Enhancing the performance of aluminum foam heat sinks through integrated pin fins

International Journal of Heat and Mass Transfer 151 (2020) 119376

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt

Enhancing the performance of aluminum foam heat sinks through integrated pin fins Yongtong Li a,b, Liang Gong a,∗, Minghai Xu a, Yogendra Joshi b,∗ a b

College of New Energy, China University of Petroleum (East China), Qingdao 266580, China The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, 30332-0405 GA, USA,

a r t i c l e

i n f o

Article history: Received 16 October 2019 Revised 26 December 2019 Accepted 12 January 2020

a b s t r a c t In this paper, the fluid flow and heat transfer performances of aluminum foam heat sink with pin fins (AFPF heat sink) are experimentally and numerically investigated. High porosity aluminum foams with the porosity of 0.88 and pore densities of 10 PPI and 20 PPI are incorporated into the pin fin array channel to form the test sections. The channel consists of five rows of 5 mm × 5 mm square cross-section staggered pin fins with height of 13 mm. The AFPF heat sinks are subjected to the steady water flow covering the Darcy-Forchheimer regime, and measurements of the flow and heat transfer are performed and compared with the aluminum foam (AF) heat sinks. The results show that the insertion of pin fins into the AF heat sink has significant effects on both flow and heat transfer characteristics. Heat transfer performance of AFPF and AF heat sinks both increases with increasing pore density. The improvement of average Nusselt number in AFPF heat sink of 20 PPI is approximately 63.5–68.1% compared to the AF heat sink, while the deduced flow resistance is increased by 49.2–88.1%. The thermal performance of the AFPF heat sink is found to be 1.5 times of the AF heat sink under a given pumping power. In addition, a numerical model capable of predicting the temperature distribution and pressure drop is developed and experimentally validated. © 2020 Elsevier Ltd. All rights reserved.

1. Introduction Power electronics components are increasingly being used in electric vehicles, wind power converters, and other energy conversion technologies [1–3]. The increasing capabilities in such systems require higher electrical power density, which results in larger rates of heat generated per volume. The metal foam heat sink is an excellent cooling solution to dissipate high heat fluxes, due to its distinctive thermal properties. Metal foam provides a large internal convective surface area per volume, promoting convection heat transfer. Also, the interconnected and torturous foam structures extend the flow paths and intensify flow mixing, leading to the augmentation of heat transfer coefficient. Therefore, the implementation of metal foams in several applications including the cooling of electronics is promising. The fundamental heat transfer mechanisms within metal foam, at both the micro/macroscopic levels, have been studied by several investigators [4–9]. The heat transfer performance of metal foam is closely related to the morphological parameters, including poros-

∗

Corresponding authors. E-mail addresses: [email protected] (L. Gong), [email protected] (Y. Joshi). https://doi.org/10.1016/j.ijheatmasstransfer.2020.119376 0017-9310/© 2020 Elsevier Ltd. All rights reserved.

ity, pore size, permeability, tortuosity, and foam strut diameter, etc. Mancin et al. [10] experimentally investigated the forced air convection through various metal foam samples with pore density varying between 5 PPI (pores per inch) and 40 PPI, and porosity ranging from 0.896 to 0.956. They found that the interstitial heat transfer coefficient increases when decreasing porosity or increasing pore density. Hwang et al. [11] and Tzeng et al. [12] experimentally investigated the flow and heat transfer in AF heat sink and found enhanced heat transfer performance at lower porosity. Hsieh et al. [13] and Jeng et al. [14] studied the jet impingement cooling performance of metal foam heat sink by examining the effects of foam morphological parameters. In [13], the heat transfer performance of the foam sample with high porosity was found better than that of the low porosity, while the opposite was found in [14]. In addition, Lu et al. [15] and Zhao et al. [16] investigated the convection heat transfer characteristics in metal foam filled pipe flow by considering various parameters, such as porosity, pore density, Reynolds number, and the foam thermal conductivity. Results showed significant thermal performance enhancement, with the heat transfer capability increasing with decreasing pore size or porosity, both of which had a negative impact on the pressure drop and pumping power consumption.

