Convective heat transfer from simulated air-cooled printed-circuit board assembly on horizontal or vertical orientation

Int. Comm. HeatMass Transfe~Vol. 25, No. 1, pp. 67--80, 1998

Copyright© 1998 Elsevier Science Ltd Printed inthe USA. An fights reserved 0735-1933/98 $19.00+.00

Pergamon PIIS0735-1933(97)00138-3

C O N V E C T I V E H E A T T R A N S F E R FROM S I M U L A T E D A I R - C O O L E D P R I N T E D - C I R C U I T B O A R D ASSEMBLY O N H O R I Z O N T A L O R VERTICAL O R I E N T A T I O N

C. W. Leung Department of Mechanical Engineering, The Hong Kong Polytechnic University Hung Horn, Kowloon, Hong Kong

H. J. Kang School of Energy and Power Engineering, Xi'an Jiaotong University Xi'an, Shaanxi, 710049 China

(Communicated by B.X. Wang and X.F. Peng)

ABSTRACT An experimental and numerical analyses had been performed to investigate the convective heat transfer in a rectangular duct flow with streamwise-periodic rectangular heated ribs mounted on one of the principal walls, which simulated a printed-circuit board (PCB) assembly. Experimental investigation were carried out with the PCB assembly orientated in both horizontal and vertical positions. Effects of varying the duct's height, and the rib's height and width on convection from the rib's surface to the air-flow were studied. The heat transfer measurements were obtained for unencumbered height-based Reynolds number from 510 to 2050. Predictive correlations valid over a range of Reynolds numbers, duct height-to-rib height ratios (H/B) and rib's width-to-height ratios (L/B) were proposed. © 1998ElsevierScienceLtd Introduction Together with the trend towards microminiaturisation, the need for rapid and effective heat removal from printed-circuit board (PCB) assembly becomes an increasing importance in its design process. Temperature of the electronic components on a PCB must be maintained within prescribed operating limits in order to prevent degradation and eventual failure. So far, there is quite a number of publications 67

68

C.W. Leung and H.J. Kang

Vol. 25, No. 1

a b o u t the heat transfer from electronic components and PCB assembly, and some of the most relevant work are cited below.

Thermal management strategies for electronic equipment were discussed by

Nakayama [ l], Incropera [2] and Yovanovich [3]. Forced convection is one of the effective methods to cool a channel formed by PCBs, and numerical and experimental investigations had been performed to study the forced convective heat transfer from simulated PCB assembly, lrdm & Boehm [4] used numerical method to predict the heat transfer from a series of heated blocks, which were mounted on the surface of a vertical channel. Lehmann &, Wirtz [5, 6] presented flow visualization in a channel containing uniformly spaced rectangular heated ribs. Davalath & Bayazitoghi [7] simulated the convective heat transfer numerically from three heated rectangular blocks. Patankar & Schmidt [8] performed extensive numerical analyses of the heat transfer, which occur in the fully developed region of a duct containing heated, uniformly spaced blocks under laminar flow condition. Irdm & A n a n d [9] reported the numerical results of heat transfer in the fully developed region of a series of parallel plates with surface-mounted discrete heated sources. Tam, Leung &, Probert [ 10] carried out investigation with a horizontally orientated simulated PCB assembly at the turbulent flow region. However, hydraulic diameter of the channel and flow velocity of these investigations were often small rending the flow laminar. T h e P r e s e n t E x p e r i m e n t a l Rig The system for thermally simulating the behaviour of the PCB assembly consisting of 12 upwardfacing, highly polished rectangular copper ribs, which were mounted with an uniform spacing of 6.35 m m on a smooth board (see Figs. 1 and 2). The whole assembly was placed either horizontally or vertically. The heated ribs, which were used to simulate the thermal behaviour of the elecrIonic components above ambient temperatures, were highly polished in order to achieve a low surface emissivity of less t h a n 0.3 (as indicated by a Minolta 505 infrared spot thermometer). Each rib had a length of 200 m m and a height (B) of 6.35 ram. There were two values of rib width (L) used in the present investigation such t h a t IdB=3 and 4 respectively. Two 0.8 ~ heater strips were embedded in the base of each copper rib to provide a uniform heat flux. Electric power supplied to the ribs was adjusted via a variable-voltage transformer and recorded by a digital wattmeter. A thermojunction was embedded in a narrow central slot in the upper surface of every rib, and the thermocouple signals were converted to temperature readings via a Fluke 2190A digital thermometer. The simulated PCB was 200 m m wide and formed by fixing a 2 m m thick mica sheet to a 6.35 mm thick bakelite substrate, and the undersurface of which was covered with a layer of glass fibre. The board was machined to have sharp leading and trailing edges in order to reduce the production of local turbulence in the air-flow. The simulated PCB assembly was placed symmetrically in the wind tunnel's rectangular test section (length 600 ram, cross-section dimension 202 m m x 120 mm) made of 6.35 m m thick bakelite sheet. The whole test section was thermally insulated from its surroundings by a 50 m m thick glass fibre layer. The internal height (H) of the wind tunnel (see Fig. 1 ) could be varied, so that H/B =2, 4, 6, 8 and

