= Radiatively heated sublimation profile
{title2=$V=\dfrac{q_0/\lambda}{\rho L+\rho c_p(T_s-T_\infty)}$}
For a sublimating surface with exponentially absorbed volumetric heating, use a frame moving into the solid at speed $V$. Its steady <heat equation> is $kT''+\rho c_pVT'+q_0e^{-\lambda z}=0$. The surface <Stefan condition> is $kT'(0)=\rho LV$. Integrating over the half-space gives the displayed energy-limited speed. The surface gradient is positive, but the far field is colder, so the temperature has a subsurface maximum where <melting> can begin.
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