Chapter 2, Problem 2.5P

Derive an expression for the temperature distribution in a plane wall in which there are uniformly distributed heat sources that vary according to the linear relation

${\stackrel{\dot{}}{q}}_G={\stackrel{\dot{}}{q}}_w\left[1-\beta \left(T-T_w\right)\right]$

where ${\stackrel{\dot{}}{q}}_w$ is a constant equal to the heat generation per unit volume at the wall temperature $T_w$. Both sides of the plate are maintained at $T_w$ and the plate thickness is 2L.