2

Y. Li, L. Gong and M. Xu et al. / International Journal of Heat and Mass Transfer 151 (2020) 119376

The arrangement of metal foam within the flow path also directly affects the fluid flow and heat transfer behaviors. The hydraulic and thermal performance of metal foam heat sink can be simultaneously enhanced when the foam configurations and morphological parameters are properly developed [17–20]. Li et al. [17] numerically investigated the thermal performance of a biporous metal foam heat sink with the computational domain of 20 mm × 2.4 mm × 7 mm and compared it with the uniform porosity foam heat sink. The optimal bi-porous heat sink design for the studied cases is using the foam of 30 PPI and 50 PPI at the bottom and top layers, respectively. Hung et al. [18] performed numerical investigations on flow and heat transfer inside micro-channel with different foam configurations, including the fully filled, outlet enlargement, trapezoidal, thin rectangular, block, and sandwich distributions. The foam/plate-fin sandwiched heat sink demonstrated the lowest thermal resistance under the same pumping power consumption. Wang et al. [19] observed that the reduction of friction factor and thermal resistance can be simultaneously achieved by utilizing a gradient-porous heat sink, with the pore size decreasing normal to the flow direction. Chen et al. [20] experimentally investigated the heat transfer characteristics of liquid-cooled heat sinks with various non-uniform copper foam distributions. It was noted that the reduction of thermal resistance of 62% can be achieved by arranging the large pore density foam at the inlet region, and the small pore density foam at the outlet region. The high porosity metal foam provides a relatively low effective thermal conductivity compared with the parent base material [21], thus making it difficult to promptly conduct heat through the foam matrix and then to the entire foam domain. In order to further improve the heat transfer capability of metal foam heat sink, Bhattacharya et al. [22] proposed a type of finned metal foam heat sink (metal foam heat sink with plate-fins) with overall dimension of 62.5 mm × 62.5 mm × 62.5 mm and experimentally examined the influence of the number of plate-fins on the thermal performance using air cooling. They reported that the finned metal foam heat sink outperforms the metal foam heat sink in heat transfer performance and the optimal fin number is around four. Under air jet impingement cooling, Feng et al. [23] and Wang et al. [24] noted that the finned metal foam heat sink was superior to the metal foam heat sink and plate-fin heat sink in heat transfer performance. Seyf et al. [25] numerically investigated the conjugate heat transfer of an elliptical pin fin heat sink with metal foam by assuming local thermal equilibrium between foam ligament and air, while DeGroot et al. [26] employed the local thermal non-equilibrium model to describe the heat transfer characteristics in the finned foam heat sink. Results show that the addition of pin fin enhances the heat transfer performance of the air-cooled metal foam heat sink. As seen from the review of literature, there have been several numerical or experimental investigations of metal foam heat sink with plate-fins (or pin fins) using air as working fluid. To the best of our knowledge, the flow and heat transfer characteristics of metal foam heat sink with pin fins subjected to forced liquid flow have not been reported yet. In this work, a combined experimental and numerical study is conducted to investigate the fluid flow and heat transfer characteristics of aluminum foam heat sink with pin fins (AFPF heat sink) subjected to forced water flow. AFPF heat sinks with foam porosity of 0.88 and pore densities of 10 PPI and 20 PPI are designed and manufactured. Aluminum foam heat sinks (AF heat sink) with the same operating condition are also tested for comparison. The testing methodology for determination and assessment of the thermal performance of the AFPF heat sink is introduced in detail. The pressure drop, friction factor, temperature difference distribution, and average Nusselt number of the AFPF heat sink are presented, and the overall thermal performance en-

Table 1 Geometrical parameters of the AFPF and AF heat sinks.

Parameters

Heat sink (Unit: mm) AFPF heat sink AF heat sink

Channel length, width and Height Total length, width and Height Fin dimension Fin transverse spacing Fin longitudinal spacing Substrate thickness

85 × 45 × 13 145 × 75 × 28 5 5 10 4

85 × 45 × 13 145 × 75 × 28 – – – 4

hancement is evaluated based on the pumping power required. The experimentally validated numerical model can serve as a benchmark for numerical simulations of water-cooled AF heat sink.

2. Experimental setup and test section The AFPF specimens are manufactured and integrated into a liquid flow loop to investigate their thermo-hydraulic performance. The details of the test sections and the experimental methodologies are described in this section.

2.1. Fabrication of heat sinks The commercially available ERG aluminum (alloy 6101-T6) foam samples with a porosity of 0.88 and pore densities of 10 PPI and 20 PPI are used, as shown in Fig. 1. All the foam samples have an overall dimension of 75 mm × 45 mm × 13 mm, which is produced by using the WEDM (wire electronic discharge machine). In addition, the holes with dimension of 5 mm are also cut by the WEDM, which are used for accommodating the pin fins. The manufacturer provided thermo-physical properties of the aluminum foams are as follows: relative density of 12%, pore densities of 10 PPI and 20 PPI, and aluminum thermal conductivity of 218 W/(m•K). The AFPF heat sink consists of a traditional pin fin heat sink with aluminum foam inserted into the void space between pin fins, as shown in Fig. 2(a) and 2(b). To manufacture the AFPF heat sink, the following steps were followed: (1) manufacture the designed aluminum pin fin heat sink; (2) cut the pin fin holes from aluminum block using a precision WEDM to ensure a good fit between the fins and the foam block; and (3) assemble the metal foam block with the pin fin heat sink by press-fitting to reduce the contact resistance. The AFPF heat sink has five staggered rows of pin fins, each row includes four square-shaped pin fins, with the transverse and longitudinal spacing of 5 mm and 10 mm. In order to compare the thermal performance with the AFPF heat sinks, the AF heat sinks are also fabricated, as shown in Fig. 2(c) and 2(d). A rectangular channel with a dimension of 85 mm (L) × 45 mm (W) × 13 mm (H) is used for accommodating the aluminum foam block. To bond the foam block into the channel and reduce the contact thermal resistance, the thermal interface material is used. During the fabrication process, a thin layer of thermal adhesive (Omega OB-200, 1.38 W/(m•K)) is pasted on the channel bottom wall in advance. The foam block is then tightly pressed into the channel and the assembly heated in an oven at a temperature of 204 °C for two hours for curing. The detailed connection between the aluminum foam/pin fin interface is illustrated in Fig. 3, with the enlarged view of the press-fit bonded foam/pin fin interface presented. In addition, the detailed geometrical parameters of the heat sinks under the present considerations are summarized in Table 1.

