Consider a one$-$dimensional plane wall with constant properties and

uniform internal generation of$.$ The left face is insulated, and the right

face is held at a uniform temperature $T_C.$

a$.$ Using the approprlate form of The Heat Equation, derive an

expression for the $x$ "dependence of the steady$-$state heat flux $q^{\text{'}\text{'}}(x)$

$($Hint$,$ you will also need an approprlate form of Fourler's Law$).$

b$.$ Solve for $q^{\text{'}\text{'}}$ when the length of the wall is $0\mathrm{.}01m(x=0\mathrm{.}01m),$

$T_G=100C,$ and $q^{}=900\frac{(W)}{m^3}.$

You may ask clarlfying questions but do not ask for the answer.

In this question, you are asked to derlve, which will requlre the use of

basle calculus, You may ask for a calculus refresher if needed.