Materials Transactions, Vol. 47, No. 9 (2006) pp. 2240 to 2247
Special Issue on Porous and Foamed Metals —Fabrication, Characterization, Properties and Applications—
#2006 The Japan Institute of Metals
Development of Lotus-Type Porous Copper Heat Sink
Tetsuro Ogushi1 , Hiroshi Chiba1 and Hideo Nakajima2
1
Mechanical Technology Department, Advanced Technology R&D Center, Mitsubishi Electric Corporation,
Amagasaki 661-8661, Japan
2
The Institute of Scientific and Industrial Research, Osaka University, Ibaraki 567-0047, Japan
Lotus-type porous copper with many straight pores is produced by precipitation of supersaturated gas when the melt dissolving gas is
solidified. Lotus-type porous copper is attractive as a heat sink because a higher heat transfer capacity is obtained as the pore diameter decreases.
The main features of lotus-type porous metals are as follows; (1) the pores are straight, (2) the pore size and porosity are controllable, and
(3) porous metals with pores whose diameter is as small as ten microns can be produced. We developed a lotus-type porous copper heat sink for
cooling of power devices. Firstly we investigated the effective thermal conductivity of the lotus copper, considering the pore effect on heat flow.
Secondly, we investigated a straight fin model for predicting the heat transfer capacity of lotus copper. Finally, we examined experimentally and
analytically determined the heat transfer capacities of three types of heat sink with conventional groove fins, with groove fins having a smaller fin
gap (micro-channels) and with lotus-type porous copper fins. The lotus-type porous copper heat sink were found to have a heat transfer capacity
4 times greater than the conventional groove heat sink and 1.3 times greater than the micro-channel heat sink at the same pumping power.
[doi:10.2320/matertrans.47.2240]
(Received February 28, 2006; Accepted May 22, 2006; Published September 15, 2006)
Keywords: porous media, lotus-type porous copper, effective thermal conductivity, fin efficiency, heat transfer capacity, heat sink
1.
Introduction
105
Maximum evaporation rate
104
LSI
IGBT
Insulated gate
bipolar transistor
LD
Laser diode
HBT
Heterojunction
bipolar transistor
Heat Flux F/ W·cm-2
In recent years, heat dissipation rates in power devices and
laser diodes have been increasing to more than 100 W/cm2
and in high frequency electronic devices it is increasing to
more than 1000 W/cm2 under the trend of miniaturization
and growing capacity. Figure 1 shows typical cooling loads
and cooling technologies by Nishio.1) When the heat flux
increases, the temperature increases. A heat flux of 100 W/
cm2 is as high as an equivalent heat flux from nuclear blast at
2000 K. But a power device or a laser diode should be kept at
normal temperature level in spite of a large heat flux of more
than 100 W/cm2 . So, novel heat sinks with high heat transfer
performance are required to cool these devices. Among
various types of heat sinks, heat sinks utilizing microchannels with channel diameters of several tens of microns
are expected to have excellent cooling performance because a
higher heat transfer capacity is obtained with smaller channel
diameters.
A milestone in the development of the micro-channel heat
sinks is the work of Tuckerman and Pease.2) They fabricated
50 mm wide channels and 50 mm wide walls by etching to a
depth of about 300 mm in silicon wafers of thickness 400 mm.
