= Superheated two-phase Stefan similarity
{title2=$a=2\lambda\sqrt{\kappa t}$}
For equal phase thermal properties, a roof undercooling $\Delta T$ and liquid superheat $\Theta$, the planar <Stefan problem> has interface $a=2\lambda\sqrt{\kappa t}$. The solid <error function> profile and liquid complementary-error-function profile give $S\lambda=e^{-\lambda^2}[1/\operatorname{erf}\lambda-(\Theta/\Delta T)/\operatorname{erfc}\lambda]/\sqrt\pi$. Here $S=L/(c_p\Delta T)$ is the <latent-to-sensible heat ratio>. Liquid heat supplied to the interface reduces crust growth.
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