Vol. 25, No. 1

HEAT TRANSFER FROM PRINTED-CIRCUIT

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70

C.W. Leung and H.J. Kang

Q~--E-Q~-Qj

Vol. 25, No. 1

(i)

The conduction loss (Q~) from a rib to the simulated PCB was assessed by using Fourier's law and from the l~mowledge of the thermal conductivity of the board material and the measured associated temperature distribution. The rate of radiation loss (Q,) from a rib to its environment was estimated by the following equation:

where the view factor (F) between the rib and its surroundings, was taken to be unity and the surface emissivity, was measured to be 0.3. After Q, and Q, were deduced from E, the value of (Qc) could be determined. Then the convective coefficient for heat transfer from the rib ' n' to the air-flow was obtained from the definition:

G---o/(A(L-L))

(3)

The steady-state temperature of air-flow (T,) is assumed to vary linearly from inlet to e ~ t of the test section (see Fig.2), and was used as the reference temperature to determine the values of d~e air's properties applicable for the investigation. The average heat transfer coefficient over the entire PCB can be obtained from:

12t

h

(4)

The vertical clearance of the simulated PCB (C=H-B, see Fig. 1) was chosen as the characteristic dimension to define the Reynolds and Nusselt numbers, i.e.

(5)

Rec:U*C/v Nuc=h *C/k

(6)

The dimensionless parameters used to describe the convective heat transfer between the simulated PCB assembly and the air-flow were related in the traditional way, i.e.

Nu c =C1Re c~Pr n(H/B)P(L/B)q

(7)

Vol. 25, No. 1

HEAT TRANSFER FROM PRINTED-CIRCUIT BOARD

71

Because the Prandtl n u m b e r of air in the considered temperature range remained almost constant (i.e. 0.7) for the present investigation, equation (7) could be simplified to become:

N u c =C 2 R e c ( H / B ) P ( L / B ) q

(8)

H e a t Transfer Results Figs. 3 and 4 show the variation of the heat transfer coefficient of the individual copper rib on the entire simulated PCB for a horizontal PCB assembly at different H/B when L/B =3 and 4 respectively. As shown, the steady-state convective heat transfer is greatest at the first rib, and thereafter decreased for each subsequent rib row until it becomes almost row-independent (i.e. from row 7 to 10 ) when the air-flow is fully developed. However, an increase in heat transfer coefficient occurs at the last two ribs (i.e. rows 1 1 and 12): this is due to the 'exit' effect (i.e. sudden enlargement of the flow aperture soon after row 12), which leads to an enhanced local turbulence around ribs 1 1 and 12. The heat transfer coefficient is enhanced by an average of 20 % w h e n the L/B ratio is increased from 3 to 4 (i.e. comparing Figs. 3 and 4):