Deionized water at approximately 296 K was fed into the
micro-channels. The micro-channel heat sink was capable of
dissipating 790 W/cm2 with a maximum substrate temperature rise of 71 K and a pressure drop of 220 kPa for a water
flow rate of 0.52 L/min. They demonstrated a thermal
resistance less than 0.1 K/W for a 1 cm2 heating area that
corresponds to a heat transfer coefficient hi , derived from net
heat input, base area and base plate mean temperature rise
from water inlet, of more than 100 kW/(m2 K). Following
this work, many experimental and theoretical studies of
micro-channel heat sinks have been carried out.3–6)
To enhance the cooling performance of heat sinks with
micro-channels, Wei and Joshi7) numerically investigated
three-dimensional stacked micro-channel heat sinks. A heat
Ballistic
Entry
Rocket
nozzle throat
Nuclear blast
103
CHF of water
LWR
102
Reentry from earth orbit
Air cooling
(Hydraulic diameter 5mm,
Air velosity 20m/s)
101
Rocket
motor case
100
Solar heating
10-1
Air conditioning
10-2
0
500 1000 1500 2000 2500 3000 3500 4000
Temperature, T / K
Fig. 1 Typical cooling loads and cooling technology.1)
sink of base area 10 mm by 10 mm with a height in the range
1.8 to 4.5 mm (2–5 layers) was considered for water flow rate
in the range 50 to 400 cm3 /min. For a single-layered water
cooled silicon structure, with water properties at 298 K and
channel width 75 mm, fin width 75 mm, channel depth 426 mm,
channel length 10 mm, the calculated thermal resistance is
0.12 Kcm2 /W (hi ¼ 83 kW/(m2 K)) under a pressure drop
of 50 kPa. For a two-layer water-cooled silicon heat sink at
exactly the same condition, the calculated thermal resistance
was 0.082 Kcm2 /W (hi ¼ 122 kW/(m2 K)). The thermal
resistance decreased as the number of layers increased. The
thermal resistance of a double-layer micro-channel was
almost half that of a single layer case for a fixed pressure drop
(P ¼ 10 kPa). For a fixed pumping power, the thermal
resistance of the multi-layered heat sink was also less than
that of the single-layered case. The effect of decreasing heat
transfer coefficients due to lower velocity was dominated by
the increasing surface area. They concluded that materials
Development of Lotus-Type Porous Copper Heat Sink
with a high thermal conductivity such as copper should be
used to improve the thermal performance of the microchannel stack.
Instead of three-dimensional stacked micro-channels,
Zhang et al.8) investigated a straight-circular-duct porous
heat sink experimentally and theoretically. The porous heat
sink fabricated by uniformly drilling 5 13 circular ducts in
a rectangular aluminum alloy block, was 60 mm long,
31.2 mm wide and 12 mm high. The diameter of each duct
was 1.5 mm. Heating power input was varied from 40 to
130 W and water flow rate from 70 to 7900 cm3 /min. The
heat transfer coefficient hi ranged from 2.1 to 16.4 kW/
(m2 K). The results were much less than the heat transfer
coefficients for micro-channels by Tuckerman and Pease.2)
They predicted heat transfer coefficients from 50 to 390 kW/
(m2 K) under reduced unit cell dimensions of 100 mm
hydraulic diameter.
As for porous heat sinks characterized by straight circular
ducts, Bower et al.9) used multiple rows of parallel channels
made of silicon carbide (SiC) oriented in the flow direction.
The heat sinks were manufactured using an extrusion
freeform fabrication (EFF) rapid prototyping technology
and a water-soluble polymer material. Silicon carbide has a
thermal expansion coefficient closely matched to that of
silicon, allowing the heat sink to be more easily integrated
directly into the electronic package. Test were performed on
six samples each measuring 32 mm 22 mm in platform area
with varying thickness 2.8–11.8 mm, number of channels 6–
155, channel diameter 0.335–2.03 mm and number of
channel rows 1–11. Overall thermal resistance Rb;i that was
derived from net heat input and base plate mean temperature
rise from water inlet was dropped for an increase in mass flow
rate and for an increase in number of rows. Thermal
resistance ranged from 0.27 to 0.39 K/W, corresponding to
a heat transfer coefficient hi from 1.8 to 2.6 kW/(m2 K) for
channel diameter of 2.03 mm and 7 channel rows for varying
flow rate from 50 to 500 cm3 /min.