Y. Li, L. Gong and M. Xu et al. / International Journal of Heat and Mass Transfer 151 (2020) 119376

3

Fig. 1. Aluminum foam samples with different pore densities (a) 10 PPI and (b) 20 PPI.

Fig. 2. Photographs of the AFPF and AF heat sinks.

Fig. 3. Enlarged view of the foam/fin connection interface.

2.2. Experimental apparatus and data acquisition The schematic diagram of the experimental setup is presented in Fig. 4. The liquid cooling loop is established to measure the fluid flow and heat transfer characteristics of the AFPF and AF heat sinks. De-ionized water is pumped through the loop by gear

pump (Micropump GJ-N27) on a variable-speed gear pump system (Cole-Parmer EW-75,211–30). The flow rate of the working fluid is measured by using a turbine wheel flowmeter (McMillan S-114–8), with the measurement range of 0.5–5 L/min. As shown in Fig. 5, the inlet connector as a part of the test section, in which metal foam material is filled in the inlet plenum to distribute the fluid

4

Y. Li, L. Gong and M. Xu et al. / International Journal of Heat and Mass Transfer 151 (2020) 119376

Fig. 4. Schematic diagram of the experimental loop.

2.3. Data reduction and uncertainty analysis The measured flow rate, pressure drop, fluid temperatures, and surface temperatures along the centerline of the bottom wall are used to calculate the pertinent parameters. The Reynolds number in this study is defined as:

Re =

Fig. 5. Connector filled with foam for flow distribution.

(1)

where ρ f is the density of the water; u is the average velocity of water through the rectangular channel; Dh is the channel hydraulic diameter, Dh =4HW/2(H+ + W); μ is the dynamic viscosity of water. The flow resistance of working fluid flowing through the heat sink is characterized by the friction factor, given as:

f = and promote flow uniformity. A stainless tube with an inner diameter of 4 mm is utilized to connect the test section within the flow loop. Five cartridge heaters are embedded into the aluminum block (6061-T6) as heat sources, as shown in Fig. 6(a). Heat is supplied from the bottom of the substrate over a heated area of 6.5 mm × 3.5 mm. The adjustable DC Power Supply (N6700B Agilent), with the maximum voltage and current of 600 V and 5.5 A, respectively, is used to control the power into the heater. The heater block and the heat sink are assembled using a clamp to reduce the thermal contact resistance between them. In addition, a thin layer (0.5 mm) high thermal conductivity thermal pad (Arctic-Thermal pad, 6 W/m•K) is employed as the thermal interface material (TIM). During the experiments, the heater and the test section are wrapped with high-temperature fiberglass insulation (0.057 W/m•K) with a thickness of 6.6 cm to reduce heat loss to the surroundings. Six T-type thermocouples of 0.5 mm diameter wire are used to measure the surface temperature of the heat sink, as shown in Fig. 6(b). An additional two T-type thermocouples are installed at the inlet and outlet of the test section to measure fluid temperatures. A differential pressure transducer (Omega PX2300-1DI) with the measurement range of 0–6895 Pa is employed to measure the pressure drop. The flowmeter, pressure transducer, heaters, and thermocouples are connected to a data acquisition system (DAQ, Agilent 37940A) to record the experimental data (Fig. 7).

ρf u D h μ

( p/L )Dh 1 / 2 · ( ρf u 2 )

(2)

where p is the pressure difference between the two measurement ports; u is the average fluid velocity through the channel; L is equal to the length of aluminum foam. In order to characterize the heat transfer performance of various heat sink configurations, the average Nusselt number is defined as:

N um =

hm Dh kf

(3)

The average heat transfer coefficient is calculated by:

hm =

Q UI = A(Tiw,m − Tf,m ) A(Tiw,m − (Tin + Tout )/2 )

(4)

where Q is the supplied heat power; U and I represent the voltage and current, respectively; A is the surface area of the heat source; Tiw,m is the average temperature of the internal bottom wall; Tf,m is the average fluid temperature. The pumping power is calculated as the product of the volume flow rate and the pressure drop through the test section, written as:

Ppum = Qv  p = uWc Hc  p

(5)

where Qv is the volumetric flow rate; Wc and Hc are the width and height of the channel; p is the pressure drop. The experimental uncertainties in this work are associated with heat power, temperature, flow rate, pressure drop, and geometrical dimensions. The uncertainties of all the parameters are listed

Y. Li, L. Gong and M. Xu et al. / International Journal of Heat and Mass Transfer 151 (2020) 119376

5

Fig. 6. Thermocouple locations and heater (a) cartridge heater and (b) thermocouples location.

and fluid. As a result, the maximum uncertainty in the heat transfer coefficient can be calculated using Eq. (6) [23], which is estimated to be 6.1%.

