forced convection heat transfer enhancement by porous pin fins in rectangular channels

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ecwsarpressure drops in such heat exchangers are usually much higherthan those in others 1; this defect greatly lowers the overall heattransfer performances of pin fin heat exchangers and as a result,tdfii

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be achieved through the emplacement of porous blocks. Huang etal. 8 later presented a similar investigation in cooling of multiple

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Downloaded Frheir applications are restricted. In order to reduce the pressurerops and improve the overall heat transfer performances for pinn heat exchangers, porous metal pin fin arrays may be used

nstead of traditional solid metal pin fin arrays.As porous media can significantly intensify the mixing of fluid

ow and increase the contact surface area with fluid inside, it haseen regarded as an effective way to enhance heat transfer bysing porous media 4. The flow and heat transfer in porous pinn heat exchangers for present study can be modeled as forcedonvective heat transfer in partially filled porous channels. Theesearches on forced convection with partially filled porous con-gurations have been investigated extensively in the last years.adim 5 studied the laminar forced convection in a fully orartially filled porous channel containing discrete heat sources onhe bottom wall. The BrinkmanForchheimer extended Darcy

odel were used for the computations. He found that when theidth of the heat source and the space between the porous layersere of same magnitudes as the channel height, the heat transfer

nhancement in the partially filled channel was almost the same ashat in the fully filled porous channel while the pressure drop was

heated blocks covered with porous media. The results showed thatsignificant cooling augmentation of the blocks can be achievedthrough the cover of finite-sized porous substance. Other similarstudies of forced convection in a channel filled with porous blockscan also be found in Refs. 9,10. Besides porous block, porousbaffles are also popular for heat transfer enhancement applica-tions. Ko and Anand 11 experimentally studied the heat transferenhancement in a rectangular channel by using a porous bafflemade up of aluminum foam. The experiments showed that the useof porous baffles resulted in heat transfer enhancement as high as300% compared with heat transfer in straight channel with nobaffles and the heat transfer enhancement ratio was found to behigher for taller and thicker porous baffles. Furthermore, Yang andHuang 12 presented a numerical prediction on the turbulent fluidflow and heat transfer characteristics for rectangular channel withporous baffles. They found that, both the solid and porous baffleswalls enhanced the heat transfer relative to the smooth channelwhile the porous baffle channel has a lower friction factor due toless channel blockage.

According to above studies, it can be concluded that withproper selection of governing parameters, significant heat transferaugmentation and pressure drop reduction can be achieved simul-taneously in partially filled porous channels. Therefore, we couldbelieve that the overall heat transfer performance of porous pin finheat exchangers with proper configurations would be better thanthat of traditional solid pin fin heat exchangers. On account of this

1Corresponding author.Contributed by the Heat Transfer Division of ASME for publication in the JOUR-

AL OF HEAT TRANSFER. Manuscript received January 8, 2009; final manuscript re-eived November 7, 2009; published online March 5, 2010. Assoc. Editor: S. A.herif.

ournal of Heat Transfer MAY 2010, Vol. 132 / 051702-1Copyright 2010 by ASMEJian Yang

Min Zeng

Qiuwang Wang1e-mail: [email protected]

State Key Laboratory of Multiphase Flow inPower Engineering,

School of Energy and Power Engineering,Xian Jiaotong University,

Xian, Shaanxi 710049, China

Akira NakayamaDepartment of Mechanical Engineering,

Shizuoka University,3-5-1 Johoku,

Hamamatsu 432-8561, Japan

Forced CEnhancein RectaThe forced convectimerically studied intwo-equation energymedia. Air and wate(Re), pore density (Pproper selection of psure drop reductionsheat transfer perfortraditional solid pinincreases, the pressuoverall heat transfercies are obtained atpin fin form are alstransfer efficienciesare the lowest in the

Keywords: porous psimulation

IntroductionPin fins have a variety of applications in industry due to their

xcellent heat transfer performance, e.g., in cooling of electronicomponents, in cooling of gas turbine blades, and recently, in hotater boilers of central heating systems, etc. 1. In the two early

tudies by Sahiti et al. 2,3, it was demonstrated that pin finrrays offer the most effective way of enhancing the heat transferate within a particular heat exchanger volume. However, theom: http://heattransfer.asmedigitalcollection.asme.org/ on 12/30/2013 Ternvection Heat Transferent by Porous Pin Finsgular Channelseat transfer in three-dimensional porous pin fin channels is nu-s paper. The ForchheimerBrinkman extended Darcy model anddel are adopted to describe the flow and heat transfer in porous

re employed as the cold fluids and the effects of Reynolds numberand pin fin form are studied in detail. The results show that, with