Porous materials are considered preferable for threedimensional micro channels based on foam metal as a heat
transfer medium. Zhang et al.10) investigated the fluid flow
and heat transfer characteristics of liquid cooled foam heat
sinks (FHSs). Copper metallic foam blocks with a size of
13 mm 12:2 mm 2 mm were used for the fabrication of
the FHSs. The pressure drops and thermal resistance of opencelled copper foam materials with pore densities of 60 and
100 PPI (pore per inch) and four porosities varying from 0.6
to 0.9 were obtained. A representative unit cell has an
approximate shape of a dodecahedron. The scale of the unit
cell consisting of a representative pore together with its fiber
struts is 0.42 mm. For a given coolant flow-rate, the FHS with
the lowest porosity of 0.6 gave the lowest thermal resistance
and highest pressure drops for both pore densities. In
addition, the FHSs were compared with a micro-channel
heat sink with a similar finned area of 12:2 mm 15 mm and
the same channel height of 2 mm and width of 0.2 mm. At
given pressure drop and pump power, the thermal resistance
of the FHS with a porosity of 0.8 and pores density of 60 PPI
was the lowest among all the FHSs and was comparable to
that of the micro-channel heat sink. The thermal resistance
0.1 of the FHS with a porosity of 0.8 and pores density of
2241
60 PPI at the flow rate 1 L/min corresponded to the heat
transfer coefficient hi of 63 kW/(m2 K).
Jiang et al.11) investigated small-scale micro-channel and
porous-media heat exchangers made of copper plates and
copper particles. In general, micro-channels can be manufactured on sheet surfaces using either X-ray lithography
(LIGA), silicon chemical etching, precision mechanical
sawing techniques or wire machining. They fabricated
micro-channel heat exchangers from 0.7 mm thick pure
copper plates on a wire-cutting machine. The width and
height of the channels were 0.2 and 0.6 mm, respectively.
The width of the fins between channels was 0.2 mm and the
active length of the channels was 15 mm with 38 channels per
sheet. Thirty sheets 21 mm wide were stacked and soldered
with tin. The area density was 2895 m2 /m3 . The microporous heat exchanger was also fabricated from 0.7 mm thick
pure copper plates by a wire-cutting machine. The average
particle diameter was 0.272 mm and the porosity was 0.47.
The area density was 5011 m2 /m3 . Over the range of test
conditions, the maximum volumetric heat transfer coefficient
of the micro-heat-exchanger using porous media was 86.3
MW/(m3 K) for a water flow rate of 4.02 L/min and a
pressure drop of 470 kPa. The maximum volumetric heat
transfer coefficient of the micro-heat-exchanger using microchannels was 38.4 MW/(m3 K) with a corresponding water
flow rate of 20.4 L/min and a pressure drop of 70 kPa. It was
concluded that the micro-heat-exchanger using micro-channels was better than porous media by considering both the
heat transfer and pressure drop characteristics of these heatexchangers.
Among porous materials such as sintered porous metal,
cellular metal and fibrous composite, lotus-type porous metal
with straight pores is preferable for heat sinks due to the
small pressure drop of cooling water flowing through the
pores.
In this work, we investigated water-cooled heat sinks
utilizing lotus-type porous copper as micro-channel fins,
noted as lotus copper heat sink (LCHS) in Fig. 2. The power
chips are cooled by flowing water through the pores in the
LCHS. The lotus-type porous copper is made of copper with
many straight pores that are formed by precipitation of
supersaturated gas dissolved in the melted copper during
solidification. Such lotus-type porous metals can be fabri-
Lotus copper
1 mm
Chips
Lotus copper
Container
Cooling water
Fig. 2
Lotus copper heat sink (LCHS) utilizing lotus-type porous copper.
2242
T. Ogushi, H. Chiba and H. Nakajima
Pressure regulation screw
Load cell
Heater
30
30
ε =0.43,
25
dpmax =0.17mm,
20
dpmin
=0.02mm,
15
dpmean
=0.08mm
10
30
40
0.
35
0.
30
0.
25
0.
20
0.
15
10
Test apparatus for measuring effective thermal conductivity.
0.
Fig. 3
0.
0
00
Cooling water
0.