The experimental data obtaining from the entire region were rearranged to form dimensionless groups and shown in Figs. 7(a) and 7(b). The resulting best-fit line in the form suggested by equation (8) for the horizontal assemblies in the range: 460 <_ Re c <_ 2300, 2_< H/B _< 10 and 3 _< L/B _( 4, is given by:

NUch=O.40Re°24(H/B)°68(L/B)°80

(9)

The variation of heat transfer coefficient of the individual copper rib on the entire simulated PCB when it is placed in a vertical orientation are shown in Figs. 5 and 6 (I. e. IdB=3 and 4 respectively). The experimental data for entire region are also shown in Figs. 7(c) and 7(d) in dimensionless groups. The corresponding correlation developed from the experimental results for the vertical assemblies operating in the same ranges of Re o H/B and L/B, in the form as suggested by equation (8) is given as:

NUcv= 0 . 1 2 R e ° 2 9 ( H / B ) ° V S ( L / B ) 1.35

(10)

The coefficients and power indices in b o t h equations (9) and (10) were determined by using the least-squares method, and the maximum deviation from the best-fit line for these equations is within -20.3 % to 25.7 %.

72

C.W. Leung and H.J. Kang

S5 |

.

Vol. 25, No. 1

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FIG. 3 Variation of local heat t.ran~fcr cocfficicnt for the uniformly spaccd heated ribs on horizontal PCB. LIB=3; B = s = 6 . 3 5 ram; (a) H/B=2; (b) H/B=4; ( c ) H/B=6; (d) H/B=8; (c) H / B = I 0

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FIG. 4 Variation of local heat txansfcr cocfficicnt for the uniformly spaced healed ribs ou hori/xmtal PCB. IEB=4 B = s = 6 . 3 5 ram; (a) H/B=2; (b) H/B=4; (c) I-l/B=6; (d) H/B=8; (c) H/B--- I0

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Vol. 25, No. I

HEAT TRANSFER FROM PRINTED-CIRCUIT BOARD

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FIG. 5 Variati(m of local heat t.r;m,slcr coclficicnt for thc u~dformly Sl)accd heated ribs on vertical PCB. IJB=3; B=s=6.35 ram; (a) H/B=2; (b) H/B=4; (c) H/B=6; (d) I-I/B=8; (c) I I/13=lO

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FIG. 6 Variatioil of local hcat transfer coc[ficicnt lor die unitOrndy ,spaccd heated rib,s oz~ vertical PCB. L/B=4; B=s=6.,35 ram; (a) H/13=2; (b) I-L/B=4; (c) I-L/I3=6; (d) H/B=8; (c) 1L/B=IO

12

74

C.W. Leung and H.J. Kang

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FIG. 7 Average Nusselt number for the PCB vcrse Reynolds number of the air-flow for horizontal assembly at IdB=3; 1. H/B= 10; 2. H/B=8; 3. H/B=6; 4. H/B=4; 5. H/B=2 for horizontal assembly at IdB=4; I. H/B= 10; 2. H/B=8; 3. H/B=6; 4. H/B=4; 5. H/B=2 for vertical assembly at IdB=3; 1. H/B= 10; 2. H/B=8; 3. H/B=6; 4. H/B=4; 5. H/B=2 for vertical assembly at U B = 4 .; 1. H/B= I0; 2. H/B=8; 3. H/B=6; 4. H/B=4; 5. FUB=2

Numerical Simulation of The Horizontal PCB Computation domain of a horizontal simulated PCB was shown in Fig. 1. Considcration was givcn only to peri(xlically fully-developed flow far from the channel entrance because of periodic positioning of the ribs [ 10 t. The governing equations used were continuity, momentum (x and y) and energy equations:

a+OVo dx , Ou

Ou,

3p

cgy O,

Ou,+ O, c?u.

