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Solutions of a non-classical Stefan problem with nonlinear thermal coefficients and a Robin boundary condition
Journal article   Open access  Peer reviewed

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

Lazhar Bougoffa, Ammar Khanfer and Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi Arabia
AIMS mathematics, Vol.6(6), pp.6569-6579
01/01/2021
DOI: https://doi.org/10.3934/math.2021387

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
Solutions of similarity-type for a nonlinear non-classical Stefan problem with temperaturedependent 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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https://doi.org/10.3934/math.2021387View
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