-
omn
ve hthimo
r aPI)hysca
mafi
reeffiPP
o rin t
sh
in
1
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
flbuficrfiHptmwwet
be achieved through the emplacement of porous blocks. Huang
etal. 8 later presented a similar investigation in cooling of
multiple
NcS
J
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
-
rphwocwmpwffn
iwc
tihtFtwvttAhBwmd
2
twwtTnflt
Fr
0
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
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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
B
w
w
x=
x
,
rou
Tf Ts u v
Ta
o
m
J
Downloaded Frz = 0,Wz
= 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
-
pf
w
Tt
whca
e
dtsgaiTpbFmtrcs
3
cmk=
battttbflff
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:
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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
Transactions of the ASMEms of Use: http://asme.org/terms
-
shrnwsnflaptpcflmcRmwnfiwipwir
o
r
t
Fw
Fpcfiw
J
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:
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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
ptcem
pdfm
flApraautd
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:
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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
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fltcta
o
snpebaha
ip2tpfi
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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
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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
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