(11)

Vol. 25, No. 1

HEAT TRANSFER FROM PRINTED-CIRCUIT BOARD

. Ov Or. O p + O , Ov, c3, Ov . . . . . . 9(U~x +V-~y)= --'~y -~xtg-~x) +--~y(g-fff )+PgPU- l.) . OT cx

OT. 0 < , . ~ c3T. 0~,. g OT. cy c~x r r ox oy t'r oy

9 ( u = -- + v--z--) = "7-"t ~--X- = - - ) + = - - ( ~ - a - - -=-- )

75

(13)

(14)

A buoyancy force term " 9g/3(T-T,) " was added to the y-momentum equation to account for the natural convection component, which was neglected when forced convection from the simulated PCB is calculated. For the flow field, no-slip boundary conditions were imposed at the entire exposed surface of the simulated PCB. The periodic boundary conditions at the inlet and outlet of the computational module were stated as:

u(0, y)=u(1, y)

v(0, y)=v(1, y)

0(0, y)=O(1 ,y)

(15)

where O was a dimensionless excess temperature and defined as:

(16)

O(x,y)=(r(x,y)- L)/( rtx,y)- ~) and Tb(X, y) was the average temperature at the x cross-section, i.e.

H

:r~(x,y) = ;0 u ( x , y ) ( r ( x , y )

A constant temperature of 20

-

H

L)dy/f o u ( x , y ) @

(17)

°C was used as the fluid inlet temperature, and another constant

temperature of 70 °C was assigned as the rib surface temperature. The residual boundary condition was assumed to be adiabatic. Thermophysical properties of the fluid were assumed to remain constant during the numerical simulation procedure. The set of governing equations with the associated boundary conditions were solved by using the finite volume technique. Velocity and pressure variables were stored at the staggered locations and solved by the SIMPLE algorithm [ 11J. W h e n the temperature field achieved its convergence, the heat flux on the entire exposed surface of the horizontal simulated PCB (Q~) and local Nusseh n u m b e r ( Nu n ) could be given by:

Q. = -~or/oy l~.o =~(~- D>/5

(i 8)

76

C.W. Leung and H.J. Kang

Nu

.C/tc=[(2j(7i

-

Vol. 25, No. 1

-'z' )/('C,-'Z;(x,y))I

,C/Y

(1,))

C o m p a r i s o n o f t h e H o r i z o n t a l a n d V e r t i c a l PCB A s s e m b l i e s The average h e a t transfer coefficients b e t w e e n the PCB's surface and the air-flow at. different H/B ratios for a horizontal simulated PCB assembly at 12B=3 and 4 respectively are shown in Fig. 8(a), whereas those for vertical simulated PCB are shown in Fig. 8(b). 40

,o II .,1

35

8 (b)

3O

2

25

25 - - - - - ~ - ~ : . "

-o

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20 r-

15 10

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3

i, 4

. . . . . . . . . 5 6 7 8

]~I 9 10

5

2

3

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5

6

7

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9

10

H/B

H/B

FIG. 8 (a) Comparison of the average heat transfer coefficients of the horizontal PCB at I213 =3 and 4 and different H/13 [2B=3 1---Rec~, =500; 2---Rcch = 1000; 3 .... gCch = 1500; 4----Rech = 2 0 0 0 12B=4 5---RCch =500; 6---Rech = lOO0; 7----Rech = 1500; 8--~-Rcct~ = 2 0 0 0

FIG. 8 (b) C o m p a r i s o n of the average heat transfer coefficients of the vertical PCB at L/B=3 and 4 and different

H/B 12B=3 1213=4

l---Rcc~ =500; 2---Re¢~ = I000; 3----Rec~ = 1500; 4----Rec~ = 2 0 0 0 5---Rec~ =500; 6---Rc¢~ = 1000; 7----Rec~ = 1 5 0 0 ; 8----Rec~ = 2 0 0 0

It can be found that the results obtained at 12B=4 arc always greater t h a n those at I213=3 at the same H/B a n d Reynolds iumlbcr. It is because the rib's u)p surface arca plays a key role in convective h e a t transfer, and m o s t of the h e a t is dissipated from the top surfacc. T h e numerical result agrees closely with this conclusion. According to the variation of local Nussclt n u m b e r over a rib's surfacc of a horizontal PCB assembly as s h o w n in Figs. 9(a) and 9(b), the convective h e a t transfcr from the side surface is relatively low. Therefore a wider top surface for the rib is suggestcd to be used fl)r b o t h the horizontal and vertical PCB assemblies, in order to e n h a n c e the convection.