δh h



=

δQ Q

2

 +

δ Tin

2

Tiw − Tfm

 +

δ Tout

2

Tiw − Tfm

 +

2

δ Tiw Tiw − Tfm

(6) 3. Numerical model

Fig. 7. Computational domain.

In order to provide a comparison with experimental results and gain more physical insights, computational fluid dynamics and heat transfer (CFD/HT) simulations of the heat sink with various configurations are performed. The details and implementation of the numerical model are given in this section. 3.1. Model description and assumptions

Table 2 Experimental uncertainties. Parameter

Uncertainty value

Flow rate Pressure drop Fluid Temperature Surface temperature Heat loss

1.0% 0.25% ±0.1 K 2.5% 0.5%

in Table 2. The uncertainty of flow rate is measured after filling a precision measuring cylinder multi-times and averaging it, and the pressure drop uncertainty measurement is performed by calibrating the differential pressure transducer with a standard pressure gage (Omega DPI 610). The length and width of the heating area are measured by vernier caliper with a resolution of 0.01 mm, and the uncertainty can be neglected. Temperatures at the inlet and outlet are measured by two T-type thermocouples calibrated using a constant water bath. The surface temperatures of AF heat sink are measured by six T-type thermocouples three times under a specific case, and the uncertainty is obtained by averaging the deviation of each thermocouple. The energy balance is also verified by the total dissipated electrical power and the calorimetric heat input to the cooling water. It is found that 99.5% of the applied heat was removed by the working fluid, and thus the heat loss is about 0.5%. According to Eq. (4), the uncertainty in the heat transfer coefficient is associated with the power dissipation, and the difference between the internal wall and the average fluid temperatures. It should be noted that the uncertainty is larger at higher velocity due to the small temperature difference between the wall

The numerical model has the same geometric dimensions as reported in the experimental section. In order to replicate the operating conditions, a full-scale numerical model including the main test section and the connector is employed for simulation. Several assumptions are adopted for the numerical modeling of the conjugate heat transfer in AF and AFPF heat sinks. (1) Thermal properties of the aluminum foam and the fluid are constant; (2) the flow is incompressible, steady-state and laminar; (3) Aluminum foam is isotropic and homogenous; (4) the fluid phase and solid phase are in the local non-equilibrium state. 3.2. Governing equation and boundary conditions The fluid flow through the aluminum foam is described by the Brinkman-Forchheimer extended Darcy equation. The two energy equations are adopted to model the non-equilibrium interfacial heat transfer between the fluid and foam ligament. The continuity, momentum, and energy equations are given as follows: Continuity equation:

∇ · (ρ V ) = 0

(7)

Momentum equation:

ρf μ ρC (V · ∇ )V = −∇ P+μf,e ff ∇ 2V − ( f + √f F V )V K ε2 K

(8)

Energy equation:

(ρ cp )f (V · ∇ Tff ) = ∇ · (kfe ∇ Tff ) + hv (Ts s − Tf f )

(9-1)

∇ · (kse ∇ Ts s ) − hv (Ts s − Tf f ) = 0

(9-2)

6

Y. Li, L. Gong and M. Xu et al. / International Journal of Heat and Mass Transfer 151 (2020) 119376

For the solid pin fins and the rectangular channel, only the steady-state heat conduction equation is considered.

∇ · (ks ∇ Ts ) = 0

(10)

where cp and μf,eff represent the fluid specific heat and effective dynamic viscosity, respectively; Tf f and Ts s denote the temperature of the fluid phase and solid phase within metal foam, separately; asf, CF , ks , and K are specific area, inertial coefficient, and permeability; hv is volumetric heat transfer coefficient. kfe and kse are the effective thermal conductivities of the fluid phase and aluminum foam matrix, respectively, where kfe =ε kf and kse =(1-ε )ks . The boundary conditions are as follows: (1) At the channel inlet:

u = uin, T = T in,

v=w=0

(11)

(2) At the channel outlet:

p = p0

(12)

Fig. 8. Comparison of pressure drop gradients with velocity for AFPF and AF heat sinks.

(3) At the bottom wall of the substrate:

qw = −ks

∂ Ts ∂y

(13)

(4) At the aluminum foam and channel interface [23]:

∂ Ts ∂T ∂ Ts = (−kfe f − kse ), Ts = Tf f = Ts s , u = v = w = 0 ∂y ∂y ∂y f

−ks

s

(14)

Table 3 Morphological parameters of metal foam. Authors

Material

PPI

ε

K (m2 )

Present

Al foam Al foam Al foam Copper foam

10 20 40 40 10 20 30

0.88 0.88 0.9 0.85 0.98 0.975 0.95

7.95 6.86 3.38 2.34 1.05 5.11 1.96

Bayomy et al. [27] Hetsroni et al. [28] Chen et al. [20]

(5) At the interfaces between the foam and pin fins [23]:

−ks

∂ Ts ∂T f ∂ Ts s = (−kfe f − kse ), Ts = Tf f = Ts s , u = v = w = 0 ∂n ∂n ∂n (15)

(6) The remaining external walls:

−ks

∂ Ts =0 ∂n

(16)

