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.
Citation: Lazhar Bougoffa, Ammar Khanfer. Solutions of a non-classical Stefan problem with nonlinear thermal coefficients and a Robin boundary condition[J]. AIMS Mathematics, 2021, 6(6): 6569-6579. doi: 10.3934/math.2021387
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.
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Lazhar Bougoffa, Ammar Khanfer. Solutions of a non-classical Stefan problem with nonlinear thermal coefficients and a Robin boundary condition[J]. AIMS Mathematics, 2021, 6(6): 6569-6579. doi: 10.3934/math.2021387
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