Question

A 12-cm 3 18-cm circuit board houses on its surface 100 closely spaced logic chips, each dissipating 0.06 Win an environment at 40°C. The heat transfer from the backsurface of the board is negligible. If the heat transfer coefficient on the surface of the board is 10 W/m2·K, determine(a) the heat flux on the surface of the circuit board, in W/m2;(b) the surface temperature of the chips; and (c) the thermalresistance between the surface of the circuit board and thecooling medium, in °C/W

Answer 1

Answer:

a)278W/m^2

b)67.8C

c)3.83 °C/W

Explanation:

Hello!

let's solve this problem by numerals

a) to find the heat transfer per unit area we multiply the amount of chips (100) by the heat they dissipate (0.06W) and divide it by the plate area

q=heat flux(W/m^2)

N=number of chips=100

a=(12cm)(18cm)=210cm^2=0.0216m^2

Q=heat disipated by each chip(W)

$q=\frac{QN}{a}=\frac{(0.06)(100)}{(0.0216m^2)}  =278W/m^2$

the heat flux is 278W/m^2

b)

to find the temperature of the chips we use the heat transfer equation by convection on the board

q=h(Ts-Tair)

h=heat transfer coefficient=10 W/m2·K

Ts=the surface temperature of the chips

Tair=temperature of enviroment=40C

q=heat flux=278W/m^2

solving for Ts

$Ts=\frac{q}{h} + Tair\\Ts=\frac{278}{10}+40=67.8C$

the surface temperature of the chips is 67.8C

finally to find the thermal resistance by convection we use the following equation

$R=\frac{1}{ha} =\frac{1}{(10)(0.0261)} =3.83 C/W$

he thermal resistance between the surface of the circuit board and thecooling medium is 3.83 °C/W