ical parameters, significant heat transfer enhancements and pres-n be achieved simultaneously with porous pin fins and the overallnces in porous pin fin channels are much better than those inn channels. The effects of pore density are significant. As PPIdrops and heat fluxes in porous pin fin channels increase while theciencies decrease and the maximal overall heat transfer efficien-I20 for both air and water cases. Furthermore, the effects of

emarkable. With the same physical parameters, the overall heathe long elliptic porous pin fin channels are the highest while theyort elliptic porous pin fin channels. DOI: 10.1115/1.4000708fin channel, forced convection, heat transfer enhancement, CFD

much lower. Hadim and Bethancourt 6 later studied the similarproblem in a partially filled porous channel. They found that whenthe heat source width was decreased, there was a moderate in-crease in heat transfer enhancement and a significant decrease inpressure drop. Huang and Vafai 7 presented a detailed investi-gation of forced convection in a channel filled with multiple em-placed porous blocks. With comparison of the local Nusselt num-ber distributions between the channel with and without porousblocks, they found that significant heat transfer augmentation canms of Use: http://asme.org/terms

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Downloaded Freason, in our previous study as reported by Yang et al. 13, weerformed a comprehensive numerical study on forced convectioneat transfer in three-dimensional 3D porous pin fin channelsith air as the cold fluid. We found that with the proper selectionf governing parameters, the pressure drops in porous pin finhannels were much lower than those in solid pin fin channelshile the heat fluxes and the overall heat transfer efficiencies wereuch higher. The overall heat transfer efficiencies in long elliptic

orous pin fin channels were the best and the maximal valuesere obtained at K=2107 m2. These findings could be useful

or understanding and optimizing the flow and heat transfer per-ormances in porous pin fin heat exchangers. However, it wasoted that, in our previous study 13, the permeability K andnertial coefficient cF in the momentum equation were modeledith Ergun equation 14 and the volumetric heat transfer coeffi-

ient hv in the energy equation was calculated with Wakao equa-ion 15. This would be reasonable for the flow and heat transfern the packed beds of particles while for the porous media withigh porosity =0.9, such as metal foams, the applicability ofhe Ergun equation and Wakao equation would be questionable.urthermore, in the work of Yang et al. 13, only air was inves-

igated and the performances for other fluids are still unknown,hich would also be important for applications. With these moti-ations in the present study, we further study the forced convec-ion heat transfer in three-dimensional porous pin fin channels andhe performances for both air and water are carefully compared.ccording to the authors knowledge, almost no such attentionsave been paid on this subject before. The Forchheimerrinkman extended Darcy model and two-equation energy modelith more reasonable model parameters K, cF, and hv for porousedia are employed and the effects of Reynolds number, pore

ensity, and pin fin form are studied in detail.

Physical Model and Computational Method2.1 Physical Model and Dimensions. As shown in Fig. 1a,

he physical model is derived from traditional pin fin heat sink,hich generally consists of a bottom wall, two side walls, a topall, and a pin fin array. The bottom wall is hot and its tempera-

ure is kept at Th. The side and the top walls are kept adiabatic.he pin fin array is made of high porosity metal foams alumi-um and arranged in stagger; air and water are used as the colduids. In order to obtain a basic understanding of flow and heat

ransfer performances in porous pin fin heat exchangers, a simpli-

ig. 1 Physical model: a porous pin fin heat sink and bepresentative computational domain

51702-2 / Vol. 132, MAY 2010om: http://heattransfer.asmedigitalcollection.asme.org/ on 12/30/2013 Terfied porous pin fin channel with appropriate boundary conditionsis adopted for the computations, which can be regarded as forcedconvection heat transfer in a partially filled porous channelHadim 5, Huang and Vafai 7, and Yang et al. 13. The com-putational domain is depicted in Fig. 1b, which is composed of adeveloping inlet block L1=10 mm, two pin fin array unit cellsL2=26.52 mm, and a developing outlet block L3=70 mm.The dimensions of the computational domain are L93.04 mmW3.26 mmH10 mm for air and L93.04 mmW3.26mmH2 mm for water, where the channel height H for wa-ter is much lower due to its higher heat transfer capacity. The totalarea of pin fin cross-sections over the base wall area in single pinfin array unit cell is 15%, which is reasonable for industry appli-cations. The temperature and velocity of inlet are kept at Tin anduin, respectively. The bottom wall of pin fin array unit cells is thehot wall and the temperature is kept at Th. Two other bottom wallsand all top walls are kept adiabatic. The symmetry boundary con-ditions are adopted for two side walls and the flow and heat trans-fer of outlet are considered to be fully developed. Furthermore,four different kinds of porous pin fins with circular, cubic, longelliptic, and short elliptic cross-section forms are employed toinvestigate the pin fin configuration effects and the cross-sectionareas of different pin fins are identical with each other Apin=3.14 mm2. The physical dimensions and cross-section forms ofdifferent porous pin fins are presented in Fig. 2.