φ 30
05
5
0.
Thermal
insulator
Copper
Block
Specimen
30 5
Distribution (%)
35
Pore diameter, dp / mm
2.
Effective Thermal Conductivity of Lotus Copper
For the design of heat sinks using lotus-type porous
copper, it is necessary to introduce the fin model of the lotus
copper. So, it is crucial to know the effective thermal
conductivity of the lotus copper, considering the pore effect
on heat flow. Behrens13) investigated the effective thermal
conductivities of composite materials analytically and proposed a simple equation for predicting the effective thermal
conductivity. Han and Cosner14) conducted a numerical
investigation into the effective thermal conductivities of
fibrous composites.
In previous work,15) we applied the following Behrens’s
analytical eq. (1) to the effective thermal conductivity of
lotus copper perpendicular to the pore axis and compared
these results with the experimental data which were
measured by the experimental apparatus shown in Fig. 3.
The temperature of the lotus copper was kept around 50 C.
The specimens’ porosity varied between 0.24 and 0.43.
Figure 4 shows a typical distribution of pore diameters. As
Fig. 4
Distribution of pore diameters in a specimen.
1.2
Experimental data
Analytical prediction
1
0.8
k s =335 W/(m·K)
keff⊥ / ks
cated by means of the Czochralski casting method and a zone
melting method.12) The main features of lotus-type porous
metals are as follows; (1) the pores are straight, (2) the pore
size and porosity are controllable, and (3) porous metals with
pores whose diameter is as small as ten microns can be
produced.
In the present work, we firstly investigated the effective
thermal conductivity of the lotus copper, considering the pore
effect on heat flow. Secondly, we investigated a straight fin
model for predicting the heat transfer capacity of lotus copper
heat sink (LCHS). Finally, we examined experimentally and
analytically determined the heat transfer capacities of three
types of heat sink with conventional groove fins, with groove
fins having a smaller fin gap (micro-channels) and with lotustype porous copper fins.
0.6
0.4
keff ⊥
0.2
ks
=
1− ε
---(1)
1+ε
0
0
0.2
0.4
0.6
0.8
1
Porosity ε
Fig. 5 Comparison of effective thermal conductivity of lotus copper
perpendicular to pores between eq. (1) and experimental data.
the diameters of the pores were distributed around a certain
range, the maximum diameter dpmax , the minimum diameter
dpmin and the mean diameter dpmean are noted in Fig. 4.
The experimental data on the thermal conductivity of lotus
copper perpendicular to the pore axis keff? showed good
agreement with the Behrens equation as shown in Fig. 5.
keff? 1 "
¼
1þ"
ks
ð1Þ
where, keff? , ks and " are the effective thermal conductivity
of the lotus copper perpendicular to the pores, the thermal
conductivity of the base material and the porosity, respectively.
Development of Lotus-Type Porous Copper Heat Sink
Q
2243
dp/2
Q
Q
dp/2
3
y
2
Thermal
conductivit
y
ks
Effecive
thermal
conductivity
k eff⊥
.
Hf
y
dp
y
Outer
surface
area
ζ . Pr
t
(a) Straight fin model
y
dp/2
3
y
2
dp/2
dp/2
Fig. 7
Analysis of Fin Efficiency
3.1 Straight fin model
In order to predict the heat transfer capacity of LCHS, it is
necessary to consider the heat conduction in the porous metal
and the heat transfer to the fluid in the pores. The heat transfer
capacity of the straight heat sink is generally expressed by a
straight fin model, in which the heat from the top surface
flows downward by heat conduction in the fin transferring the
heat to the fluid from the fin surface along the way. The lotus
copper is modeled as a straight fin as shown in Fig. 6(a). In
the lotus-type porous copper heat sink, the heat is also input
from the top surface and flows downward by conduction,
with the heat transferred to the fluid in the pores along the
way as shown in Fig. 6(b). The heat transfer rate Q under
temperature difference T between the top surface of the fin
and the fluid in the pores is calculated from eq. (2),
ð2Þ
where is the fin efficiency, S f is the total surface area of the
pores and h is the heat transfer coefficient in the pores.
