Design of an optimal pin-fin heat sink with air impingement cooling

Pergamon

Int. Comm. Heat Mass Transfer, Vol. 27, No. 2, pp. 229-240, 2000 Copyright © 2000 Elsevier Science Ltd Printed in the USA. All rights reserved 0735-1933/(D/S-see front matter

PH S0735.1933(00)00104-4

DESIGN OF AN o F r I M A L PIN-FIN HEAT SINK WITH AIR IMPINGEMENT COOLING

J.G. Maveety and H.H. Jung IA-64 Processor Division Intel Corporation 2200 Mission College Blvd. M/S: SC12-201 Santa Clara, California 95052, USA

(Communicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT A comparative investigation between experiments and nmnefical simulation is presented for turbulent air impingement flow on a square pin-fin heat sink. Experiments were conducted using an aluminum heat sink subjected to a uniform heat flux by using a silicon test chip. The numerical method incorporates the k - z turbulence model. The numerical results illustrate the complex pressure gradients within the fin array. The predicted thermal resistance of the heat sink agrees well with those obtained from experiments. This study illustrates the utility of numerical experiments in the design and optimization of heat sinks. © 20ooElsevier Science Ltd

Introduction

Advances in microprocessor physics along with continued efforts to reduce operational execution time has resulted in length scale reductions of semiconductor devices. However, as the physical size of the semiconductor devices has decreased, the heat flux levels within these devices has increased. An important trend that has exacerbated the thermal management problem involves the addition o f circuit layers and gates on the silicon substrate. With device sizes continuing to decrease the thermal management problems associated with maintaining a safe device operating temperature become more prevalent. Such increases in the microprocessor designs has elevated the importance of heat dissipation and thermal designs [1 ]. 229

230

J.G. Maveety and H.H. Jung

Vol. 27, No. 2

Designers are attacking thermal performance problems using both passive and active thermal control systems [2]. Advancements in material technology [3,4], heat sink optimization techniques [5] and the use of heat pipes have led to better thermal control. Active techniques such as the use of thermoelectric coolers [6] and closed-loop cooling systems [1] has provided integrated solutions for numerous applications.

The aim of this paper is to present a computational analysis illustrating pressure and heat transfer characteristics in an optimized heat sink. In the discussion that follows both the details of the optimization technique and numerical analysis are presented.

These include the governing

equations, computational method and results. A comparison between numerical and experimental values of temperature are represented in terms of sink-to-ambient thermal resistance.

Numerical Method

The k - 6 turbulence model is used to describe the characteristics of impinging air flow onto a heat sink.

The assumptions invoked here are: incompressible flow (Ma<0.3), buoyancy and

radiation heat transfer effects negligible and constant thermodynamic properties. Assuming that the flow variables can be expanded in the form f = f + f ' where f is the mean value and f ' is a

fluctuation about the mean, then the continuity and Navier-Stokes equations can be written as ~' = 0

where R,) =

u'u'j

(1)

Ou, +~- tTffi - 1 -off - +-/'tV2~ - - -3R~ (2) gt ~; p a3ci p 3x, is the Reynolds stress term. A turbulence model which is less complicated than

the full equations above can be performed by substituting a simper representation for the Reynolds stress term. Models which have been used with wide success for engineering analysis are the two-equation boundary-layer models [7]. These models postulate a relationship for the Reynolds stress in terms o f the mean flow such as

-R¢ = kt' ( cgi' + vuWij)-2r~,jk p/,3xj

~,

(3)

Vol. 27, No. 2

DESIGN OF AN OPTIMAL PIN-FIN HEAT SINK

where/a, is the turbulent viscosity andk =

231

(u:uj)/2 is the turbulent kinetic energy.