Vol. 25, No. 1

HEAT TRANSFER FROM PRINTED-CIRCUIT BOARD

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i-

0.5

- i . . I. ' . ~.

0

¢;'~ 0.~

"~--

0.2

0.3

Fig. 9(a)

0.4

o.s

o.s

0.7

x/c

o.s

Fig. 9(b)

FIG. 9 Distribution of local NtJsselt n u m b e r on a smgh: rib along the flow direction at various Reynolds nuinl)er for the horizontal PCB asseml)ly (a) L/B=3 H / B = 8 (b) IJB=,t I-t/B= 10

30

45

............... 511

40 35 30 25 20 15 10

2

3

4

5

6 H/B

7

8

9

10

5 2

3

4

5

6

7

8

9

10

H/B

FIG. 10 Coml)arist)n of average heat transfi'r cocl]'icicnts ()1"horizontal and vertical PCBs at different H/B (a) I J B = 3 (b) L/B=4 For horizontal PCB: l---Reel , =500; 3---RCch = 1000; 5---Rot:. = 1500; 7---Rcch = 2 0 0 0 For vertical PCB: 2---Rcc, =500; 4---Rcc, = 1000; 6---Rec, = 1500; 8---Rcc, = 2 0 0 0 Fig. 10 shows the comparison between the average heat transfer coefficicnt,s of tile horizontal and vertical sinudatcd PCB assemblies at different H/B and Reynolds numbers. For L/B=3, the heat transfer coefficients ofw:rtical PCB assembly is smaller than those of the horizontal counlcrpart at all H/B ratios. However, when IJB =4, the vertical PCB assembly is always more effective to dissipate heat by convection

78

C.W. Leung and H.J. Kang

Vol. 25, No. 1

than the horizontal PCB assembly. Numerical simulations of the forced convection and mixed convection on a rib's surface of the horizontal PCB assembly at I2B=3 and 4 are shown in Figs. 9(a) and 9(b) respectively. It is found that when L/B = 3, natural convection (i.e. difference between forced convection and mixed convection) plays an important role in heat dissipation for the horizontal PCB assembly, and therefore the mixed convection is enhanced. However, there is no significant difference between the forced convection and mixed convection when IJB=4. The reason may be that at the horizontal rib surface, the natural convective heat transfer strength depends on the width of the rib. The wider the rib surface, the more difficult the natural convection to be developed. However, for a vertical PCB assembly, the natural convection thermal boundary layer develops along the length of the rib and is less affected by the width of the rib. At !.JB=4, a higher natural convection is obtained at the vertical PCB assembly whereas that from the horizontal PCB assembly is low. Therefore the vertical assembly is always thermally more effective at L/B =4. However, when the natural convection is significant at L/B =3, the mixed convection from a horizontal PCB assembly is enhanced and a better thermal performance over its counterpart can be achieved.

Conclusions Based on results obtained from the present investigation for the cooling of the horizontal and vertical simulated PCB assemblies under steady-state condition, the following conclusions can be drawn: 1. For both the horizontal and vertical PCB assemblies, heat transfer coefficients at the board surface at L/B=4 are always greater than those obtained at IJB=3 for the same Reynolds number and H/B ratio. It is therefore suggested that a flat rib with a large top surface should be adopted to enhance heat dissipation. 2. For LIB=3, the heat transfer coefficients of the vertical PCB assembly are lower than those of the horizontal PCB assembly. However, when !_JB=4, the vertical PCB assembly is more effective to dissipate heat by convection than its horizontal counterpart. 3. Average heat transfer coefficients between the simulated PCB assembly and the air-flow for the range, 3 <_L/B ~ 4,460 < Rec < 2300 and 2~ H/B <_i0 can be obtained by equation (9) for horizontal assembly, and equation (10) for vertical assembly.