3.3. Mesh independence test Mesh independence tests were conducted before undertaking parametric numerical simulations. For this testing, the AF heat sink of 20 PPI was selected for consideration at Re of 600. The average bottom wall temperature and the pressure drop under different numbers of mesh elements are used for the mesh sensitivity analysis. There are total four sets of grid systems containing elements of (1) 1.23 million, (2) 2.48 million, (3) 4.51 million and (4) 6.73 million adopted for analysis. The calculated results from Mesh (4) are recognized as the comparison baseline. The discrepancies of the average temperature of the bottom wall and pressure drop between Mesh (3) and Mesh (4) are 0.64% and 1.03%, respectively. In order to compromise accuracy and the execution time, Mesh (3) is selected for further simulations. 4. Results and discussion The following sections will focus on the comprehensive assessment of the experimental data and the comparison of numerical simulations. In addition, overall thermal performance assessments are also carried out based on the pumping power consumption. 4.1. Hydrodynamic performance The measured pressure drop gradients through the heat sink with velocity for various heat sinks are plotted in Fig. 8. It is seen that the pressure drop gradients for all the heat sinks exhibit a

× × × × × × ×

CF 10−8 10−8 10−8 10−9 10−7 10−8 10−8

0.0418 0.0460 – 0.09 0.056 0.048 0.071

non-linear increase with the velocity, indicating that the flow is in the non-Darcy regime dominated by the inertial resistance, especially in high velocity. The pressure drop of AFPF heat sinks with pore densities of 10 PPI and 20 PPI is larger than the AF heat sinks with the same morphological parameters, because the insertion of impermeable solid fins increases the flow passage blockage, thus increasing the flow resistance. Among the four tested heat sinks, the AFPF heat sink of 20 PPI has the largest pressure drop, while the AF heat sink of 10 PPI has the smallest pressure drop. At the maximum flow velocity of 0.08 m/s, the pressure drop gradients of AFPF heat sinks with pore density of 10 PPI and 20 PPI increased by 51.04% and 39.03%, respectively, compared with the corresponding AF heat sinks. The results suggest that the addition of pin fins into the AF heat sink leads to a dramatic increase in pressure drop, which in return requires more pumping power to pump the fluid at the same flow rate. Based on the data in Fig. 8, the morphological parameters of metal foam including the permeability and inertial coefficient can be obtained by using the quadratic fitting according to the DarcyForchheimer law:

−

dp μu ρCF 2 = +√ u dx K K

(17)

where CF is the inertial coefficient; K is the permeability; u is the average fluid velocity through the channel. The obtained permeability and inertial coefficient for both the 10 PPI and 20 PPI aluminum foams are summarized in Table 3. The permeability decreases with increasing pore density, while the inertial coefficient increases because the flow mixing is stronger with the increase of pore density. Table 3 compares the present results with several available published data using water as working coolant. Based on the obtained permeability and inertial coefficient, the pressure drop of the heat sinks can be calculated from the numerical model. Fig. 9 shows the comparison of the friction factor

Y. Li, L. Gong and M. Xu et al. / International Journal of Heat and Mass Transfer 151 (2020) 119376

7

Table 4 Nusselt number coefficients for various heat sinks.

Fig. 9. Comparison of friction factors with Re for AFPF and AF heat sinks.

ε

PPI

Re

AFPF heat sink c n

AF heat sink c n

0.88 0.88

10 20

590–1630 590–1630

29.56 35.18

15.06 17.47

4.2. Thermal performance Fig. 10 illustrates the sectional view of the heat sink, as well as a simplified one-dimensional heat transfer thermal resistance network. The heat sink internal wall temperature is calculated by using the measured bottom wall temperature according to the Fourier law:

Tiw = Tw −

Q y ks A

(18)

Finally, the heat is removed via convection heat transfer between the working fluid the metal foam ligament. The average convection heat transfer coefficient can be calculated using the Eq. (5). Based on the above analysis, the convection heat transfer performance comparisons in terms of the average Nusselt numbers (Num ) for the AFPF and AF heat sinks are shown in Fig. 11. As expected, the average Num increases with Re for the various heat sinks. For both the AFPF and AF heat sinks, a modest improvement in heat transfer performance can be obtained by using the large pore density foam. Both the AFPF and AF heat sinks with 20 PPI would lead to about 5% enhancement in Num , compared with that of 10 PPI. However, compared with the AF heat sinks, the heat transfer performances of AFPH heat sinks present a dramatic enhancement, which becomes even more pronounced at high Re. The Num of AFPF heat sinks with 10 PPI and 20 PPI both demonstrate over 65% enhancement in comparison with the AF heat sinks. Therefore, the addition of pin fins into aluminum foam is a very effective solution for heat transfer improvement, due to the enhanced overall effective thermal conductivity and increased internal heat transfer area.