Equation (3)

introduces two unknowns ( ~ , and k ) which require two equations for closure. Using dimensional analysis, it can be shown for high Reynolds number flows that the turbulent viscosity is proportional to the energy o f dissipation rate. This can be represented as

k2 /z, _ C~ (4) p c where C 1 = C1 (Re) and e is the dissipation rate o f energy. The closure equations used to evaluate the turbulent viscosity and energy dissipation rate follow an analogy with classical energy transport equations and take the form

Dk

1 0

I~t ( c~, +

D~- - p dr k C2/~t De

1 d (C3/6 -~-k) + C

Dt

p ~xk

+

c~, - ~

/6 e ( c ~ , + c~-,) c~-

(5) e2

4 --P--k'~'-~k-k ~ICI ~k-k -65 k

(6)

For the I - 6 model, the (7. terms take the values C~ = 0.09

C 2 = 1.0

C 3 = 0.769

when modeling plane jets and mixing layers [7].

C 4 = 1.44

Q = 1.92

(7)

The energy equation that is solved for the

conduction heat transfer within the heat sink is

PC~51"~-dt ~,d(k'-~,,)+( 1

(8)

where q is the heat generated per unit volume within the test chip, k s is the heat sink thermal conductivity and T, is the temperature within the heat sink. The energy equation that is solved for the fluid flow is

pC--zctC~+ u' CgF, - o3: d , ( k ~ - T'u' )

(9)

The boundary conditions invoked on the walls o f the heat sink are: all velocity components are zero (no slip), conservation o f energy between conduction and convection, natural boundary conditions on pressure and wall function for the turbulence model variables.

For the inflow:

specified velocity which has been matched to experiments, natural boundary conditions on pressure, specified turbulence model variables and specified ambient temperature and pressure.

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J.G. Maveety and H.H. Jung

Vol. 27, No. 2

For the outflow: specified pressure, temperature and natural botmdary conditions on all other variables. Symmetry was invoked along the centerlines of the heat sink. The natural boundary conditions are the flux terms of the dependent variables These terms are automatically calculated by Flotherm.

Numerical experiments were performed using the Flotherm CFD package produced by Flomerics. A grid structure fine enough to give grid independent results was determined. A variable grid structure was used in order to capture the resolution necessary to resolve steep pressure, temperature and velocity gradients. The high resolution grid was only necessary in the impingement area of the heat sink.

Experimental Method

The heat sink studied here was constructed from aluminum. The heat sink had square pin-fins (see Fig. 1) and a 7 x 7pin-fin army. As shown in Fig. l(a), the air supplied from the air delivery system passed through a filter, pressure regulator and flow meter before entering the nozzle. All of the experiments were conducted using a round nozzle of diameter D = 6.4ram. The nozzle-tosink spacing used throughout this work was z / D = 10. As discussed in [4], the best cooling performance occurs when the nozzle-to-sink spacing is within the range 8 < z / D < 12.

Figure

l(b) shows more heat sink details.

The heat sink had a square base

measuring 50.8ram x 50.8ram. The fins were square (W x gO and had height H. A silicon test chip having dimensions of 12 x 12 x 3ram and capable of generating 30W was used. All measurements were collected using a NetDaq data-acquisition system. For each data point the nozzle height was set, and the air flow rate and chip-power adjusted. The test setup was allowed to reach steadystate prior to taking any data. A measurement capability analysis (MCA) study was performed to ensure the testing conditions would produce repeatable and reproducible results. Figure 1 (e) is the plan view showing the channel spacing numbering scheme. supplements our pressure and flow discussion presented below.

The numbering scheme

Vol. 27, No. 2

DESIGN OF AN OPTIMAL PIN-FIN HEAT SINK

233

Flow

Filter

!

-- To, Po

---. z~

jet

Processor B e a r d ~ w

~TJ[J ~[~

Y~ 3

2

1

L J U*t t_

1

2

Y

H

[3 E3 E3 ~ I

3 x

(c) 9Fql~

I~ E3 E3 ~ Vq ~ Fq r-

FIG. 1 (a) Schematic illustrating the experimental setup, (b) heat sink geometry and (c) top view showing channel numbering and coordinate system.

Uncertainty estimates in the experimental quantities were determined using the ANSI/ASME Standard [8] which accounts for both bias and precision errors. components were estimated at 95% confidence.

