Chapter 2, Problem 2.29P

Consider a one-dimensional plane wall with constant properties and uniform internal generation $\stackrel{.}{q}.$
The left face is insulated, and the right face is held at a uniform temperature.

(a) Using the appropriate form of the heat equation, derive an expression for the x-dependence of the steady-state heat flux $q"\left(x\right).$
(b) Using a finite volume spanning the range $x\le x\le \xi ,$ derive an expression for $q"\left(\xi \right)$ and compare the expression to your result for part (a).