Question

A 69-cm x 69-cm circuit board that contains 121 square chips on one side is to be cooled by combined natural convection and radiation by mounting it on a vertical surface in a room at 25°C. Each chip dissipates 0.18 W of power, and the emissivity of the chip surfaces is 0.7. Assume the heat transfer from the back side of the circuit board to be negligible, and the temperature of the surrounding surfaces to be the same as the air temperature of the room. Evaluate air properties at a film temperature of 30°C and 1 atm pressure.

Given: The properties of air at 1 atm and the anticipated film temperature of 30°C.

k = 0.02588 W/m∙°C,

v = 1.608 x 10^-5 m²/s,

Pr = 0.7282,

β = 0.0033 K^-1

1. Assuming the circuit board to be positioned horizontally with chips facing up, determine the surface temperature of the chips.

2. Assuming the circuit board to be positioned horizontally with chips facing down, determine the surface temperature of the chips.

Answer 1

Solution : Given that Coefficient of thermal Expansion B=0.0033 K1 K = 0.02586 Wmc. V = 1.608 x 10 ms Pr = 0.7282. .: PN = Prand il number. 8 = 981 substitute all the values in Below Equation Ra= gВ(1-2) Le Ra 2) Rayleigh's number. obtain Here, og is the acceleration due to gravity, . I is surface Temperature of Plate To is a mospheric temperature obtain the air Properties at a film temperature of 30°c from the air at a Im Pressure. kinematic viccosity V- 16.00 x10 , 9.880.0033 x 25-25 ) x(0.5)...zres Ra= Rg = . 11:39 8107 X 0.7292

on Consider the equation for Dusselt number based Ra for natural convection for verticle plate doen Nu (6.95 + 0.887 (Rajć (049 Por Wyp = 0.625 + 0.387 (11.39x10738 +10.4926 0.7282 . a = 63.7 Consider the caution for heat transfer coefficient hat she Here, is thermal Conductivity k. 0.02588 le=0.5 horeda du = 63.7 OS h= 0.02586 xE5.7 h = 3.29 w/mk the heat loss from Calculate natural convention and radiation Q zhd (Is-To)+ € 40 (T-1)

. 5.6 10 y tere h is convective heat transfer coefficient As is Surface area, & is emissivity fubstitute 12180.18 w for Q ? h = 3.29 w/mic 25°c for too, oir for & aid 'Asi 5.67 x 108 for o 13140.16 = 2.29% 0.47 x (;°s) +(0.7 xo:49 X569 x00F) (614+023)" – 65 +233)" ) 24.12=3.99 (1.-2597132654 x 1059 (Chs 112259-74 Ts = 36.80 X109) requined surface temperature is [ 36.2°C which is nearest to assumed value of 35€. The assumption is good.