The Stefan problem in nonlinear heat conduction

DOI10.1007/BF00945083zbMath0624.73130OpenAlexW2015767943MaRDI QIDQ579054

Vincent G. Hart, James M. Hill

Publication date: 1986

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00945083

zbMATH Keywords

moving boundaryStefan problemsliquid metalexact parametric solutionparametric solutionapproximate analysisinitial estimatescoupled transcendental equationsfull two phase problemsidealized one phaseinfinite half-spacenonlinear thermal characteristicsplanar solidificationStorm type

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Thermodynamics in solid mechanics (74A15) Heat equation (35K05) Free boundary problems for PDEs (35R35)

Related Items (8)

Nonlinear Stefan problem with convective boundary condition in Storm's materials ⋮ One-dimensional nonlinear Stefan problems in Storm's materials ⋮ Two-phase Stefan problem for generalized heat equation with nonlinear thermal coefficients ⋮ Florin-type problem for the parabolic equation with power nonlinearity ⋮ Similarity solutions for nonlinear diffusion - A new integration procedure ⋮ Determination of unknown thermal coefficients in a Stefan problem for Storm's type materials ⋮ A freezing problem with varying thermal coefficients and convective boundary condition ⋮ Free boundary problems with nonlinear diffusion

Cites Work

• Some exact solutions for nonlinear desorptive diffusion
• A note on some similarity solutions of the diffusion equation
• Exact solutions in nonlinear diffusion
• Existence and Uniqueness for Similarity Solutions of One Dimensional Multi-Phase Stefan Problems
• Heat Conduction in Simple Metals
• Similarity solutions of the nonlinear diffusion equation
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