Nomenclature A

surface area (i.e. top and two sides) of each rib exposed to air, m 2

B

rib height above the base of the simulated PCB, m ; see Fig. l

E

electric power supplied to each rib, w

F

view factor for thermal radiation from a rib to its surroundings

g

gravitational acceleration, m/s 2

Vol. 25, No. 1

h

HEAT TRANSFER FROM PRINTED-CIRCUIT BOARD

convective coefficient for heat transfer from a rib to the air-flow, w/(m 2 K)

H

vertical free height within the unencumbered duct, m; see Fig. 1

k

thermal conductivity of the fluid, w/(m K)

K

thermal diffusivity, m2/s

L

width of a rib, i.e. dimension in the direction of the mean air-flow, m; see Fig. 1

m Nu n

power indices in equations (7) and (8) Nusselt number number of the rectangular ribs on the simulated PCB, also power index in equation(7)

Pr

Prandtl number of the air-flow

Q

steady-state rate of heat loss from the simulated PCB, w

Re

Reynolds number for the air-flow

T

temperature, K

u, v velocity in the x and y-direction, respectively, m/s U

mean air speed in the duct, m/s; see Fig. 1

x, y

streamwise and cross-stream coordinates

e

mean surface emissivity with respect to thermal radiation

/x

dynamic viscosity of the fluid, kg/(m s)

v

kinematic viscosity of the fluid, m:/s

o

Stefan-Boltzmann constant, w/(m 2 K a )

p

density, kg/m 3

13

coefficient of thermal expansion, I/K

(~

dimensionless excess temperature

Subscripts a

of the air-flow

b

average value at the x cross-section

c

via forced convection

f

fully developed region

h

horizontal orientation

1

via conduction

n

for the n th rib

p

position of the first internal point

r

via thermal radiation

s

of the rib's surfaces

v

ver~dcal orientation

79

80

C.W. Leung and H.J. Kang

w x

Vol. 25, No. 1

for the entire exposed surface of the simulated PCB at a local point on the rib surface

Acknowledgement Leung and ILang wish to thank the University Grant Council of Hong Kong for the financial support. of the present investigation.

References 1. F. P. Incropera, ASME Journal of Heat Transfer, 110, 1097-1110 (1988). 2. M. M. Yovanovich, Heat transfer in electronic packaging, Proceedingsof the Tenth International Heat Transfer Conference, 1, 93-104, Brighton, UK (1994). 3. W. T. Kim, & R , F. Boehm, NumericalHeat Transfer, 22, Part A, 421-434 (1992). 4. G. L, Lehmann, &- R. A. Wirtz, Convection from surface-mounted repeated ribs in a channel flow, ASME Paper No.84-WA/HT-88 (1984). 5. G. L. Letunaml, &R. A. Wirtz, The effect of variations in stream-wise sparing and length on convection from surface-mounted rectangular components, ASME HTD- 48, New York, 39-47 (1985). 6. J. Davalath, &Y. Bayazitonglu, ASME Journal of Heat Transfer, 109, 321-328 (1987). 7. S.V. Patankar, &. ~ C. Schmidt, A numerical study of laminar forced-convection across heated blocks in two-dimensional ducts, ASME Paper No. 86-WA/HT-88 (1986). ) 8. S. H. I(dm, & N. K. Anand, ASME Journal of Electronic Packaging, 117, 52-62 (1995). 9. W. C. Tam, C. W. Leung, & S . D. Probert, Applied Energy, 46, 197-214 (1993). 10. S. V. Patankar, C. H. Liu, &E. M. Sparrow, ASME Journal of Heat Transfer, 99, 180-186 (1977). 11. S. V. Patankar, Numerical heat transfer andfluid flow, McGraw-Hill, (1980).

Received August 14, 1997