All bias and precision

Experimental uncertainty estimates were

determined to be; 0.2°C in heat sink temperatures, 0.1 °C in silicon junction temperature, 3.2% in device power and 1.67 x 10-sin 3 / sin air flow rate.

The Reynolds number is based on nozzle

diameter. The uncertainty in the Reynolds number decreases with increased flow rate and the uncertainty in Rio is consistently between 3 and 3.5%.

The heat transferred t~om a heat-dissipating chip to the ambient is a complicated conjugate process depending on flow conditions, geometry and thermophysical properties o f the working

234

J.G. Maveety and H.H. Jung

Vol. 27, No. 2

fluid. However, for practical reasons, it is common in the thermal characterization of steady-state conditions to quantify the die-to-ambient thermal resistance as

8j.=

(10)

Q- T°

where ~ is the die junction ternperature, TOis the ambient temperature and Qis the thermal power dissipated from the die.

The optimization study developed by Ledzma et al.[5] was shown to be successful for low Reynolds number flows. Maveety and Hendricks [4] used the technique and showed it could be extended to higher Reynolds number flows. In this work, we investigate the sensitivity of fin geometry on heat dissipation.

In addition we illustrate the effects fin geometry has on the

pressure field. Referring to Fig. 1(c), the flags 1, 2 and 3 represent the heat sink channel locations in which the pressure distribution was investigated.

Here we represent the pressure in

dimensionless form as Cp ~

(11)

P-P° 2

poUo / 2

where Po and u o are the pressure and mean nozzle velocity, respectively.

Results and Discussion

Figure 2 shows the comparison between numerical and experimental values of Oj~ for the7 x 7heat sink geometry over the range7,800 < Re D < 19,700.

Figure 2 shows poor

agreement between numerical and experimental values for low Reynolds number flow. The over prediction in thermal performance indicates that the C, values need to be adjusted from those listed in equation (7) for lower Reynolds number flows.

However, the data is in excellent

agreement forRe o > 11,000. An important feature illustrated in Fig. 2 is that there is little gain in cooling performance for flows in excess of 15,000. This is important to the computer industry because it allows for a reduction in pumping power and noise level without any loss in cooling performance.

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DESIGN OF AN OPTIMAL PIN-FIN HEAT SINK

2.5

--e

235

Numerical

A

2 e=

1.5

o, I-

1

IT'

I "

\

Experimentai

\

0.5 0

10000

5000

15000

20000

25000

Rea

FIG. 2 Comparison between numerical and experimental values of sink-to-ambient thermal resistance 0j~.

Numerical experiments were also performed to assess the effects of fin height on cooling performance. Guided by the work of Ledezma et al.[5] the optimal fin height is obtained when H~ L = 053. This corresponds to a fin height of 15ram when the hase-plate is 12ram thick. In

the computational study we increased and decreased the fin height by 6ram in order to quantify the impact of fin height on cooling performance. The data is represented in Fig. 3. Clearly the shorter fin does not provide an optimal cooling condition. However Fig. 3 shows that the cooling capability is extremely sensitive as the fin length is increased from 9ram to 15ram. The cooling performance is increased by 13.8% over this range. The longer fin has slightly better performance (2.13%), over the 15ram fin, but the gain could be offset by material and manufacturing costs.

1.1 •

! I

I I

| el

L

0.9

0.4

.

.

.

0.5

.

.

.

0.6

.

.

0.7

H/L

FIG. 3 Numerical experiments showing the effects of fin height on sink-to-ambient thermal resistance 0i~.

236

J.G. Maveety and H.H. Jung

Vol. 27, No. 2

The next objective o f the optimization study was to assess the effect o f fin width (i.e., fin cross-sectional area) on cooling. Using the technique discussed in [5], the optimal fin width was determined to be W / L = 0.1. In this study we increased and decreased the fin width by lmm. The cooling characteristics are shown in Fig. 4.

