSPPFHS with 1 = 3D] - FN[R.sub.PPFHS]/FN[R.sub.PPFHS]] (17)

The reduction of failures obtained from Equation (17) for different velocities and heat flux of 50 (W) are shown in Figure 9 for both PCPFHS and PSPFHS. A further temperature reduction in PSPFHS leads to an increase in Failure Number Reduction Percentage in this case compared to circular PPFHS heat sink. In other words, the failure number reduces due to lower temperature in square PPFHS which is show in Figure 9.

5. Conclusion

In this paper, the effect of using V-shaped splitter plates behind the circular and square pins inside the heat sink was studied numerically for the first time. The most important advantage of this new type of V-shaped splitter plates is reduction in pressure drop and thermal resistance as well as increase in the profit factor and reliability.

The most important results are summarised below:

(1) The minimum pressure drop can be achieved with PFHS, where pressure drop in PCPFHSs is considerably less than that of PSPFHSs. Placing pins inside the heat sink increases the pressure drop, the V-shaped splitter plates are used behind the pin which led to significant improvement in reducing the pressure drop.

(2) Moreover, the V-shaped splitter with longer length L has fewer pressure drop. For example, the percentage reduction in pressure drop in VSPSPFHSs and VSPCPFHSs with L/D = 3 was obtained 40 and 17.4%, respectively, compared to the heat sink lacking splitter plate at the velocity of 12.2 m/s and heat flux of 50 W

(3) Placing the V-shaped splitter plates in VSPCPFHSs and VSPSPFHSs causes the heat transfer coefficient of the fluid to reduce, but the total thermal resistance for both the heat sinks decreases. Also, by increasing the ratio of plate's length to pins diameter, the thermal resistance decreases for both types of heat sinks.

(4) In general, for all the cases by increasing the velocity, the values of J are reduced. Also at constant flow speed, the values of J are higher for PCPHFS compared to PSPHFS, with and without using splitter plate. By increasing the ratio of L/D in both VSPCPHFS and VSPSPHFS, the J parameter increases where the amount of this increase is greater in VSPCPHFS.

(5) The VSPSPFHS due to a further decrease in temperature compared to VSPCPFHS, causes an increase in the Failure Number Reduction Percentage. For instance, the Failure Number Reduction Percentage for VSPSPFHS and VSPCPFHS at the velocity of 4.5 m/s and heat flux of 50 W were achieved 18 and 14%, respectively.

Nomenclature

Latin symbols P Pressure [pa] Q Heating power [W] Re Reynolds number [--] R overall thermal resistance [K[W.sup.-1]) T Temperature [K] U flow velocity [m/s] k thermal conductivity [W/m K] [C.sub.p] Specific heat [J/kg*K] [C.sub.1], [C.sub.2], [C.sub.[mu]] Turbulent constants J Profit factor [--] E Pumping power [W] Greek symbols [DELTA] Differential [mu] Fluid dynamic viscosity [Pa.s] [[mu].sub.t] Eddy viscosity of the air [kg/s m] [[mu].sub.l] Kinematic viscosity[[m.sup.2]/s] [rho] Fluid density [kg/[m.sup.3]] [epsilon] Dissipation rate of turbulent energy [[m.sup.2]/[s.sup.3]] [[sigma].sub.[epsilon]],[[sigma].sub.k] k-[epsilon] turbulence model constant for [epsilon] and k Subscript bp Base plate in Inlet out outlet th Thermal f Fluid s Solid

Notes on contributors

Akbar Mohammadi Ahmar is a PhD candidate in Mechanical Engineering at the University of Tehran. His research interests are numerical modeling, CFD analysis, renewable energy and turbulence.

Behzad Osanloo is a MSc graduate in Mechanical Engineering at the University of Tabriz. His research interests are numerical modeling, CFD analysis and heat transfer.

Ali Solati is a PhD candidate in Mechanical Engineering at the University of Tehran. His research interests are numerical modeling, laser material processing and CFD analysis.

Mohammad Taghilou is a PhD graduate in Mechanical Engineering at the University of Tabriz. His research interests are numerical modeling, CFD analysis and heat transfer.

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Akbar Mohammadi-Ahmar (a), Behzad Osanloo (a), Ali Solati (b) and Mohammad Taghilou (c)

(a) Young Researchers and Elite club, Zanjan Branch, Islamic Azad University, Zanjan, Iran; (b) Young Researchers and Elite club, Central Tehran Branch, islamic Azad university, tehran, iran; (c) school of Mechanical engineering, college of engineering, university of tabriz, tabriz, iran

KEYWORDS

V-shaped splitter plate; pressure loss; thermal resistance; profit factor; reliability

ARTICLE HISTORY

Received 13 January 2017

Accepted 26 March 2017

https://doi.org/10.1080/14484846.2017.1316027

Table 1. Detailed information of PFHS, PPFHS and VSPPFHS. Fin length Fin width Fin height Fin thickness l (mm) w (mm) H (mm) t (mm) 51 53.5 11.5 1.5 fin spacing fin number Pin height Pin diameter [delta] (mm) N h (mm) D (mm) 5 9 10 2 Pin spacing Pin number splitter plate cross section area length S (mm) n L (mm) A ([mm.sup.2]) 12.75 24 1D, 2D and 3D 50

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Author: | Mohammadi-Ahmar, Akbar; Osanloo, Behzad; Solati, Ali; Taghilou, Mohammad |
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Publication: | Australian Journal of Mechanical Engineering |

Geographic Code: | 7IRAN |

Date: | Oct 1, 2018 |

Words: | 4758 |

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