0.294 0.280

In the present study, a constant temperature water bath is used to ensure uniform fluid inlet temperatures. In addition, the temperature rise of the coolant flowing through the test section is small. As a result, the variation of the thermal properties of the working fluid can be neglected. When the thermal properties of the fluid and the morphological parameters of metal foam are constant, the complex function of Num related to Re, Pr, PPI, and ε can be reduced as the only function of Re, and the corresponding correlation can be expressed as:

N um = cRen (f) obtained from the experiments and numerical simulations as a function of Re for the AFPF and AF heat sinks. The f is obtained using Eq. (2). The friction factors for all the AFPF and AF heat sinks decrease with Re. The f values of AFPF heat sinks are much higher than the AF heat sinks, in light of the higher flow resistance, which requires a larger pumping power to pump the fluid at a given flow rate. The AF heat sink of 10 PPI has the smallest f, while the AFPF of 20 PPI has the largest one. The f values of AF heat sinks of 10 PPI and 20 PPI with the addition of pin fins increased by approximately 58.1–91.2% and 49.2–88.1%, respectively. All heat sinks have a larger decrease rate in f at small Re, and the f values gradually decrease and tend to be constant values with increasing Re. In addition, it is seen that the numerical prediction agrees well with the experimental measurements with the maximum discrepancy of 13.0% for all of the cases studied.

0.271 0.252

(19)

where c and n are the coefficients. Based on the present experimental results of the steady water flow through the AFPF and AF heat sinks, the values of these coefficients can be obtained by using curve fitting and are listed in Table 4. The varied values of coefficients c and n are attributed to the different foam structures of the foam material. Then the empirical correlations of the average Nusselt number can be used to perform numerical simulations for the prediction of the temperature field distributions, and the experimentally validated numerical model also provides a reference for simulations. Fig. 12 presents the experimental and numerical results of the bottom wall temperature difference (Tw -Tin ) distributions along the centerline of the bottom wall of the AFPF and AF heat sinks at a heat flux of 10 W/cm2 . The symbols represent the experimental values, while the solid lines represent the corresponding numerical predictions. The results reveal that for a given heat flux, the wall temperature first rises with the axial distance, and then drops near the outlet region for all of the heat sinks. Since the heated area is located at the center of the bottom wall, and the length of the heating area is smaller than the aluminum foam block as well as the rectangular channel. Thermal spreading would occur from the heating area to its surroundings due to the effect of the axial heat conduction, especially at the beginning and end regions of the heating area. As a result, the temperature distribution does not present a monotonic increase along the flow direction. Additionally, when pin fins are incorporated into the foam block, the wall temperatures of the AFPF heat sinks is greatly decreased compared to the AF heat sinks. The insertion of fin pins into the AF heat sinks of 10 PPI and 20 PPI would lead to the reduction of bottom wall temperature up to 30%. For both the AF and AFPF heat sinks, the numerical results are in good agreement with the experimental results, demonstrating the effectiveness of using the present numerical model for predicting the thermal behaviors of the conjugate heat transfer within the AF and AFPF heat sinks. Fig. 13 shows the predicted temperature difference (Tw -Tin ) field distributions for the four heat sinks at Re of 600. It is noted that the hot region is located in the center-right region of the heated wall, which matches well with measured data as depicted in Fig. 12. The results of most interest are related to the thermal performance of the AFPF heat sinks. It shows that the implementation of the AFPF heat sink leads to a great suppression of the bottom wall maximum temperature, reduced by about 14 °C. In contrast, the AF or AFPF heat sink with 20 PPI only has a slight improvement in heat transfer performance, compared to that of 10 PPI. The small temperature reduction of the bottom wall means that the aluminum foam with pore density of 10 PPI and 20 PPI of-

8

Y. Li, L. Gong and M. Xu et al. / International Journal of Heat and Mass Transfer 151 (2020) 119376

Tin

Tf,m

Tout

Rconv Tiw Rcond Tw

(a) Sectional view of the test section

(b) Heat transfer network

Fig. 10. Detailed heat transfer process (a) Sectional view of the test section and (b) Heat transfer network.

fer almost the same heat transfer capability under the investigated conditions. The results confirm that the heat transfer performance can be significantly improved by using the AFPF heat sink. 4.3. Overall performance assessment AFPF heat sinks provide the enhanced heat transfer capability accompanied by high-pressure drop. In order to evaluate their

overall thermal performance, the cooling performance of the heat sinks is estimated by investigating the results of the thermal resistance and average Nusselt number with the pumping power. For electronics cooling applications, the local surface temperature is more important than the average temperature, and it is of particular interest for temperature control. Accordingly, the overall thermal resistance based on the maximum temperature is expressed

Fig. 12. Comparison of bottom wall temperature difference (Tw -Tin ) distribution.

