 Heat-balance correction to a premelted-film growth model

Combine the full quasi-steady Stefan condition above with $\delta T=T_m{p}_T/(\rho L)$, $a=(A/(6\pi p_T){)}^{1/3}$ and the Darcy flow law to obtain an implicit pressure-growth system. Even when latent heat is negligible, a conductivity ratio $K_s/K_l=r$ changes the leading molecular driving pressure by $r^{3/4}$. Thus a reduced equal-conductivity formula requires an explicit material and rate approximation.