Development of Lotus Type Porous Copper Heat Sink

Development of Lotus-Type Porous Copper Heat Sink

Tetsuro Ogushi

, Hiroshi Chiba

and Hideo Nakajima

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

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 micro-channels 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 50mmwide channels and 50mmwide walls by etching to a depth of about 300mmin silicon wafers of thickness 400mm. 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}

temper-ature 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 coefficienthi, derived from net heat input, base area and base plate mean temperature rise from water inlet, of more than 100 kW/(m2K). 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

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 75mm, fin width 75mm, channel depth 426mm, channel length 10 mm, the calculated thermal resistance is 0.12 Kcm2_{/W (h}

i¼83kW/(m2K)) 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 (h}

i¼122kW/(m2K)). 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 (P¼10kPa). 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

LSI IGBT

Insulated gate bipolar transistor LD

HBT

LWR LWR Laser diode

Heterojunction

0 500 1000 1500 2000 2500 3000 3500 4000

Temperature,T/ K

Solar heating Rocket motor case

Reentry from earth orbit Nuclear blast

Rocket nozzle throat

Ballistic Entry

Air conditioning CHF of water

LWR 105

104

103

2

10

101

100

10-1

10-2

-2

bipolar transistor _{Heat Flux}

F

/ W·cm

Maximum evaporation rate

Air velosity 20m/s) (Hydraulic diameter 5mm, Air cooling

Fig. 1 Typical cooling loads and cooling technology.1)

with a high thermal conductivity such as copper should be used to improve the thermal performance of the micro-channel 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 drilling513circular 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/ (m2K). 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/ (m2K) under reduced unit cell dimensions of 100mm

hydraulic diameter.

As for porous heat sinks characterized by straight circular ducts, Boweret 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 measuring32mm22mm 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 resistanceRb;ithat 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/(m2K) 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 three-dimensional 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

13mm12:2mm2mm were used for the fabrication of the FHSs. The pressure drops and thermal resistance of open-celled 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 of12:2mm15mm 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

60 PPI at the flow rate 1 L/min corresponded to the heat transfer coefficienthiof 63 kW/(m2K).

Jianget 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 manu-factured 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 micro-porous 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 heat-exchanger using micro-channels 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-chan-nels was better than porous media by considering both the heat transfer and pressure drop characteristics of these heat-exchangers.

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-mm 1

Chips

Container Lotus copper

Lotus copper

Cooling water

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 lotus-type porous copper fins.

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 pro-posed 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 50C. The specimens’ porosity varied between 0.24 and 0.43. Figure 4 shows a typical distribution of pore diameters. As

the diameters of the pores were distributed around a certain range, the maximum diameterdpmax, the minimum diameter

dpmin and the mean diameterdpmeanare 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?

ks

¼1"

1þ" ð1Þ

where,keff?,ksand"are the effective thermal conductivity of the lotus copper perpendicular to the pores, the thermal conductivity of the base material and the porosity, respec-tively.

5

30

Heater

Cooling water

30

Specimen

Load cell

φ

30

30

30

Copper

Block

insulator

Pressure regulation screw

Thermal

Fig. 3 Test apparatus for measuring effective thermal conductivity.

0 5 10 15 20 25 30 35

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

dpmax

dpmin

dpmean

Pore diameter, dp / mm

Distribution

(%)

=0.08mm =0.02mm, =0.17mm, =0.43,

ε

Fig. 4 Distribution of pore diameters in a specimen.

+ =

1 1 k k

s eff

---(1)

0 0.2 0.4 0.6 0.8 1 1.2

0 0.2 0.4 0.6 0.8 1

ks

ε

ε

ε

+

−

= ⊥

1 1 k k

s eff

---(1) keff

⊥

/ k

s

Porosity

Experimental data

Analytical prediction

=335 W/(m·K)

3. 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 differenceT between the top surface of the fin and the fluid in the pores is calculated from eq. (2),

Q¼hSf T ð2Þ

whereis the fin efficiency,Sfis the total surface area of the pores andhis the heat transfer coefficient in the pores.

