Similarity solution with a constant$-$flux boundary condition. Consider a semi$-$infinite slab initially at temperature $T_{}.$ A constant heat flux $q_0$ is imposed at $x=0$ beginning at $t=0.$ Rewrite the energy equation in terms of the local heat flux $q_x(x,t)$ rather than $T(x,t),$ and show that $q_x$ can be evaluated by the method of similarity. Use this approach to obtain an expression for $T(x,t).$