2.2 Governing Equations and Computational Method. Theflow in the computational domain is considered to be three-dimensional, laminar, incompressible, and steady for both clearfluid and porous regions. For clear fluid region, the flow and heattransfer are modeled with NavierStokes and energy equations.For porous region, the metal foams are assumed to be homoge-neous, isotropic, high porosity =0.9, and high thermal conduc-tivity aluminum: ks=238 W m1 K1. The ForchheimerBrinkman extended Darcy model 16 is adopted to simulate theflow in porous media, where the inertia and viscosity effects areconsidered. Furthermore, the porous matrix is assumed to be inlocal thermal nonequilibrium with fluid phase inside due to theirlarge thermal conductivity difference. Therefore, the two-equationenergy model 16 is employed to account for the heat transferbetween porous matrix and fluid inside. The conservation equa-tions for mass, momentum, and energy are as follows.

Continuity

V = 0 1

Fig. 2 Different forms of porous pin fin cross-section: a cir-cular form, b cubic form, c long elliptic form, and d shortelliptic form

Transactions of the ASMEms of Use: http://asme.org/terms

Momentum

1 f

2

1 f

E

fluid phase: cp fV Tf = kf Tf + hTs T f 3wtphlc

where Pr is the Prandtl number with the definition of Pr=

td

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= 0,z

= 0 porous region,z

=

z= 0,w = 0

he thermal physical quantities of interest in present investigationre the heat flux of the hot wall q, the pressure drop p, theverall heat transfer efficiency , and the heat transfer perfor-ance ratio , which are defined as follows:

q =cp f uin Ain Tout Tin

Ah; p = pin pout; =

q

p

;

=Nuhav,p/Nuhav,s

fp/fs1/36

where Ain is the area of inlet. Ah is the base area of hot wall andTout is the average temperature of outlet. Nuhav is the averageNusselt number of the hot wall. f is the friction factor. The sub-scripts p and s represent values obtained in porous and solid

ournal of Heat Transfer MAY 2010, Vol. 132 / 051702-3 f / k / cp f. f is the kinetic viscosity of fluid and kf is thehermal conductivity of fluid. dp and df are the pore size and fiberiameter of the metal foams, respectively. is the tortuosity of the

oundary conditions

x = 0 Tf = Tin, u = uin, v =

x = LTfx

= 0,u

x=

vx

=

y = 0Tfy

= 00 x L1,L2

Ts = Th porous region

y = HTfy

= 0,Tsy

= 0 poom: http://heattransfer.asmedigitalcollection.asme.org/ on 12/30/2013 TerG = 1 exp 1 /0.04 5

where PPI is the pore density of the metal foams.

= 0

0

L, Tf = ThL1 x L2

u = v = w = 0

s region, u = v = w = 0 Porous region: porous matrix: 0 = 1- ks Ts + hvTf-Ts

here V is the velocity vector. Tf and Ts are the temperatures ofhe fluid and porous matrix, respectively. is the porosity. Theermeability K, Forchheimer coefficient cF, and volumetriceat transfer coefficient hv are calculated with following corre-ations developed from high porosity metal foams by Bhatta-harya et al. 17 and Calmidi and Mahajan 18.

K = 0.00926

1 dp

2

cF = 0.0095 G0.8 3 11.181 3 1G1

hv =3dfG

0.59dp2

kf0.52Pr0.37Vdf/ f0.5df

4porous matrix and G is a shape function that takes into accountthe variation in fiber cross-section with porosity. The definitionsof dp, df, , and G are as follows:

dp = 0.0254/PPI; df = 1.181 3 dpG ;

= 41 1.181 3 1G21;Clear fluid region: V V = Porous region: 12

V V =

nergy

Clear fluid region: cp fV Tf = p + v f V

p +v f2V

v fK

V cF

KVV 2

kf Tfms of Use: http://asme.org/terms

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Table 1 Hot wall heat flux, pressure drop, and overall heattransfer efficiency in circular porous pin fin channel with differ-ent grids =0.9, PPI=30, Tin=293 K, Th=343 K, Pr=0.7, Re=

T

q

Table 2 Computational grids for different pin fin models

Pin fin models Circular Cubic Long elliptic Short elliptic

0

Downloaded Frin fin channels, respectively. The Nusselt number Nuhav andriction factor f are defined as follows:

Nuhav =q D

Th Tin + Tout/2 kf; f = p/L D

1/2 fuin2

7

here D=2H is the hydraulic diameter of inlet.The Reynolds number Re is defined as follows:

Re =uin D f

8

he Darcy Number Da and average Nusselt number Nuav inhe middle section z=0.5W of each heater for model validationssee Figs. 4 and 5 are defined as follows:

Da =KH2

; Nuav = q HThav Tin kfy=0, z=0.5W 9here K is the permeability of porous blocks, H is the channeleight, q is the constant heat flux of each heater, kf is the thermalonductivity of fluid, Tin is the temperature of inlet, and Thav is theverage temperature in the middle section y=0, z=0.5W ofach heater.

The governing equations Eqs. 13 for the computationalomain are solved with commercial code CFX10. The convectiveerm in momentum equations is discretized with high resolutioncheme. The continuity and momentum equations are solved to-ether with coupled solver based on finite control volume methodnd the discrete equations are solved with multigrid acceleratedncomplete lower upper factorization technique CFX 10 19.he user-define expressions for the additional energy equation oforous matrix Ts and source terms of interphase heat transfer inoth energy equations of fluid and porous matrix Tf and Ts, Eq.3 are developed and compiled with CFX expression language.urthermore, the conservative interface flux conditions for mass,omentum, and heat transfer are adopted at the interfaces be-

ween clear fluid and porous regions. For convergence criteria, theelative variations in temperature and velocity between two suc-essive iterations are demanded to be smaller than the previouslypecified accuracy levels of 1.0106.

Grid Independence Test and Model ValidationBefore proceeding further, the grids used for present study are

hecked at first. As shown in Fig. 2a, the circular porous pin finodel is selected for the test and the computational parameters are

ept constant with =0.9, PPI=30, Tin=293 K, Th=343 K, Pr0.7, and Re=2291 Air: uin=2 m s1. In present test, a multi-lock, O-type, structural grid with hexahedral elements is usednd the grid is intensified on solid walls and pin fin regions. Theotal numbers of grid elements vary from 94,809 to 766,080 andhe computational results are presented in Table 1. It shows that,he grid with total element number of 297,864 is good enough forhe test case with the maximal lengths of the grid elements ofeing 0.47 mm for central flow region and 0.1 mm for near wallow region. Therefore, similar grids are finally employed for theollowing studies and the total numbers of grid elements for dif-erent pin fin models are listed in Table 2.

2291otal elements 94,809 297,864 766,080

/kW m2 25.17 25.05 25.02p /Pa 5.59 5.86 5.93/kW m2 Pa1 4.50 4.27 4.22

51702-4 / Vol. 132, MAY 2010om: http://heattransfer.asmedigitalcollection.asme.org/ on 12/30/2013 TerFurthermore, the reliability and accuracy of present computa-tional models and method are validated. According to the authorsknowledge, most studies of forced convection heat transfer in par-tially filled porous channels were based on two-dimensional 2Dmodel and almost no three-dimensional researches have been re-ported on this subject before. Therefore, a two-dimensional simi-lar problem as reported by Hadim 5 see Fig. 3a is finallyselected for the validations. In the present study, the 2D partiallyfilled porous channel 5 is extended along z coordinate withwidth of W=10H and a reasonable 3D physical model is finallyobtained for the computation see Fig. 3b. The 3D partiallyfilled porous channel with dimensions of LHW is equippedwith four porous blocks and each block is heated at bottom withconstant heat flux. The inlet temperature and velocity are keptconstant and all other walls are kept adiabatic. The computationalmodel and method used for this problem are similar to those pre-sented in Sec. 2 and the predicted average Nusselt numbers Nuavin the middle sections y=0, z=0.5W of different heaters arecompared with those as reported in Ref. 5 see Fig. 4. Theaverage deviation of Nuav is 3.5%. This indicates that the compu-tational models and method presented in the present study arereliable and capable of modeling flow and heat transfer phenom-ena in 3D partially filled porous channels.

4 Results and Discussion4.1 Performance Comparison for Solid and Porous Pin

Fin Models. First, the flow and heat transfer performances insolid and porous pin fin channels are compared. The circular pinfin form see Fig. 2a is selected for present study. Air Pr=0.7 and water Pr=3.9 are used as cold fluids and the Reynoldsnumber Re varies from 1000 to 2291 with =0.9, PPI=30,Tin=293 K, and Th=343 K.

