Small-interface-parameter growth with liquid superheat ($A=2/[\sqrt{{\vartheta }^2/\pi +2S}+\vartheta /\sqrt{\pi }]$)

The small-$\lambda$ limit of superheated two-phase Stefan similarity gives $a\simeq A\sqrt{\kappa t}$, where $A=2/[\sqrt{{\vartheta }^2/\pi +2S}+\vartheta /\sqrt{\pi }]$ and $\vartheta =\Theta /\Delta T$. For fixed superheat at large latent-to-sensible heat ratio, $A\sim \sqrt{2/S}$. For much larger superheat, $A\sim \sqrt{\pi }/\vartheta$. The approximation retains the leading effect of a hot interior and its coefficient need not be exact when $S$ is only order one.