Approximate Solution of the Nonlinear Heat Conduction Equation in a Semi-Infinite Domain

Figure 3

Heat wave front for numerical integrated (solid), linear approximate (dashed), quadratic approximate (dotted), and Marshak's (dotted-dashed) solutions as a function of time for the case where $E_0(t)=\exp \hspace{0.17em}(1.8t)$ and $k_e(E)=E^4$.