In the straight fin, the fin efficiency is expressed as the
following equations:
tanhðm H f Þ
m Hf
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
h & Pf
m¼
keff? Ac
¼
Hf
dp/2
t
x
(b) Lotus copper fin
Q ¼ h S f T
y
dp/2
Fig. 6 Analytical fin model: (a) straight fin model, (b) lotus copper fin
model.
3.
y
dp/2
dp/2
Pf (=2(x+t))
x
dp/2
dp/2
A c (=2 x t)
Hf
y
ð3Þ
ð4Þ
where H f is the fin height, keff? is the effective thermal
conductivity perpendicular to the pore axis and P f is the
peripheral length of the fin. Furthermore Ac is the crosssectional area of the fin, while is the ratio between the total
y
x
Numerical model to predict fin efficiency.
surface area of the lotus copper S f and the total surface area
of the straight fin P f H f , which can be expressed as the
following,
&¼
Sf
Pf Hf
ð5Þ
3.2 Numerical analysis
In order to verify the efficiency of the straight fin model,
we conducted a numerical analysis to predict the fin
effectiveness. The numerical model of the lotus copper is
shown in Fig. 7.
The mean temperature difference T between the top
surface of the fin model and the surrounding temperature Ts
in the pores were calculated using the finite differential
method under the following boundary conditions: uniform
heat input Q at the top surface, uniform heat transfer
coefficient h in the pores, a constant surrounding temperature
Ts and symmetry along lateral walls.
In the calculation, the spacing of pores ðx; yÞ and h were
changed under the conditions of pore diameter dp of 200 mm
and a material thermal conductivity ks of 400 W/(mK).
A comparison of the fin efficiency between the numerical
results and results from eq. (3) is shown in Fig. 8. Equation (3) showed good agreement with the numerical simulation; therefore, the fin efficiency of the lotus fin was
verified to be predictable by eq. (3) derived from the straight
fin model.
2244
T. Ogushi, H. Chiba and H. Nakajima
1
Lotus type porous copper fin
(dp = 0.3mm, ε = 0.39)
Numerical prediction
Analytical prediction
Fin Efficiency, ηf
0.8
0.7
Flow direction
3 mm 5.5 mm
Hf =9 mm
0.9
pore
0.6
0.5
20 mm
30 mm
0.4
0.3
Fig. 10 Lotus type porous copper heat sink.
0.2
0.1
0
0
1
2
m .Hf
3
4
Temperature measure points
Pressure measure points
5
Heater
Fig. 8 Comparison of fin efficiency between numerical and analytical
prediction from eq. (3).
Thermal
insulator
Mesh
Heat sink
Test duct
Flow direction
ft
fg
Tb
Heating block
Copper base
To
Ti
5
Length
= 20mm
Cooling water flow direction
Hf
5
20 mm
30 mm
Filter
5
duct
Circulator
(pump and
water cooler)
Flow meter
Fig. 9
Table 1
Conventional groove fins and micro-channels.
Specification of conventional groove fins and micro-channels.
Fin gap
fin tichkness
Fin Height
fg /mm
ft /mm
H f /mm
Investigation
Conventional
groove fins
3
1
9
Calc.
Micro-channels
0.5
0.5
9
Calc. & measured
4.
Fig. 11 Schematic of experimental apparatus for measuring heat transfer
capacity.
Heating Block
Copper base
Heat Transfer Capacity and Pressure Drop of Heat
Sinks
4.1 Investigated heat sinks
We examine the heat transfer capacity of three types of
heat sink, namely-(i) with conventional groove fins, (ii)
groove fins with smaller fin gaps (micro-channel) and (iii)
lotus-type porous copper. The configuration and the specifications of the conventional groove fins and micro-channels
are shown in Fig. 9 and Table 1. The conventional groove
fins have a fin gap of 3 mm and a fin thickness of 0.5 mm. The
micro-channels have a fin gap of 0.5 mm and a fin thickness
of 0.5 mm. The heat transfer capacity of the conventional
groove fins is only derived from calculation.
