PROBLEM $2\mathrm{.}6$

A plane wall of thickness $2$ L has internal heat sources whose strength varies according to

$q_G^{}=q_0^{}cos(ax)$

where $q_o^{}$ is the heat generated per unit volume at the center of the wall $)=(0$ and $a$ is a constant. If both sides of the wall are maintained at a constant temperature of $T_w,$ derive an expression for the total heat loss from the wall per unit surface area.

PROBLEM $2\mathrm{.}7$

A very thin silicon chip is bonded to a $6-mm$ thick aluminum substrate by a $0\mathrm{.}02-mm$ thick epoxy glue. Both surfaces of this chip$-$aluminum system are cooled by air at $25C,$ where the convective heat transfer coefficient of air flow is $100\frac{W}{m^2(K)}.$ If the heat dissipation per unit area from the chip is ${10}^4\frac{W}{m^2}$ under steady state condition, draw the thermal circuit for the system and determine the operating temperature of the chip.