Solutions of a non-classical Stefan problem with nonlinear thermal coefficients and a Robin boundary condition

Abstract

<abstract> Solutions of similarity-type for a nonlinear non-classical Stefan problem with temperature-dependent thermal conductivity and a Robin boundary condition are obtained. The analysis of several particular cases are given when the thermal conductivity $ L(f) $ and specific heat $ N(f) $ are linear in temperature such that $ L(f) = \alpha +\delta f $ with $ N(f) = \beta+\gamma f. $ Existence of a similarity type solution also obtained for the general problem by proving the lower and upper bounds of the solution. </abstract>