An asymptotic, large time solution of the convection Stefan problem with surface radiation (Q1072880)

An asymptotic, large time solution has been obtained for the convection Stefan problem with surface radiation. The moving boundary problem has been reformulated as a fixed boundary problem where Lagrange-Bürmann expansions are used to complete the variable transformation. An asymptotic solution of the problem is obtained by requiring that the asymptotic expansions assumed for the interface position X(t) and wall temperature \(u_ w(t)\) for large times are consistent with the resulting interfacial Lagrange-Bürmann expansions. It is found that the asymptotic expansions admit Neumann's solution as the leading terms and that logarithmic terms start intervening at the third-order terms of the expansions for nonzero Stefan number.