As the cross-sectional area o f the fins are

reduced, the thermal mass o f the heat sink is reduced. This in turn reduces the heat sinks capacity to dissipate heat. As the fin cross-sectional area is increased over the range 0.08 _
As the fins are allowed to increase

beyond W / L = 0.1 the cooling capability starts to degrade again. The degradation in cooling over this range is attributed to the narrow channel spacing between the fins. As the channel width is reduced (fin cross-sectional area is increased) less air flows between the fins and more air is deflected in the z-direction away from the heat sink into the ambient surroundings. The increased resistance to air flow increases the overall heat sink temperature. 1.9 1.7 ~

\\\

Numerical

\\

1.5

\

m

\

1.3

\\

\

1.1

\

®

0.9

0.7 0.5 0.06

0.08

0.1 WIL

0.12

0.14

FIG. 4 Numerical experiments showing the effects o f fin width on sink-to-ambient thermal resistance Oj=.

Figures 5(a) - (f) show the pressure profiles o f channels 1, 2, and 3 starting from the base o f the beat sink channel (z = 0) to the respective fin height (z = 9mm, ere). Figures 5(a) - (c) illustrate the effects o f fin height on channel pressure and Figs. 5(d) - (f) illustrate the effects o f fin thickness on channel pressure.

The flow under the nozzle in the pin fin array is mostly in the downward direction due to the strong momentum. The high fluid velocity creates the large pressure gradients due to circulation and eddies resulting from the flow changing from a vertical direction to a horizontal direction.

Vol. 27, No. 2

DESIGN OF AN OPTIMAL PIN-FIN HEAT SINK

237

The large pressure gradient within the heat sink centerline channels induces mixing o f the air which produces a more uniform air temperature and higher heat transfer coefficient.

25

H = 9mm, W = 5.08mm

20

15 10

(d)

25

H = 15ram, W = 4.08ram

20

~1~~'~"&~ /

/

15

~ I L ~ ' ~ ~A. -~._ .~

10 5

o -5 a -10

~coll I

-is

--m-co~l

-10 -15

-20 25 20

:

~

-~-~ ~

~.-,

~co11 ~co12

-20 H = 15mm, W = 5.08mm

25

H = 15ram, W -- 5.08mm

2O

15

15

10

o, ~

b~_~..~.._

o:

-10

-15 -20 25

- 0 - - oo11 - - n - - col2

+

\/

-10 -15 -20

col3

H = 21mm, W = 5.08mm

2O

15

15

10

10

.~__./. 1

--e-- call ~ B - - cd2 ~ cd3

25

2O

0 -5 -10 -15 -20

~ ~ t r - ~ ,

•-5

\1

\'~

--/ /

5

)

~

W = 6.08ram

5

- O - - co11 co43

"~

Channel Height (mm)

-10 -15 -20

~ ~

cdl cd2 cd3

Channel Height (ram)

FIG. 5 Cp versus channel z-height; Re D = 15,700.

The largest percentage o f air flows along the heat sink centerline channels (col 3) as indicated by the large values of Cp. Figure 5(b) does provide insight into why the H = 15mm,W = 5.08ram fin geometry is the most optimal

The pressure gradient in channel 2 is the largest for this

geometry. This implies that more air is directed through channel 2 which enhances the heat

238

J.G. Maveety and H.H. Jung

Vol. 27, No. 2

transfer from the heat sink. The H = 21mm, W = 5.08ram heat sink illustrated in Fig. 5(c) also shows evidence of a high pressure drop along channel 2.

Recall from Fig. 3 that this fin

configuration produced the most optimal 0jo results.

Both t h e H = 9mm, W = 5.08ram (short fin) a n d H = 15mm,W = 4.0gram (wide channel) heat sinks produce large pressure gradients along the centerline channel.

These large gradients

produce flow reversals and stagnation points. In addition, the pressure profiles within channels 1 and 2 are small indicating little air is passing through these channels.

This information helps

explain the poor thermal performance for these two particular fin geometries. Finally, the small pressure patterns shown in Fig. 5(0 result from reducing the flow resistance by increasing the fin spacing.