In the straight fin, the fin efficiencyis expressed as the following equations:

¼tanhðmHfÞ

mHf

ð3Þ

m¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

h&Pf

keff?Ac s

ð4Þ

where Hf is the fin height, keff? is the effective thermal conductivity perpendicular to the pore axis and Pf is the peripheral length of the fin. Furthermore Ac is the cross-sectional area of the fin, whileis the ratio between the total

surface area of the lotus copperSf and the total surface area of the straight fin Pf Hf, which can be expressed as the following,

&¼ Sf

PfHf

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 temperatureTs 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 coefficienthin the pores, a constant surrounding temperature

Ts and symmetry along lateral walls.

In the calculation, the spacing of poresðx;yÞandh were changed under the conditions of pore diameterdpof 200mm

and a material thermal conductivityks of 400 W/(mK). A comparison of the fin efficiencybetween the numerical results and results from eq. (3) is shown in Fig. 8. Equa-tion (3) showed good agreement with the numerical simu-lation; therefore, the fin efficiency of the lotus fin was verified to be predictable by eq. (3) derived from the straight fin model.

x

H

t

A

(=2

x

.

t

)

P

(=2(

x+t

))

Outer

surface

area

ζ

.

P

Effecive

thermal

conductivity

k

x

H

Thermal

conductivit

y

k

t

Q

Q

(a) Straight fin model

(b) Lotus copper fin

dp

Fig. 6 Analytical fin model: (a) straight fin model, (b) lotus copper fin model.

dp

/2

dp

/2

y

y

y

y

y

y

y

y

2 3

y

2 3

dp

/2

dp

/2

dp

/2

dp

/2

dp

/2

dp

/2

dp

/2

dp

/2

dp

/2

x

Q

H

4. 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 speci-fications 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

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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 1 2 3 4 5

m.H_f

Fin Efficiency,

ηf

Analytical prediction Numerical prediction

Fig. 8 Comparison of fin efficiency between numerical and analytical prediction from eq. (3).

f_t

fg

Hf

30 mm 20 mm

Flow direction

Fig. 9 Conventional groove fins and micro-channels.

Table 1 Specification of conventional groove fins and micro-channels.

Fin gap fin tichkness Fin Height

fg/mm ft/mm Hf/mm Investigation Conventional

groove fins 3 1 9 Calc.

Micro-channels 0.5 0.5 9 Calc. & measured

30 mm 20 mm

3 mm

(dp = 0.3mm, ε= 0.39)

pore

Hf

=9 mm

5.5 mm Lotus type porous copper fin

Flow direction

Fig. 10 Lotus type porous copper heat sink.

Test duct Heat sink

Length

5 5

T_b

T_i 5

Circulator (pump and

water cooler) Mesh

T_b

T_o

duct

Temperature measure points Pressure measure points

Heater

Heating block Copper base Thermal

insulator

Flow meter

Cooling water flow direction = 20mm

Filter

Fig. 11 Schematic of experimental apparatus for measuring heat transfer capacity.

Heating Block

Copper base

Test duct

Pressure taps

Fins Duct

plate. The heating block with a heater is soldered onto the other side of the base plate. The inlet temperature of the cooling waterTi, the temperature of the copper base plateTb, 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 coefficienthibased on the base plate areaAbas follows,

hi¼

Q

Ab ðTbTiÞ

ð6Þ

whereQis 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 of5% 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)

Nug¼

Nu1Nu2

100:71 ðPr0:71Þ þNu2 ð7Þ

Nu1¼2:801362:10514Xþ0:411783X2þ4:11 ð8Þ

Nu2¼4:188803:14709Xþ0:611075X2þ4:11 ð9Þ

X ¼ln L

fg

RegPr

ð10Þ

whereReg(¼ufg=) is the Reynolds number defined by the fin gap,Nug(¼hfg=kl) is the Nusselt number defined by the fin gap, L is the length of the groove fin along the flow direction,uis 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.

f ¼ 3:44

X0:5_Re d

þ

24þ 0:674

4X

!

3:44 X0:5

!

ð1þ0:000029X2_{Þ Re} d

ð11Þ

X¼L=ðRedDeÞ ð12Þ

P¼ f 4L De

1

2u

2

ð13Þ

where,De(¼4fgHf=2ðfgþHfÞ) is the hydraulic diameter, andRed (¼uDe=) 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 (Rep <3000):18)

Nup¼5:364ð1þ fð220=ÞXþg10=9Þ3=10

1þ =ð115:2X

þ_Þ

½1þ ðPr=0:0207Þ2=31=2_{½1þ fð220=ÞX}þ_g10=93=5

5=3

( )3=10

1 ð14Þ

Xþ¼ ðL=dpÞ=ðRepPrÞ ð15Þ

P¼ 64 Rep

L

dp

1 2u

2

ð16Þ

where Rep (¼udp=) is the Reynolds number, and Nup (¼hdp=kl) is Nusselt number.

