Consider a semi$-$infinite slab initially at temperature $T_i.$ A constant heat flux, $q_0,$ is

imposed at the surface $(x=0)$ beginning at time $t=0.$ Rewrite the conduction equation in

terms of the local heat flux vec$(q_x)(x,t)$ rather than $T(x,t)$ and show that vec$(q_x)$ can be solved

using similarity methods. Use this approach to obtain an expression for $T(x,t).$