The temperature distributions in solid and porous pin fin chan-nels are shown in Fig. 5. It shows that the internal temperatures of

Total elements air 297,864 320,040 298,410 316,512Total elements water 147,920 173,580 179,200 179,120

Fig. 3 Physical models for model validation: a 2D physicalmodel reported in Ref. 5 and b 3D physical model used forpresent computation based on a


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Downloaded Frolid pin fins are quite uniform and the average temperatures areigh, which are 342.0 K for air case and 340.4 K for water case,espectively, while the internal temperatures of porous pin fins areot so uniform and the average temperatures are much lower,hich are 330.1 K for air case and 308.2 K for water case, re-

pectively. However, the fluid temperatures in porous pin fin chan-els are higher than those in solid pin fin channels. The averageuid temperatures in porous pin fin channels are 311.0 K for airnd 297.7 K for water while they are 308.2 K and 296.4 K in solidin fin channels. These results indicate that more heats can beransported away by using porous pin fins and their heat transfererformances would be better. This is because the porous pin finsan greatly enlarge the contact surface areas and mix the fluidow inside, which may lead to significant heat transfer enhance-ents. The velocity vector distributions in solid and porous pin fin

hannels are presented in Fig. 6. It shows that with the sameeynolds number, the fluid velocities in solid pin fin channels areuch higher than those in porous pin fin channels for both air andater cases. Large vortices are formed behind solid pin fins whileo such vortices are found in porous pin fin channels. In solid pinn channels, the solid pin fins are totally impermeable and thisould narrow the flow passages and enhance the flow tortuosities

nside. While in porous pin fin channels, the porous pin fins areermeable and the fluid can flow through them directly. Thisould widen the flow passages and lower the flow tortuosities

nside. Therefore, the flow resistances and pressure drops in po-ous pin fin channels would be lower.

The variations in pressure drop p, hot wall heat flux q,verall heat transfer efficiency , and heat transfer performanceatio with Reynolds number are presented in Fig. 7. It showshat the pressure drops in porous pin fin channels are much lower

ig. 4 Comparison of average Nusselt number of each heaterith Ref. 5

ig. 5 Temperature distributions in solid and circular porousin fin channels =0.9, PPI=30, Re=1000: a solid pin finhannel with air, b porous pin fin channel with air, c solid pinn channel with water, and d porous pin fin channel withater

ournal of Heat Transferom: http://heattransfer.asmedigitalcollection.asme.org/ on 12/30/2013 Terthan those in solid pin fin channels 36.9% lower for air and 9.5%lower for water at Re=2291, see Fig. 7a while the heat fluxes inporous pin fin channels are much higher than those in solid pin finchannels 38.6% higher for air and 45.7% higher for water atRe=2291, see Fig. 7a. Therefore, the overall heat transfer effi-ciencies in porous pin fin channels are much higher 119.5%higher for air and 37.9% higher for water at Re=2291, see Fig.7b. It is also obvious that as Re increases from 1000 to 2291, all

Fig. 6 Velocity vector distributions in solid and porous pin finchannels =0.9, PPI=30, Re=1000: a solid pin fin channelair: y=5 mm, b porous pin fin channel air: y=5 mm, csolid pin fin channel water: y=0.5 mm, and d porous pin finchannel water: y=0.5 mm

Fig. 7 Variations in pressure drop, hot wall heat flux, overallheat transfer efficiency, and heat transfer performance ratiowith Re in solid and porous pin fin channels =0.9, PPI=30:a pressure drop and hot wall heat flux and b overall heattransfer efficiency and heat transfer performance ratio

MAY 2010, Vol. 132 / 051702-5ms of Use: http://asme.org/terms

tuwppaptamFancoreidwjtFfit

pcc

crtaaar=

o

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Table 3 Characteristics of metal foams

Sample PPI dp /m df /m K /m2 cf ks /W m1 K1

1010101010

0

Downloaded Frhe values of heat transfer performance ratios are larger thannit for both air and water cases see Fig. 7b, which means thatith the same pumping powers, the heat transfer performances inorous pin fin channels are also much better than those in solidin fin channels. These results are consistent with the formernalysis of temperature and flow variations, which confirms theoint that with proper selection of physical parameters, the heatransfer augmentations and flow resistance reductions can bechieved simultaneously and the overall heat transfer perfor-ances will be significantly improved by using porous pin fins.urthermore, it can be found that with different fluids, the flownd heat transfer performances are different. With the same Rey-olds number, the pressure drops and heat fluxes in porous pin finhannels for water are much higher than those for air while theverall heat transfer efficiencies and heat transfer performanceatios are much lower. Due to the intrinsic thermophysical differ-nces between air and water, the viscosity and heat transfer capac-ty of water are much higher, which would lead to higher pressurerops and heat fluxes. However, due to the same reasons, whenater is used as cold fluid, most heats will be transported away

ust through the lower parts of the porous pin fins and the heatransfers in the upper parts of the porous pin fins are inactive seeig. 5d. Therefore, the overall utilization ratios of the porousns are low for water, which would lead to lower overall heat

ransfer efficiencies and heat transfer performance ratios.