Figure 10 shows the configuration of the lotus-type porous
copper heat sink, which features three lotus copper fins with
lengths of 3 mm along the flow direction. The lotus-type
porous copper fins have pores with a mean diameter of 0.3
mm and a porosity of 0.39.
4.2 Experimental method
Figures 11 and 12 show the schematic and outer view of
the experimental apparatus for measuring the heat transfer
Test duct
Pressure taps
Duct
Fins
Fig. 12 Outer view of experimental apparatus.
capacity of heat sink. Cooling water was circulated through a
filter and the test duct in which the heat sink is located. The
circulator has a pump and a water cooler. The heat sink itself
consists of fins that are brazed on one side of a copper base
Development of Lotus-Type Porous Copper Heat Sink
plate. The heating block with a heater is soldered onto the
other side of the base plate. The inlet temperature of the
cooling water Ti , the temperature of the copper base plate Tb ,
and the outlet temperature of the cooling water To are
measured by K type thermocouples.
We evaluated the heat transfer capacity by computing the
heat transfer coefficient hi based on the base plate area Ab as
follows,
hi ¼
Q
Ab ðTb Ti Þ
ð6Þ
where Q is the heat transfer rate evaluated by deducting the
heat loss through the thermal insulator around the heater from
heat input. The pressure drop between the inlet and the outlet
of the fins of all the heat sinks were measured within an
experimental accuracy of 5% by a pressure sensor (Krone
Corp, model: DP-15).
4.3 Predictions
4.3.1 Conventional groove fins and micro-channels
Correlations for the heat transfer coefficient and a pressure
drop of the conventional groove fins and micro-channels are
expressed by the following equations under the laminar flow
regime (Re < 3000)16,17)
Nu1 Nu2
ðPr 0:71Þ þ Nu2
10 0:71
Nu1 ¼ 2:80136 2:10514X þ 0:411783X 2 þ 4:11
Nug ¼
ð7Þ
ð8Þ
Nu2 ¼ 4:18880 3:14709X þ 0:611075X 2 þ 4:11 ð9Þ
L
X ¼ ln
Reg Pr
ð10Þ
fg
where Reg (¼ u fg =) is the Reynolds number defined by the
fin gap, Nug (¼ h fg =kl ) is the Nusselt number defined by the
fin gap, L is the length of the groove fin along the flow
direction, u is the velocity of a fluid through the fin gaps, is
the dynamic viscosity of the fluid, and kl is the thermal
conductivity of the fluid.
!
!
0:674
3:44
24 þ
4X
X 0:5
3:44
f ¼ 0:5
þ
ð11Þ
X Red ð1 þ 0:000029 X 2 Þ Red
X ¼ L=ðRed De Þ
4L
1 2
P ¼ f u
De
2
ð14Þ
ð16Þ
4.4 Experimental data
4.4.1 Heat transfer capacity
Heat transfer coefficients based on the base-plate surface
area Ab defined by eq. (6) for experiment and eq. (17) for the
calculated results are plotted for all of heat sinks as a function
of the inlet velocity to the heat sinks uo in Fig. 13.
h Sf Ab
ð13Þ
ð15Þ
where Re p (¼ u dp=) is the Reynolds number, and Nu p
(¼ h dp=kl ) is Nusselt number.
hi ¼
ð12Þ
where, De (¼ 4 fg H f =2ð fg þ H f Þ) is the hydraulic diameter,
and Red (¼ u De =) is the Reynolds number.
