Micro Capillary Pumped Loop (MCPL) and Its Dimensional Effect for Electronic Cooling

Siddhartha KostiMechanical Engineering

11105079Fluid Science and Thermal Engg.

IIT KANPURME600

Micro Capillary Pumped Loop(MCPL) And its

Dimensional effect for Electronic Cooling

Abstract:

As we are seeing that now a days the size of the electronic devices has been minimizing con-

tinuously but opposite to their small sizes the performance of those is becoming better and

better. But these high power devices dissipates higher amount of heat that must be cooled, but

todays traditional cooling methods are not sufficient to cool them. Therefore we have tried to

analyse the data which is available on this topic and tried to summarize this data so that we

can make some new cooling methods and devices with high thermal density which will suit for

thin packaging structure system.

Keywords:Micro Capillary Pumped Loop(MCPL), Operating limits, Dimensional ef-fect.

1 Introduction:

A micro capillary pumped loop can be defined as a device used for electronic cooling. A MCPL

consists different parts like an evaporator, a wicking structure, a condenser, a reservoir, and

liquid and vapor lines. A MCPL has three plates of substrate upper substrate, lower substrate,

middle substrate. The lower substrate includes an evaporator with a two-stage grooves struc-

ture and a condenser with meandering structure. The middle substrate includes liquid line and

vapor line. The upper substrate acts as a protecting cover and has grooves corresponding to

the evaporator on lower substrate to prevent creating water-drops. The wicking structure is a

two-stage grooves wet etched in a borofloat glass wafer, which acts as a protecting cover plate.

Glass is used here because of its transparent property. Finally this wicking structure will going

to be fitted in the backside of the electronic device which requires cooling.

C ompare to conventional heat pipes, MPCL has separated liquid line and vapor line, which

help in eliminating the viscous resistance between the liquid and vapor flow. In this, generally

we use water as a working fluid. Water is changing its phase from vapor to liquid when it passes

through the condenser and from liquid to vapor when it passes through the evaporator. The

curved surface of a liquid in a tube which are known as meniscus, are formed at liquid-vapor

line interface within the evaporator, which develops the capillary forces and finally which help

in driving the cycle.

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Figure 1: Schematic diagram of a MCPL

H eat is given at the evaporator input and removed at the condenser output. As we know

that the evaporator has been fitted with a wicking structure, so at the entrance to evaporator

liquid line is grooved, and surface tension which is a property of the fluid, forces the fluid to

pass into the evaporator from the fluid line, replenishing the removed liquid. The exit to the

evaporator does not have a grooved structure, so finally vapor will easily pass through the evap-

orator from the vapor line, maintaining the fluid flow in a specific direction. The latent heat of

vaporisation which released during the phase change process provides cooling methods for the

system.

As we know that the high power devices can dissipates high amount of heat of the order of

50W to 100W. These devices have very high voltage and currents. But for small devices this

high amount of heat translate to high heat fluxes of the order of 200W/cm2 or even more. High

heat fluxes devices occurs in the range of 100W/cm2 to 1000W/cm2. And the ultra high heat

flus devices occurs in the range of 1000W/cm2 to 100, 000W/cm2. For most of the devices the

maximum junction temperature limit is of the order of 200oC. The devices and methods which

are used for removing heat from low power devices, like heat sink, are not sufficient for cooling

high power devices. That is by we need to develop some new cooling devices which we can use

cooling high power devices.

Some of traditional cooling methods like natural convection, forced convection, thermal

conduction are used for low power devices. Some high power applications like super comput-

ers, diodes and transistors and complex high density interconnect (HDI) systems for military

and aerospace applications requires different cooling approaches like jet impingement, micro-

channels, spray-cooling, heat pipes, LHP(loop heat pipes), and CPL(capillary pumped loop).

But as we are seeing that the sizes of the devices getting small and small due to this, some of

the cooling methods which we use for large applications likes jet impingement and spray cool-

ing can not be use for these devices because of their small sizes. Also some of passive cooling

methods also used for cooling, because they reduces the extra amount of heat or power supply

which required, when we use some mechanical system.