4.2 The Effect of Pore Density. In this section, the effect ofore density PPI for different metal foams is investigated. Theircular pin fin form see Fig. 2a is selected again for presentomputations. Both air Pr=0.7 and water Pr=3.9 are used asold fluids. In the present study, five different kinds of high po-osity metal foams with 20PPI40 are selected for the compu-ations, which are similar to those as studied by Bhattacharya etl. 17 and Calmidi and Mahajan 18. These metal foams wouldlso be common in industry applications and their characteristicsre presented in Table 3. Furthermore, besides PPI, the other pa-ameters are kept at constant with =0.9, Tin=293 K, Th343 K, and Re=2291.The variations in pressure drop p, hot wall heat flux q, and

verall heat transfer efficiency with pore density PPI areresented in Fig. 8. It shows that, as PPI increases from 20 to 40,he pressure drops and heat fluxes in porous pin fin channels in-rease for both air and water cases while the overall heat transferfficiencies decrease. This is because, as PPI increases, the per-eability K decreases rapidly and the viscosity effects inside

orous media increase, which would lead to increases in pressurerops. Meanwhile, as PPI increases, the solid-fluid interfacial sur-ace areas inside porous media also increase quickly and the volu-etric heat transfer coefficient hv between porous matrix anduid phase increases, which would lead to increases in heat fluxes.s PPI increases from 20 to 40, the pressure drops in the porousin fin channels increase by 52.9% and 24.2% for air and water,espectively, and the corresponding heat fluxes increase by 15.6%nd 21.1%. It is obvious that the increase rates of pressure dropsre much higher than those of heat fluxes, especially when air issed as cold fluid. Therefore, as PPI increases, the overall heatransfer efficiencies decrease. Furthermore, with different poreensities 20PPI40, the pressure drops in porous pin fin

1 0.9 20 1.3103 1.72 0.9 25 1.0103 1.33 0.9 30 8.5104 1.14 0.9 35 7.3104 9.65 0.9 40 6.4104 8.4

51702-6 / Vol. 132, MAY 2010om: http://heattransfer.asmedigitalcollection.asme.org/ on 12/30/2013 Terchannels are lower than those in solid pin fin channels 50.5%lower for air and 20.2% lower for water at PPI=20 while the heatfluxes in porous pin fin channels are higher 23.4% higher for airand 30.1% higher for water at PPI=20. Therefore, the overallheat transfer efficiencies in porous pin fin channels are muchhigher and their maximal values are obtained at PPI=20, whichare 149.2% and 63.1% higher than those in solid pin fin channelsfor air and water cases, respectively. These results indicate thatwith proper selection of pore density, the flow and heat transferperformances in porous pin fin channels will be improved.

4.3 The Effect of Porous Pin Fin Form. Finally, the effect ofporous pin fin form is examined. Four different kinds of porouspin fins are compared here, including circular, cubic, long elliptic,and short elliptic cross-section forms see Fig. 2. Air Pr=0.7and water Pr=3.9 are used as cold fluids and the Reynolds num-ber Re varies from 1000 to 2291 with =0.9, PPI=40, Tin=293 K, and Th=343 K.

The temperature distributions in different porous pin fin chan-nels are presented in Figs. 9 and 10. It shows that, the temperaturedistributions in circular and cubic porous pin fin channels aresimilar while they are quite different in long elliptic and shortelliptic porous pin fin channels for both air and water cases. Theaverage temperatures of air are 311.09 K, 311.30 K, 307.07 K, and316.18 K in circular, cubic, long elliptic, and short elliptic porouspin fin channels, respectively, and they are 298.13 K, 298.11 K,297.75 K, and 298.50 K for water, respectively. It is obvious that,the average temperatures of air and water in short elliptic porouspin fin channels are the highest and they are the lowest in longelliptic porous pin fin channels. The flows in short elliptic porouspin fin channels are intensively mixed and most of the fluids in thechannels, including central flow regions, have taken part in heattransfer actively while in long elliptic porous pin fin channels, the

4 7.91108 0.102 2384 5.06108 0.102 2384 3.51108 0.102 2385 2.58108 0.102 2385 1.98108 0.102 238

Fig. 8 Variations in pressure drop, hot wall heat flux, and over-all heat transfer efficiency with pore density =0.9, Re=2291


fltcta

o

snpebaha

ip2tpfi

5

pwn

Fccp

Fclfi

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Downloaded Frows are less mixed, the central flow regions are almost not dis-urbed. Therefore, the heat transfers in short elliptic porous pin finhannels would be the highest. However, with the same reasons,he pressure drops in short elliptic porous pin fin channels wouldlso be the highest.