4.4 Experimental data 4.4.1 Heat transfer capacity

Heat transfer coefficients based on the base-plate surface areaAbdefined 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 sinksuoin Fig. 13.

hi¼

hSf

Ab

ð17Þ

The prediction for the lotus-type porous copper heat sink showed good agreement with the experimental data within an accuracy of15%. The experimental data for the lotus-type porous copper heat sink showed a very large heat transfer coefficient of 80 kW/(m2K) under the velocityuoof 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 ofuo. The predicted pressure drop of the lotus-type porous copper heat sink showed good agreement with the experimental data within an accuracy of5%. On comparing the pressure drop among all of the heat sinks at a velocityuoof 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

smaller heat sink height comparing with the lotus copper heat sink.

The heat-transfer coefficienthiis shown as a function of pumping power that is defined by the product of flow rateU

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-channel design from Zhanget 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;i¼

TbTi

Q ¼

1

hiAb

ð18Þ

The size of the heat sink is 13 mm (length)12.2 mm (width)2 mm (fin height). The thermal resistanceRb;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 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Velocity, uo/ m·s-1

160

140

120

100

80

60

40

20

0

Heat Transfer Coefficient,

hi

/ kW

·m -2·

K

-1

Conventional Groove Fins (Pred.) Micro-channel (Pred.)

Lotus Copper Heat Sink (Pred.) Micro-channel (Exp.)

Lotus Copper Heat Sinks (Exp.)

Fig. 13 Comparison of heat transfer coefficienthibetween experimental and predicted data.

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Velocity,

u

/ m·s

Pressure Drop,

∆

P

/ kPa

Lotus Copper Heat Sink (Exp.) Micro-channel (Exp.)

Lotus Copper Heat Sink (Pred.) Micro-channel (Pred.)

Conventional Groove Fins (Pred.)

Fig. 14 Comparison of pressure drop P between experimental and predicated data.

1000

100

10

0.01 0.1 1 10 100 1000

Pressure Drop, ∆P / kPa

Heat Transfer Coefficient,

hi

/ kW·m

-2·K

-1

Foam Heat Sinks [10]

Stacked Micro-channel Heat Sinks [7] Micro-channel Heat Sinks [2] Conventional Groove Fins Lotus Copper Heat Sink Micro-channel

Fig. 15 Comparison of heat transfer coefficienthias a function of pressure drop.

0.0001 0.001 0.01 0.1 1 10

Heat Transfer Coefficient,

hi

/ kW·

m

-2·K

-1

Pumping Power, ∆P·U / W

1000

100

10

Foam Heat Sinks [10]

Stacked Micro-channel Heat Sinks [7] Micro-channel Heat Sinks [2] Conventional Groove Fins Lotus Copper Heat Sink Micro-channel

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 cor-relation for cylindrical pipes within an accuracy of

15% and5%, 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/(m2K) can be expected by the LCHS with pore diameter of 0.1 mm.

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

10−4 ₁₀−3 ₁₀−2 ₁₀−1 ₁₀0

= 0.9

Thermal Resistanve,

Rb,i

/

K·W

-1

Pumping Power, ∆P·U / W

LCHS dp=0.1mm, =0.5ε

LCHS dp=0.3mm, =0.5ε

LCHS dp=0.5mm, =0.5ε

FHS 100 PPI FHS 60 PPI

MicrochannelWg=0.2mm

ε ε= 0.8

Fig. 17 Comparison of thermal resistanceRb;i with foam heat sink and Micro-channel.10)

10−4 10−3 10−2 10−1 100

ε

=0.5

Pumping Power, ∆P·U / W

Heat Transfer Coefficient,

h

/ kW·m

-2

·K

-1 1000

100

10

FHS 100 PPI FHS 60 PPI

= 0.9 = 0.8

LCHS dp=0.5mm,

ε=0.5 LCHS dp=0.1mm,

ε=0.5 LCHS dp=0.3mm, Microchannel Wgε =0.2mm

ε