Problem$-2$:

Approximately ${10}^6$ discrete electrical components can be placed on a single integrated circuit $($chip$),$ with

electrical heat dissipation as high as $30,000\frac{W}{m^2}.$ The chip, which is very thin, is exposed to a dielectric

liquid at its outer surface, with $h_0=1000\frac{W}{m^2}K$ and $T_{,0}=20C,$ and is joined to a circuit board at its inner

surface. The thermal contact resistance between the chip and the board is ${10}^{-4}{m}^2\frac{K}{W},$ and the board

thickness and thermal conductivity are $L_b=5mm$ and $k_b=1\frac{W}{m}K,$ respectively. The other surface of the

board is exposed to ambient air for which $h_i=40\frac{W}{m^2}K$ and $T_i=20C.$

$($a$)$ Sketch the equivalent thermal circuit corresponding to steady$-$state conditions.

$($b$)$ Under steady$-$state conditions for which the chip heat dissipation is $q_c=30,000\frac{W}{m^2},$ what is the chip

temperature?