The variations in pressure drop p, hot wall heat flux q, andverall heat transfer efficiency with Reynolds number are pre-ented in Figs. 11 and 12. It shows that with the same Reynoldsumber, the pressure drops and heat fluxes in short elliptic porousin fin channels are the highest and they are the lowest in longlliptic porous pin fin channels. The differences in pressure dropsetween each other are 95.9% and 48.7% for air and water casest Re=2291, respectively, and the corresponding differences ineat fluxes are 60.6% and 14.3%. However, the variations in over-ll heat transfer efficiencies are reverse, which are the highestn long elliptic porous pin fin channels and lowest in short ellipticorous pin fin channels and the differences between each other are1.9% and 30.1% for air and water cases at Re=2291, respec-ively. These results indicate that, with proper selection of porousin fin forms, the overall heat transfer performances in porous pinn channels will be greatly improved and optimized.

ConclusionsThe forced convective heat transfer in three-dimensional porous

in fin channels is numerically studied in this paper. Both air andater are used as the cold fluids and the effects of Reynoldsumber, pore density, and pin fin form are carefully investigated.

ig. 10 Temperature distributions in different porous pin finhannels with water =0.9, PPI=40, Pr=3.9, Re=1000 a cir-ular pin fin channel, b cubic pin fin channel, c long ellipticin fin channel, and d short elliptic pin fin channel

ig. 9 Temperature distributions in different porous pin finhannels with air =0.9, PPI=40, Pr=0.7, Re=1000: a circu-

ar pin fin channel, b cubic pin fin channel, c long elliptic pinn channel, and d short elliptic pin fin channel

ournal of Heat Transferom: http://heattransfer.asmedigitalcollection.asme.org/ on 12/30/2013 TerThe flow and heat transfer performances in porous pin fin chan-nels are also compared with those in traditional solid pin fin chan-nels in detail. The major findings are as follows.

1 With proper selection of metal foams, such as PPI=30, sig-nificant heat transfer enhancements and pressure drop re-ductions can be achieved simultaneously by using porouspin fins for both air and water cases, and the overall heattransfer efficiencies in porous pin fin channels are muchhigher than those in solid pin fin channels, which are119.5% and 37.9% higher for air and water cases at Re=2291, respectively.

Fig. 12 Variations in pressure drop, hot wall heat flux andoverall heat transfer efficiency with Re in different porous pinfin channels =0.9, PPI=40, Pr=3.9

Fig. 11 Variations in pressure drop, hot wall heat flux andoverall heat transfer efficiency with Re in different porous pinfin channels =0.9, PPI=40, Pr=0.7

MAY 2010, Vol. 132 / 051702-7ms of Use: http://asme.org/terms

2 The effects of pore density are significant. As pore densityincreases from 20 to 40, the maximal overall heat transferefficiencies are obtained at PPI=20 for both air and watercases, which are 149.2% and 63.1% higher than those insolid pin fin channels at Re=2291, respectively.

3 The effects of pin fin form are also remarkable. With samephysical parameters, the pressure drops and heat fluxes arethe highest in short elliptic porous pin fin channels andlowest in long elliptic porous pin fin channels while theoverall heat transfer performances are the highest in longelliptic porous pin fin channels and lowest in short ellipticporous pin fin channels. The differences in overall heattransfer efficiencies between each other are 21.9% for air

A

p

N

G

heat transfer performance ratio, Eq. 6 kinetic viscosity m2 s1 density kg m3 porosity tortuosity of porous matrix, Eq. 5

Subscriptsf fluid phase, fiberh hot wall

hav average value of each heaterin inlet

out outletp value obtained in porous pin fin channel

0

Downloaded Frcase and 30.1% for water case at PPI=40 and Re=2291,respectively.

cknowledgmentWe would like to acknowledge financial support for this work

rovided by the National Natural Science Foundation of ChinaGrant No. 50821064.

omenclatureA area m2

cF Forchheimer coefficient, Eq. 4cp specific heat at constant pressure J kg1 K1D hydraulic diameter of inlet m

Da Darcy number, Eq. 9df fiber diameter of metal foam mdp pore size of metal foam m

f friction factor, Eq. 7G shape function for metal foam, Eq. 5H channel height mhv volumetric heat transfer coefficient, Eq. 4

W m3 K1K permeability, Eq. 4 m2k thermal conductivity W m1 K1L total channel length m