A loop heat pipe(LHP) is somewhat similar to CPL, because they both increases the heat

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transport.There is only one difference between the LHP and MCPL is that instead of remote

reservoir, LHP has a compensation chamber. This compensation chamber is placed near to the

evaporator and is separated by a secondary wick structure. The MCPL have no moving parts

in it, and can be use for transporting high heat fluxes. The MCPL methods are very promising

for cooling the high power devices.

2 Analysis:

Here we will analyze some of the geometrical parameters which effects the performance of MCPL.

Now firstly we will analyze the energy balance for the evaporator for steady state condition.

QInput = Qhfg +QCpTLiq +QCpTV ap (1)

W here:

QCpTLiq = Is the heat energy required for temperature variation of liquid.

QCpTV ap = Is the heat energy required for temperature variation of vapor.

Qinput = Is the total heat energy required for the system.

Qhfg = Is the latent heat energy for phase change from liquid to vapor.

H ere we can neglect the amount heat energy required for vapor for its temperature

variation compare to the amount heat energy required for liquid for its temperature variation.

we can write it QCpTLiq and Qhfg as,

QCpTLiq = mCp(TS TL) (2)

Qhfg = mhfg (3)

N ow equation(1) is simplified to form,

QInput = mhfg + mCp(TS TL) (4)

N ow the driving forces which comes due to the capillary pressure drop due to grooved

structure and the pressure drop in the evaporator are the primary sources for the MCPL. Now

for the proper system circulation the total driving force must be greater than the total resisting

forces developed due to the pressure drop in grooved structure and for fluid flow in vapor line

(PV ) and in liquid line (PL)

PC + PT PW + PL + PV + PG (5)

W here:

PT = Is the pressure loss due to the temperature gradient around the wick.

PW = Is the pressure loss across the wicking structure.

PC = Is the capillary pumping pressure loss.

PL = Is the pressure loss in liquid line.

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PV = Is the pressure loss in vapor line.

PG = Is the pressure loss due to gravity.

This equation(5) must be hold good for the proper system circulation otherwise system failure

or evaporator dry out can be occur. N ow the capillary pressure loss can be written as,

PC = 2cosc

(1

hg+

1

w g

)(6)

W here:

hg= Is the depth of the evaporator.

wg= Is the width of the evaporator.

c = Is the angle of contact.

= Is the surface tension.

N ow the pressure drop due the temperature gradient around the wick can be obtained

with the help of Clausius-Clapeyron eqn as,

PT =(hfgPV T )

(RT 2v )(7)

W here:

T = Is the temperature gradients at inside of channel.

hfg = Is the latent heat of vaporisation.

Tv = Is saturated vapor temperature.

PV = Is saturated vapor pressure.

R = Is the gas constant.

N ow according to the Darcys law, if considered flow as laminar, and neglect the inertial

forces in microfluidcs. Factoring in the viscosity of the liquid, permeability, and other parameters

the pressure drop across the wicking structure PW can be written as,

PW =

Le0

(mlllAwK

)dx =

Le0

(lQ

lhfgAwK

)dx (8)

PW =

(lQLe

lhfgAwK

)=

{lQLe(flRel)(2hg + wg)

2

8lhcNg(hgwg)3

}(9)

W here:

Aw = Is cross-sectional area from where fluid pass through.

K= Is the permeability of the capillary groove.

Q= Is the heat flux input for the system.

hc = Is heat convection coefficient.

Le = Is length of the evaporator.

Ng = Is the number of grooves.

l = Is coefficient of viscosity.

m = Is mass flow rate.

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l = Is density of liquid.

Permeability number can be defined as,

K =

(2r2h,lflRel

)=

{8wg(hgwg)

2NgflRelwe(2hg + wg)2

}(10)

H ydraulic radius can be defined as,

rh,l =2hgwg

2hg + wg(11)

Porosity of wick can be defined as,

=hgwgNgLeAwLe

=wgNgwe

(12)

H ere (flRel) defines a fractional relationship inside the channel as,

flRel = 24(1 1.3553+ 1.94672 1.70123 + 0.95644 0.25375) (13)

Groove aspect ration can be defined as = hg/wg.

