Chapter 1, Problem 1.12P

A wall with a thickness $L$ is made of a material with a thermal conductivity that varies with its thickness $x$ according to the equation, $k=\left(ax+b\right)\text{ W/mK}$, where $a$ and $b$ are constants. If the heat flux applied at the surface of one end $\left(x=0\right)$ of the wall is ${\text{20 W/m}}^{\text{2}}$, derive an expression for the temperature gradient and the temperature distribution across the wall thickness (between $x=0$ and $x=L$). Use and define appropriate notations for the surface temperatures at each end of the wall.