Consider a one-dimensional plane wall with constant properties and uniform internal generation qdot. The left face is insulated, and the right face is held at a uniform temperature Tc. The diagram depicts a vertical wall, with the origin in the bottom right corner indicating that positive x is to the right. Epsilon (the greek symbol) represents a portion of the wall's width across, which will be used in part b.
(a) Using the appropriate form of the heat equation, derive an expression for the x-dependence of the steady-state heat flux qdoubleprime(x).
(b) Using a finite volume spanning the range 0<=x<=epsilon, derive an expression for qdoubleprime(epsilon) and compare the expression to your result for part (a).