= Heat-balance correction to a premelted-film growth model
{title2=$\rho L\dot h=K_s(\Delta T-\delta T)/h-K_l\delta T/a$}
Combine the full quasi-steady <Stefan condition> above with $\delta T=T_mp_T/(\rho L)$, $a=(A/(6\pi p_T))^{1/3}$ 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.
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