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One-phase Stefan problem with temperature-dependent thermal conductivity and a boundary condition of Robin type
-
Adriana C. Briozzo
and
María Fernanda Natale
Published/Copyright:
November 4, 2015
Abstract
We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a boundary condition of Robin type at the fixed face x = 0. We obtain sufficient conditions for data in order to have a parametric representation of the solution of similarity type for t ≥ t0 > 0 with t0 an arbitrary positive time. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.
Keywords: Stefan problem; free boundary problem; phase-change
process; nonlinear thermal conductivity; similarity solution
Funding source: CONICET-UA, Rosario (Argentina) and Fondo de ayuda a la investigacion from Universidad Austral (Argentina)
Award Identifier / Grant number: PIP No. 112-200801-00460
Received: 2014-12-9
Revised: 2015-6-10
Accepted: 2015-7-21
Published Online: 2015-11-4
Published in Print: 2015-12-1
© 2015 by De Gruyter
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- Frontmatter
- Approximation of common fixed points of left Bregman strongly nonexpansive mappings and solutions of equilibrium problems
- Global existence and stability results for partial fractional random differential equations
- One-phase Stefan problem with temperature-dependent thermal conductivity and a boundary condition of Robin type
- On Janowski harmonic functions
- Oscillation results for higher order nonlinear neutral differential equations with positive and negative coefficients
- Averaging of a nonlinear bipolar model with phase transition and oscillating external forces
- Evolution and monotonicity of the first eigenvalue of p-Laplacian under the Ricci-harmonic flow
Keywords for this article
Stefan problem;
free boundary problem;
phase-change
process;
nonlinear thermal conductivity;
similarity solution
Articles in the same Issue
- Frontmatter
- Approximation of common fixed points of left Bregman strongly nonexpansive mappings and solutions of equilibrium problems
- Global existence and stability results for partial fractional random differential equations
- One-phase Stefan problem with temperature-dependent thermal conductivity and a boundary condition of Robin type
- On Janowski harmonic functions
- Oscillation results for higher order nonlinear neutral differential equations with positive and negative coefficients
- Averaging of a nonlinear bipolar model with phase transition and oscillating external forces
- Evolution and monotonicity of the first eigenvalue of p-Laplacian under the Ricci-harmonic flow