Y. Li, L. Gong and M. Xu et al. / International Journal of Heat and Mass Transfer 151 (2020) 119376

9

Fig. 14. Comparison of thermal resistance with pumping power. Fig. 11. Average Nusselt number versus Re for the AFPF and AF heat sinks.

as:

Rt =

Tmax − Tin qw A

(20)

where Tmax is the maximum bottom wall temperature; A is the heating area. The pumping power is calculated using Eq. (5), as the product of the volume flow rate and the pressure drop across the heat sink. The comparison of the thermal resistance of the AFPF and AF heat sinks is plotted in Fig. 14. Results show that the increase of pumping power significantly reduces the thermal resistance for both the AFPF and AF heat sinks. In addition, as the pumping power becomes larger, the decrease rate in thermal resistance decreases. Among the various heat sinks, the AFPF heat sink with pore density of 20 PPI has the smallest thermal resistance, while the AF heat sink with pore density of 10 PPI produces the largest ther-

mal resistance, suggesting that the AFPF heat sink has better cooling performance than AF heat sink. For instance, at the pumping power of 0.0075 W, the thermal resistances of the AFPF heat sinks of 10 PPI and 20 PPI are reduced by about 30%, respectively. The thermal effectiveness of AFPF heat sink for improving heat transfer is further evaluated, by comparing the Num of AFPF and AF heat sinks under the same pumping power. The Num versus the pumping power is shown in Fig. 15. It increases with increasing pumping power for various heat sinks. Under the same pumping power, the AFPF heat sink of 20 PPI provides the highest Num , followed by the AFPF of 10 PPI, because the 20 PPI foam provides more internal convection heat transfer area. Additionally, it is seen that the AFPF and AF heat sink with a large pore density (20 PPI) have a slight increase in Num compared with that of a small pore density (10 PPI). Compared with the AF heat sinks, the Num of AFPF heat sinks is increased approximately 1.5 times in the entire

Fig. 13. Comparison of the heated wall temperature field difference (Tw -Tin ) distributions.

10

Y. Li, L. Gong and M. Xu et al. / International Journal of Heat and Mass Transfer 151 (2020) 119376

CRediT authorship contribution statement Yongtong Li: Data curation, Writing - original draft, Conceptualization, Validation. Liang Gong: Methodology, Supervision, Writing - review & editing. Minghai Xu: Methodology, Supervision, Writing - review & editing. Yogendra Joshi: Methodology, Supervision, Writing - review & editing.

Acknowledgment

Fig. 15. Average Nusselt number versus pumping power.

pumping power range. It suggests that the heat transfer enhancement by using AFPF exceeds the pressure drop penalty. As a result, the implementation of the AFPF heat sink is an efficient cooling solution for the thermal management of high power electronic devices.

5. Conclusion In this work, a combined experimental and numerical study is conducted to investigate the flow and heat transfer characteristics of water-cooled AFPF heat sink for the potential application of cooling high powered electronics. Aluminum foam samples with porosity of 0.88 and pore density of 10 PPI and 20 PPI are used to fabricate the test sections. The AF heat sinks with the same foam parameters and operating conditions are employed as the comparison models. The following main conclusions can be drawn: (1) Compared with the AF heat sink, the implementation of the AFPF heat sink significantly improves the heat transfer performance. The enhancement in Num of AFPF heat sinks is over 65%. The heat transfer performance of AFPF and AF heat sinks both increases with increasing the pore density of foam material, but the improvement is not pronounced when using 20 PPI instead of 10 PPI. (2) The permeability and inertia coefficient of the aluminum foam samples are determined based on the measurements of pressure drop gradients through the AF heat sinks. The pressure drop through the heat sink rises as the pore size declined, and the addition of impermeable pin fins leads to increased flow resistance. (3) Based on the results of the present experiments, empirical correlations of Num for water-cooled AFPF and AF heat sinks with porosity of 0.88 and pore density of 10 PPI and 20 PPI are proposed in terms of Re in the range of 590–1630. (4) A robust numerical model capable of accurately predicting the temperature distribution and flow resistance is validated by the present experimental results, which provide a benchmark for future simulations. (5) Under the same pumping power consumption, the AFPF heat sink demonstrates a better convection heat transfer performance, with the Num of AFPF heat sink approximately 1.5 times higher than the AF heat sink, suggesting that the AFPF heat sink is a promising cooling solution for high powered electronics cooling.

