Chapter 2, Problem 2.60P

A plane wall with constant properties is initially at a uniform temperature $T_O.$ Suddenly, the surface at $x=L$ is exposed to a convection process with a fluid at $T_{\infty }\left(>T_O\right)$ having a convection coefficient h. Also, suddenly the wall experiences a uniform internal volumetric heating that is sufficiently large to induce a maximum steady-state temperature within the wall, which exceeds that of the fluid. The boundary at $x=0$ remains at $T_O.$

(a) On $T-x$ coordinates, sketch the temperature distributions for the following conditions: initialcondition $\left(t\le 0\right),$ steady-state condition $\left(t\to \infty \right),$ and for two intermediate times. Show also thedistribution for the special condition when there is no heat flow at the $x=L$ boundary.
(b) On $q_x^n-t$ coordinates, sketch the heat flux for the locations $x=0$ and $x=L,$ that is, $q_x^n\left(0,t\right)$ and $q_x^n\left(L,t\right),$ respectively.