Figures 6 and 7 summarize the centerline pressure distributions for the six geometries investigated. Representing the abscissa in units of dimensionless channel height, Fig. 6 shows how the centerline pressure varies as the fin height is changed. Over the range 0 _
The increase in pressure resulting from

deceleration of the flow increases the overall heat transfer coefficient. However the convective thermal resistance is the reciprocal of the hA -product, where A is the heat sink surface area and h is the area-average heat transfer coefficient. In the range 0.8 _
flow reversal and recirculation occurring within all three geometries.

25 20 15 10 5 0 2

-5 -10 -15 -20 -25

Z~Zmax FIG. 6 Cpversus dimensionless channel z/z,~ for W = 5.08ram and Re D = 15,700.

Vol. 27, No. 2

DESIGN OF AN OPTIMAL PIN-FIN HEAT SINK

239

Figure 7 illustrates how the centerline pressure varies as the fin diameter is changed. As can be seen, the optimized fin diameter (W = 5.08ram) generates the largest pressure distribution over the range 0 -< z / Zm~ < 1. It is through the optimization o f both the flow conditions and heat sink mass distribution that the lowest overall thermal resistance can be achieved.

20 F

l

i

T

~

[

1

15 10 5

d

OI 2

-5 -10 -15 -20

t

vw-'*.uu i

i ~

w-s.o8

~

W=6"08~

-4

~ \

i

1

?

!1

~

i !

Z/Zmax

FIG. 7

Cpversus dimensionless channel Z/Zmaxfor

H = 15mm and Re D = 15,700.

Conclusions

This paper presents comparisons between computational and experimental results for heat transfer from a heat sink array. The results show excellent agreement between Flotherm and the experimental results f o r R % > 11,000. The beat transfer results indicate that t h e k - e adequate for predicting Oja.

model is

In addition, optimization studies were performed to quantify the

effects o f changing the fin length and fin cross-sectional area on cooling performance. The results show that the cooling performance can be greatly affected by minor changes in fin dimensions.

Computations were carried out to investigate the flow characteristics within the fin array. The flow is observed to be very strong along the array centerline channels o f the heat sink, and diminishes in the channels away from the heat sink centerline. The predicted values o f pressure drop show complex flow patterns with large pressure gradients that generate vorticity, circulation and flow reversals.

240

J.G. Maveety and H.H. Jung

Vol. 27, No. 2

The present study demonstrates the utility o f computational analysis in both optimizing a heat sink geometry, and providing physical insight into the flow and heat transfer characteristics o f a heat sink

Nomenclature C p = Pressure coefficient, ( P - Po) / (1/2poUo)

D = Nozzle diameter, m H = Fin height, m P = Pressure, N / m 2 Q = Heat transfer from fin array, W ReD = UoD / v , Reynolds number based on nozzle diameter = Ambient air temperature, o c = Air free stream velocity exiting nozzle, m / s = Fin width, m = Density o f air, kg / m 3

TO uo W Po OjQ

= ( Tj - To) / Q , junction-to-ambient thermal resistance, ° C / W

References

1. M. Malinoski, J. Maveety, S. Knostman and T. Jones, IEEE Proceedings o f the International Test Conference, 119 (1998)

2. F.P. Ineropera, Bulletin o f the International Center f o r Heat and Mass Transfer, 3, 1261 (1972) 3. M. Montesano, Materials Technology, 3, 87 (1996) 4. J.G. Maveety and J.F. Hendricks, A S M E J. Electronic Packaging, 121, 156 (1999) 5. G. Ledzma, A.M. Morega and A. Bejan, A S M E J . Heat Transfer, 118, 570 (1996) 6. R.L. Webb, M.D. Gilley and V. Zarnescu, .4SME J. Electronic Packaging, 120, 98 (1988) 7. B.E. Launder and D.B. Spalding, Computer Methods in Applied Mechanics and Engineering, 3, 269 (1974) 8. ANSUASME PTC 19.1-1985, Part 1 Measurement Uncertainty - Instruments and Apparatus, (1986) Received October 5, 1999