4.3.2 Lotus-type porous copper fins
As flow through the pores in the lotus copper fins are
considered to be similar in a cylindrical pipe, the heat transfer
coefficient and pressure drop of the lotus copper fins are
expressed by the following correlations for circular pipe
under laminar flow (Re p < 3000):18)
Nu p ¼ 5:364ð1 þ fð220=ÞX þ g10=9 Þ3=10
(
5=3 )3=10
=ð115:2X þ Þ
1þ
1
½1 þ ðPr=0:0207Þ2=3 1=2 ½1 þ fð220=ÞX þ g10=9 3=5
X þ ¼ ðL=dpÞ=ðRe p PrÞ
64
L
1 2
u
P ¼
Re p
dp
2
2245
ð17Þ
The prediction for the lotus-type porous copper heat sink
showed good agreement with the experimental data within an
accuracy of 15%. The experimental data for the lotus-type
porous copper heat sink showed a very large heat transfer
coefficient of 80 kW/(m2 K) under the velocity uo of 0.2 m/s,
which is 1.7 times higher than that for the micro-channels and
6.5 times higher than that for the conventional groove fins.
4.4.2 Pressure drop
The pressure drops in all of the heat sinks are compared in
Fig. 14 as a function of uo . The predicted pressure drop of the
lotus-type porous copper heat sink showed good agreement
with the experimental data within an accuracy of 5%. On
comparing the pressure drop among all of the heat sinks at a
velocity uo of 0.2 m/s, the experimental results show that the
pressure drop of the lotus-type porous copper heat sink is 2.5
times greater than that of the micro-channels and 38 times
greater than that of the conventional groove fins.
4.5 Discussions
Figure 15 shows the heat transfer coefficient hi as a
function of the pressure drop P. On comparing the heat
transfer coefficients among all of the heat sinks under the
same pressure drop, the experimental data for the lotus-type
copper heat sink is around 1.2 times greater than that of the
micro-channels and twice as high as that of the conventional
groove fins. The data from other heat sinks such as microchannel heat sink,2) stacked micro-channel heat sink7) and
foam heat sink (FHS)10) are plotted in the figure. They show
comparable values of the heat transfer coefficient to the
lotus copper heat sink under larger pressure drops due to
Heat Transfer Coefficient, hi / kW·m-2·K-1
T. Ogushi, H. Chiba and H. Nakajima
160
Lotus Copper Heat Sinks (Exp.)
Micro-channel (Exp.)
Lotus Copper Heat Sink (Pred.)
Micro-channel (Pred.)
Conventional Groove Fins (Pred.)
140
120
100
80
60
40
Micro-channel
Lotus Copper Heat Sink
Conventional Groove Fins
Micro-channel Heat Sinks [2]
Stacked Micro-channel Heat Sinks [7]
Foam Heat Sinks [10]
100
0.01
0.1
1
10
100
1000
Pressure Drop, ∆ P / kPa
0
0
0.05
0.1
0.15
0.2
Velocity, uo /
0.25
0.3
0.35
m·s-1
Fig. 13 Comparison of heat transfer coefficient hi between experimental
and predicted data.
4.0
Pressure Drop, ∆P / kPa
1000
10
20
Lotus Copper Heat Sink (Exp.)
Micro-channel (Exp.)
Lotus Copper Heat Sink (Pred.)
Micro-channel (Pred.)
Conventional Groove Fins (Pred.)
3.5
3.0
2.5
2.0
1.5
Fig. 15 Comparison of heat transfer coefficient hi as a function of pressure
drop.
Heat Transfer Coefficient, h i / kW·m-2·K-1
Heat Transfer Coefficient, hi / kW·m-2·K-1
2246
1000
Micro-channel
Lotus Copper Heat Sink
Conventional Groove Fins
Micro-channel Heat Sinks [2]
Stacked Micro-channel Heat Sinks [7]
Foam Heat Sinks [10]
100
1.0
10
0.5
0.0001
0.001
0.01
0.1
1
10
Pumping Power, ∆ P·U / W
0
0
0.05
0.1
0.15
0.2
0.25
Velocity, uo /
m·s-1
0.3
0.35
Fig. 14 Comparison of pressure drop P between experimental and
predicated data.
smaller heat sink height comparing with the lotus copper
heat sink.