As the flow passes through the channel, according to the Darcy-Weiswach equation the

pressure drop and fractional relationship can be defined as,

P =(v

2

)(fLD

)and fRe =

64{23 + (

1124)(

hw )(2 hw )

} (14)W hen h/w 1.0 and the hydraulic diameter D = 2hw/(h+w), the pressure drop, Pl, for

flow passing through the liquid line can be defined as,

PL =

Rel

64{23 + (

1124)(

hlwl

)(2 hlwl )}(LlDl

)(v2l2

)(15)

Reynolds number for liquids Rel can be defined as, Rel = lvlDl/l and velocity can be

defined as vl = ml/lAl

S imilarly we can defined the pressure drop for the vapor line can also be written as,

PV =

Rev

64{23 + (

1124)(

hvwv

)(2 hvwv )}(LvDv

)(v2v2

)(16)

Reynolds number for vapor Rev can be defined as, Rev = vvvDv/v and velocity can be

defined as vv = mv/vAv

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Pressure drop due to the gravity can be neglected here because it does not affect the per-

formance of MCPL.

N ow we can calculate the mass flow rate m from eqn4 as,

Q = m(hfg + CpT ) => m =Q

hfg + CpT= Av (17)

N ow the final equation for mass flow rate can be written as,

m2{CphfgAchc

}+ m

{hfg + CpTs

(CpQtotalAchc

) CpTw,c

}= Qtotal (18)

Average velocityv found according to this eqn can be written as,

v =

{Q

hfg + CpT

}(1

A

)=(Q

hfg

)(1

A

)=

(Q

hfg

)(1

hw

)(19)

N ow when we will put the values of all pressure drop term and all other parameters in

equation(5) finally we will get,{2cosc

(1

hg+

1

w g

)+

(hfgPV T )

(RT 2v )

}(1

Q

)=

{lQLe(flRel)(2hg + wg)

2

8lhcNg(hgwg)3

}

+

Rev

64{23 + (

1124)(

hvwv

)(2 hvwv )}(LvDv

)(v2v2

)

+

Rel

64{23 + (

1124)(

hlwl

)(2 hlwl )}(LlDl

)(v2l2

)(20)

W hen we will define the dimension of a MCPL, we can also define the heat transfer required

by the system on the basis of equation(20). For determining the better design for MCPL, We

will collect both theoretical data determined by equation(20) and numerical data for MPCL and

then we will analyze this data for maximum heat transfer and for pressure variation for vapor

line, liquid line, grooved structure, evaporator and condenser to provide a good specification in

designing a MPCL system.

As we know that it is not easy to make numerical solution for such a vast group of equation,

for making this easy, we have made some assumption,

(1.) We assume atmosphere pressure as 1atm.

(2.) Temperature gradient of the groove is assumed as 100C.

(3.) The working fluid which is water, we have assumed that its property are constant.

(4.) Summation of PW+PL+PV has been taken as equal to the summation of PC+PT at the

equivalent state of MCPL.

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3 Operating Limits:

MCPL Specification

Vapor Line Height (hv) 150m

Vapor Line width (wv) 800m

Vapor Line Length (Lv) 32mm

Liquid Line Height (hl) 150m

Liquid Line width(wl) 400m

Liquid Line Length (Ll) 20mm

Groove Width (wg) 40m

Groove Height (hg) 40m

Number of Grooves (Ng) 11

Evaporator Width(We) 1mm

Evaporator Length(Le) 2mm

Estimated Heat Flux (Q) 178w/cm2

4 Result And Discussion:

4.1 Effect of Dimensions of Vapor Line on the Performance of system:

Here we will discuss the effect of different parameters like length of vapor line Lv, width of vapor

line wv, depth of vapor line hv on the heat transfer rate and on pressure drop. From figure( ??