L1 length of developing inlet block mL2 length of hot wall mL3 length of developing outlet block m

Nuav average Nusselt number, Eq. 9Nuhav average Nusselt number of hot wall, Eq. 8

p pressure PaPPI pore density

Pr Prandtl numberq heat flux of hot wall, Eq. 6 W m2

q constant heat flux of each heater, Eq. 9Re Reynolds number, Eq. 8

T temperature Ku ,v ,w velocity in x, y, z directions m s1

V velocity vector m s1W channel width m

x ,y ,z coordinate directions m

reek Symbols overall heat transfer efficiency, Eq. 6

W m2 Pa1

51702-8 / Vol. 132, MAY 2010om: http://heattransfer.asmedigitalcollection.asme.org/ on 12/30/2013 Terpin pin fin cross-sections solid phase, value obtained in solid pin fin

channel

References1 Sahiti, N., Lemouedda, A., Stojkovic, D., Durst, F., and Franz, E., 2006, Per-

formance Comparison of Pin Fin In-Duct Flow Arrays With Various Pin Cross-Sections, Appl. Therm. Eng., 26, pp. 11761192.

2 Sahiti, N., Durst, F., and Dewan, A., 2005, Heat Transfer Enhancement by PinElements, Int. J. Heat Mass Transfer, 48, pp. 47384747.

3 Sahiti, N., Durst, F., and Dewan, A., 2006, Strategy for Selection of Elementsfor Heat Transfer Enhancement, Int. J. Heat Mass Transfer, 49, pp. 33923400.

4 Jiang, P. X., Li, M., Lu, T. J., Yu, L., and Ren, Z. P., 2004, ExperimentalResearch on Convection Heat Transfer in Sintered Porous Plate Channels, Int.J. Heat Mass Transfer, 47, pp. 20852096.

5 Hadim, A., 1994, Forced Convection in a Porous Channel With LocalizedHeat Sources, ASME J. Heat Transfer, 116, pp. 465472.

6 Hadim, A., and Bethancourt, A., 1995, Numerical Study of Forced Convec-tion in a Partially Porous Channel With Discrete Heat Sources, ASME J.Electron. Packag., 117, pp. 4651.

7 Huang, P. C., and Vafai, K., 1994, Analysis of Forced Convection Enhance-ment in a Channel Using Porous Blocks, J. Thermophys. Heat Transfer, 8,pp. 563573.

8 Huang, P. C., Yang, C. F., Hwang, J. J., and Chui, M. T., 2005, Enhancementof Forced-Convection Cooling of Multiple Heated Blocks in a Channel UsingPorous Covers, Int. J. Heat Mass Transfer, 48, pp. 647664.

9 Fu, W., Huang, H., and Lion, W., 1996, Thermal Enhancement in LaminarChannel Flow With a Porous Block, Int. J. Heat Mass Transfer, 39, pp.21652175.

10 Ould-Amer, Y., Chikh, S., Bouhadef, K., and Lauriat, G., 1998, Forced Con-vection Cooling Enhancement by Use of Porous Materials, Int. J. Heat FluidFlow, 19, pp. 251258.

11 Ko, K. H., and Anand, N. K., 2003, Use of Porous Baffles to Enhance HeatTransfer in a Rectangular Channel, Int. J. Heat Mass Transfer, 46, pp. 41914199.

12 Yang, Y. T., and Hwang, C. Z., 2003, Calculation of Turbulent Flow and HeatTransfer in a Porous-Baffled Channel, Int. J. Heat Mass Transfer, 46, pp.771780.

13 Yang, J., Zeng, M., and Wang, Q. W., 2008, Numerical Study on ForcedConvective Heat Transfer in Porous Pin Fin Channels, ASME Paper No.HT2008-56216.

14 Ergun, S., 1952, Fluid Flow Through Packed Columns, Chem. Eng. Prog.,48, pp. 8994.

15 Wakao, N., and Kaguei, S., 1982, Heat and Mass Transfer in Packed Beds,McGraw-Hill, New York.

16 Nield, D. A., and Bejan, A., 2006, Convection in Porous Media, 3rd ed.,Springer, New York.

17 Bhattacharya, A., Calmidi, V. V., and Mahajan, R. L., 2002, ThermophysicalProperties of High Porosity Metal Foams, Int. J. Heat Mass Transfer, 45, pp.10171031.

18 Calmidi, V. V., and Mahajan, R. L., 2000, Forced Convection in High Poros-ity Metal Foams, ASME J. Heat Transfer, 122, pp. 557565.

19 CFX Inc., 2005, User Guide, CFX 10.
