Exercise #$3(10$ points$)$:

A $20-mm$ thick solid wall has a thermal conductivity of $20\frac{W}{m-K}.$ At a steady$-$state condition,

it is observed that the temperature distribution within the wall, assuming a one$-$dimensional $(1$D$)$

approximation, follows the following relationship: $T(C)=a+b{x}^2$ with $a=120C$ and $b=$

$-800\frac{C}{m^2},$ with $x$ in unit meter.

$($a$)$ Compute the heat generation rate $[$W$]$ within the wall, if any.

$($b$)$ Compute the heat fluxes at the two wall faces that are perpendicular to the $x-$axis. How

do these heat fluxes relate to the heat generation rate?

Assume the surface area of the wall $($in the direction perpendicular to the $x-$axis$)$ is $4m^2.$