) we can observe that as we will increase the length of the vapor line from Lv = 2mm to 30mm,

the pressure drop will increase by a noticeable amount, by which heat transfer will increase

simultaneously. From figure( ?? ) we can observe that by increasing the width of the vapor line

to a value of wv = 1400m heat transfer increase by a little amount but there is no change

observe in the pressure drop. From figure( ?? ) we can observe that by increasing the depth of

the vapor line from hv = 20mto150m heat transfer will increase and a little variation in the

pressure drop simultaneously.

4.2 Effect of Dimensions of Liquid Line on the Performance of system:

From figure( ?? ) we can observe that as we will increase the length of the liquid line from

Ll =10mm to 50mm, the pressure drop will increase by slight amount, but heat transfer decreases

slightly. From figure( ?? ) we can observe that by increasing the width of the liquid line from

a value of wl = 200m to 1400m decrease the pressure drop but opposed the heat transfer

rate. From figure( ?? ) we can observe that by increasing the depth of the liquid line from

hl = 20m to 160m cause a marginal increase in heat transfer and decrease in the pressure

drop.To summarize these results, the dimensional effect of the liquid line seems unable to increase

heat transfer effectively.

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4.3 Effect of Dimensions of Groove on the Performance of system:

Recently we have seen that the study of heat transfer, pressure drop, and flow characteristics in

small scale groove structure is increasing. So in this section we will study the effect of different

parameters of groove structure on the performance on cycle. From figure( ?? ) we can observe

that as we will increase the length of the groove from wg = 20m to 40m, both the pressure drop

PW andPC will decrease, by which heat transfer will increase simultaneously. From figure( ?? )

we can observe that by increasing the dept of the groove from a value of h hg = 10m to 40m

heat transfer increase by a little amount but both the pressure drop PW andPC will decreases

slightly. From figure( ??) we can observe that by increasing the number of grooves does not affect

the heat transfer but there is a decrease in pressure drop.To summarize these results, increasing

the width and depth of the groove in evaporator will decrease both the pressure resistantPW

and pressure driving term PC . Thus, it cannot promote heat transfer effectively.

4.4 Effect of Dimensions of Evaporator on the Performance of system:

As we know that the in evaporator maximum temperature occurs because of the phase change.

So it is essential to study the effect of different parameters on heat transfer rate and on pressure

drop. From figure( ?? ) we can observe that as we will increase the length of the evaporator from

Le = 0.4mmto 4.0mm, the pressure drop PW will increase by slight amount, but heat transfer

remains same. From figure( ?? ) we can observe that by increasing the width of the evaporator

from a value of we = 0.2mmto 3.8mm similar result have been obtained.Now we can say that

the dimensions of evaporator does not effect the performance of the system.

4.5 Effect of variation of heat input on the thermal resistance of the MCPL:

From figure( ?? ) we can observe that as we increase the heat input for constant cooling con-

dition of condenser the thermal resistance between the evaporator and the condenser decreased

simultaneously. From this data we observe a heta transfer rate of 8.5W at 120oC of the wall

temperature at the evaporator.

5 Conclusion:

As we know that high power electronic devices generate a large amount of heat than the conven-

tional cooling methods. MCPL(Micro Capillary Pumped Loop) and LHP(Loop Heat Pipe)can

cool these devices. Here we have obtained a maximum of 120oC temperature. And due to

separated liquid and vapor line we can transport the heat to a particular direction as per the

requirement. From the available data we have observed that the performance of the MCPL has

increases by two times with the working fluid. And we have also observed that the thermal

resistance between the evaporator and the condenser increased as we increased the heat input.

Here we have observed a maximum of 8.5W of heat transfer.

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6 Figures:

(a) Variation of width with heat transfer and

with pressure drop for vapor line.

(b) Variation of length with heat transfer and


Figure 2: Variation of width and length with heat transfer and with pressure drop for vapor

line.

(a) Variation of depth with heat transfer and


(b) Variation of length with heat transfer and

with pressure drop for liquid line.