This work is financially supported by the Natural Science Foundation of China (No. 51676208) and the Fundamental Research Funds for the Central Universities (No. 18CX07012A and No. 19CX05002A). The authors are also grateful for the support from the Major Program of the Natural Science Foundation of Shandong Province (No. ZR2019ZD11). The first author is grateful for a China Scholarship Council award (No. 201806450030) during the course of this work as a visiting doctoral student at the Georgia Institute of Technology. References [1] S. Hazra, A. De, L. Cheng, et al., High switching performance of 1700-V, 50-A sic power Mosfet over Si IGBT/bimosfet for advanced power conversion applications, IEEE Trans. Power Electron. 31 (7) (2015) 4742–4754. [2] J. Zhang, Z. Qiu, E. Zhang, et al., Comparison and analysis of power cycling and thermal cycling lifetime of IGBT module, in: Proceedings of the 21st International Conference on Electrical Machines and Systems (ICEMS), IEEE, 2018, pp. 876–880. [3] W. Lai, M.Y. Chen, L. Ran, et al., Experimental investigation on the effects of narrow junction temperature cycles on die-attach solder layer in an IGBT module, IEEE Trans. Power Electron. 32 (2) (2016) 1431–1441. [4] K.S. Al-Athel, A computational methodology for assessing the thermal behavior of metal foam heat sinks, Appl. Therm Eng. 111 (2017) 884–893. [5] M. Bai, J.N. Chung, Analytical and numerical prediction of heat transfer and pressure drop in open-cell metal foams, Int. J. Thermal Sci. 50 (6) (2011) 869–880. [6] S. Krishnan, J.Y. Murthy, S.V. Garimella, Direct simulation of transport in open– cell metal foam, J. Heat Transf. 128 (8) (2006) 793–799. [7] H.J. Xu, L. Gong, S.B. Huang, et al., Non-equilibrium heat transfer in metal-foam solar collector with no-slip boundary condition, Int. J. Heat Mass Transf. 76 (2014) 357–365. [8] A. Zehforoosh, S. Hossainpour, Numerical investigation of pressure drop reduction without surrendering heat transfer enhancement in partially porous channel, Int. J. Thermal Sci. 49 (9) (2010) 1649–1662. [9] C.C. Chen, P.C. Huang, H.Y. Hwang, Enhanced forced convective cooling of heat sources by metal-foam porous layers, Int. J. Heat Mass Transf. 58 (1–2) (2013) 356–373. [10] S. Mancin, C. Zilio, A. Diani, et al., Air forced convection through metal foams: experimental results and modeling, Int. J. Heat Mass Transf. 62 (2013) 112–123. [11] J.J. Hwang, G.J. Hwang, R.H. Yeh, et al., Measurement of interstitial convective heat transfer and frictional drag for flow across metal foams, J. Heat Transf. 124 (1) (2002) 120–129. [12] S.C. Tzeng, T.M. Jeng, Convective heat transfer in porous channels with 90-deg turned flow, Int. J. Heat Mass Transf. 49 (7–8) (2006) 1452–1461. [13] W.H. Hsieh, J.Y. Wu, W.H. Shih, et al., Experimental investigation of heat-transfer characteristics of aluminum-foam heat sinks, Int. J. Heat Mass Transf. 47 (23) (2004) 5149–5157. [14] T.M. Jeng, S.C. Tzeng, Forced convection of metallic foam heat sink under laminar slot jet confined by parallel wall, Heat Transfer Eng. 28 (5) (2007) 484–495. [15] W. Lu, C.Y. Zhao, S.A. Tassou, Thermal analysis on metal-foam filled heat exchangers. part I: metal-foam filled pipes, Int. J. Heat Mass Transf. 49 (15–16) (2006) 2751–2761. [16] C.Y. Zhao, W. Lu, S.A. Tassou, Thermal analysis on metal-foam filled heat exchangers. part II: tube heat exchangers, Int. J. Heat Mass Transf. 49 (15–16) (2006) 2762–2770. [17] Y.T. Li, L. Gong, M.H. Xu, et al., Thermal performance analysis of biporous metal foam heat sink, J. Heat Transf. 139 (5) (2017) 052005. [18] T.C. Hung, Y.X. Huang, W.M. Yan, Thermal performance analysis of porous-microchannel heat sinks with different configuration designs, Int. J. Heat Mass Transf. 66 (2013) 235–243. [19] B.C. Wang, Y.F. Hong, X.T. Hou, et al., Numerical configuration design and investigation of heat transfer enhancement in pipes filled with gradient porous materials, Energy Convers. Manag. 105 (2015) 206–215. [20] K.C. Chen, C.C. Wang, Performance improvement of high power liquid-cooled heat sink via non-uniform metal foam arrangement, Appl. Therm. Eng. 87 (2015) 41–46.

Y. Li, L. Gong and M. Xu et al. / International Journal of Heat and Mass Transfer 151 (2020) 119376 [21] K. Boomsma, D. Poulikakos, On the effective thermal conductivity of a threedimensionally structured fluid-saturated metal foam, Int. J. Heat Mass Transf. 44 (4) (2001) 827–836. [22] A. Bhattacharya, R.L. Mahajan, Finned metal foam heat sinks for electronics cooling in forced convection, J. Electron. Packag 124 (3) (2002) 155–163. [23] S.S. Feng, J.J. Kuang, T. Wen, et al., An experimental and numerical study of finned metal foam heat sinks under impinging air jet cooling, Int J Heat Mass Transf 77 (2014) 1063–1074. [24] J. Wang, H. Kong, Y.B. Xu, et al., Experimental investigation of heat transfer and flow characteristics in finned copper foam heat sinks subjected to jet impingement cooling, Appl. Energy 241 (2019) 433–443.

11

[25] H.R. Seyf, M. Layeghi, Numerical analysis of convective heat transfer from an elliptic pin fin heat sink with and without metal foam insert, J. Heat Transf. 132 (7) (2010) 071401. [26] C.T. DeGroot, A.G. Straatman, L.J. Betchen, Modeling forced convection in finned metal foam heat sinks, J. Electron. Packag 131 (2) (2009) 021001. [27] A.M. Bayomy, M.Z. Saghir, T. Yousefi, Electronic cooling using water flow in aluminum metal foam heat sink: experimental and numerical approach, Int. J. Thermal Sci. 109 (2016) 182–200. [28] G. Hetsroni, M. Gurevich, R. Rozenblit, Metal foam heat sink for transmission window, Int. J. Heat Mass. Transf. 48 (18) (2005) 3793–3803.