The heat-transfer coefficient hi is shown as a function of
pumping power that is defined by the product of flow rate U
and P, as shown in Fig. 16. A comparison of the heat
transfer coefficients among all of the heat sinks under a
pumping power of 0.01 W reveal that the experimental data
for the lotus-type copper heat sink are 1.3 times greater than
that for the micro-channels and 4 times greater than that for
the conventional groove fins. The data from other heat sinks
are also plotted in the figure. They show comparable values
of heat transfer coefficient to the lotus copper heat sink, but
under larger pumping power.
Figure 17 shows a comparison of the thermal resistance
Rb;i of LCHS with the foam heat sinks (FHS) and a micro-
Fig. 16 Comparison of heat transfer coefficient hi as a function of pumping
power.
channel design from Zhang et al.10) as a function of pumping
power. The thermal resistance Rb;i is based on the base
temperature to the coolant inlet temperature as defined by the
following equation.
Rb;i ¼
T b Ti
1
¼
h i Ab
Q
ð18Þ
The size of the heat sink is 13 mm (length) 12.2 mm
(width) 2 mm (fin height). The thermal resistance Rb;i of
the LCHS is calculated by the eqs. from (14) to (18). The pore
diameters of the LCHS are 0.1, 0.3 and 0.5 mm under the
same porosity of 0.5. The LCHS of pore diameter 0.3 mm has
a thermal resistance almost equivalent to the micro-channel
heat sink. The lowest thermal resistance can be obtained by
the LCHS of pore diameter 0.1 mm.
A comparison of the heat transfer coefficient hi based
on eq. (18) is also provided in Fig. 18. A heat transfer
coefficient of more than 100 kW/(m2 K) can be expected by
the LCHS with pore diameter of 0.1 mm.
0.7
Thermal Resistanve, Rb,i / K·W-1
0.6
0.5
Heat Transfer Coefficient, hi / kW·m-2·K-1
Development of Lotus-Type Porous Copper Heat Sink
FHS 100 PPI ε = 0.9
FHS 60 PPI ε = 0.8
Microchannel Wg=0.2mm
LCHS dp=0.5mm, ε =0.5
LCHS dp=0.3mm, ε =0.5
LCHS dp=0.1mm, ε =0.5
0.4
0.3
0.2
0.1
0
10 −4
10 −3
10 −2
10 −1
100
Pumping Power, ∆ P·U / W
Fig. 17 Comparison of thermal resistance Rb;i with foam heat sink and
Micro-channel.10)
1000
2247
FHS 100 PPI ε = 0.9
FHS 60 PPI ε = 0.8
Microchannel Wg=0.2mm
LCHS dp=0.1mm, ε =0.5
LCHS dp=0.3mm, ε =0.5
LCHS dp=0.5mm, ε =0.5
100
10
10 −4
10 −3
10 −2
10 −1
100
Pumping Power, ∆ P·U / W
Fig. 18 Comparison of heat transfer coefficient hi with foam heat sink and
micro-channel.10)
5.
Conclusions
From the experimental and analytical investigations on the
lotus-type porous copper heat sink (LCHS), we obtained the
following conclusions:
(1) The fin efficiency of the lotus-type porous copper fin is
verified to be predictable by the straight fin model by
using the effective thermal conductivity perpendicular
to the pore axis and the surface area ratio between the
surface area of the lotus copper and the straight fin.
(2) The heat transfer coefficient, which is based on the
base-plate area and the pressure drop of the lotus-type
copper heat sink, can be predicted by using the correlation for cylindrical pipes within an accuracy of
15% and 5%, respectively.
(3) The heat transfer capacity of the lotus-type porous
copper heat sink was very high and was found to be 4
times greater than the conventional groove fins and 1.3
times greater than micro-channel heat sink under the
same pumping power.
(4) A heat transfer coefficient of more than 100 kW/(m2 K)
can be expected by the LCHS with pore diameter of
0.1 mm.
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