Figure 3: Variation of depth for vapor line and length for liquid line with heat transfer and

with pressure drop respectively.

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(b) Variation of depth with heat transfer and


Figure 4: Variation of width and depth with heat transfer and with pressure drop for liquid line.


with pressure drop for Groove.

(b) Variation of depth with heat transfer and

with pressure drop for Groove

Figure 5: Variation of width and depth with heat transfer and with pressure drop for Groove.

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(a) Variation of number of groove with heat

transfer and with pressure drop for Groove.

(b) Variation of width with heat transfer and

with pressure drop for evaporator

Figure 6: Variation of width and depth with heat transfer and with pressure drop for Groove.

(a) Variation of length with heat transfer and

with pressure drop for evaporator.

(b) Variation of width with heat transfer and

with pressure drop for evaporator

Figure 7: Variation of length with heat transfer for evaporator and heat input with thermal

resistance.

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7 Nomenclature:

QCpTLiq =Is the heat energy required for temperature variation of liquid.

QCpTV ap =Is the heat energy required for temperature variation of vapor.

Qinput =Is the total heat energy required for the system.

Qhfg =Is the latent heat energy for phase change from liquid to vapor.

PT =Is the pressure loss due to the temperature gradient around the wick.

PW =Is the pressure loss across the wicking structure.

PC =Is the capillary pumping pressure loss.

PL =Is the pressure loss in liquid line.

PV =Is the pressure loss in vapor line.

PG =Is the pressure loss due to gravity.

he =Is the depth of the evaporator.

we =Is the width of the evaporator.

hg =Is the depth of the Groove.

Ng =Is the number of groove.

hl =Is the depth of the liquid line.

wl =Is the width of the liquid line.

hv =Is the depth of the vapor line.

wv =Is the width of the vapor line.

c =Is the angle of contact.

Ll =Is the length of the liquid line.

Lv =Is the length of the vapor line.

=Is the surface tension.

T =Is the temperature gradients at inside of channel.

hfg =Is the latent heat of vaporisation.

Tv =Is saturated vapor temperature.

PV =Is saturated vapor pressure.

R =Is the gas constant.

Aw =Is cross-sectional area from where fluid pass through.

K =Is the permeability of the capillary groove.

Q =Is the heat flux input for the system.

hc =Is heat convection coefficient.

Le =Is length of the evaporator.

Ng =Is the number of grooves.

l =Is coefficient of viscosity.

m =Is mass flow rate.

l =Is density of liquid.

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References

[1] Jeffrey Kirshberg, Cooling effect of a MEMS based micro capillary pumped loop for chip-

level temperature control. Kirshberg J, Kirk Yerkes,Dorian Liepmann and David Trebotich,

Proceedings of the ASME International Mechanical Engineering Congress and Exposition

2000.

[2] Leu, T. S Dimensional effect of micro capillary pumped loop. Leu, T. S., Huang, N. J. Wang,

C. T. Journal of Mechanics, 26(2), 157-163. 2010.

[3] A silicon-carbide micro-capillary pumped loop for cooling high power devices. Meyer, L.,

Dasgupta, S., Shaddock, D., Tucker, J., Fillion, R., Bronecke, P., . . . Kraft, P. 2003.

[4] Development of the micro capillary pumped loop for electronic cooling. Moon, S. H., Hwang,

G. 2007.

[5] Development of a flat-plate cooling device for electronic packaging. Moon, S. H., Hwang, G.,

Lim, H. T. 2011.

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Introduction:Analysis:Operating Limits:Result And Discussion:Effect of Dimensions of Vapor Line on the Performance of system:Effect of Dimensions of Liquid Line on the Performance of system:Effect of Dimensions of Groove on the Performance of system:Effect of Dimensions of Evaporator on the Performance of system:Effect of variation of heat input on the thermal resistance of the MCPL:

Conclusion:Figures:Nomenclature:

Documents

Micro Capillary Pumped Loop (MCPL) and Its Dimensional Effect for Electronic Cooling