Next Article in Journal
On the Folded Normal Distribution
Next Article in Special Issue
Some New Integral Identities for Solenoidal Fields and Applications
Previous Article in Journal
Sign-Periodicity of Traces of Singular Moduli
Mathematics 2014, 2(1), 1-11; doi:10.3390/math2010001

One-Dimensional Nonlinear Stefan Problems in Storm’s Materials

1,2,*  and 2
1 National Scientific and Technical Research Council, Rivadavia 1917, Buenos Aires C1033AAJ, Argentina 2 Departmant of Mathematics, Faculty of Business, University of Austral, Paraguay 1950, Rosario S2000FZF, Argentina
* Author to whom correspondence should be addressed.
Received: 17 October 2013 / Revised: 12 December 2013 / Accepted: 20 December 2013 / Published: 27 December 2013
(This article belongs to the Special Issue Mathematics on Partial Differential Equations)
Download PDF [224 KB, 30 December 2013; original version 27 December 2013]


We consider two one-phase nonlinear one-dimensional Stefan problems for a semi-infinite material x > 0; with phase change temperature Tf : We assume that the heat capacity and the thermal conductivity satisfy a Storm’s condition. In the first case, we assume a heat flux boundary condition of the type q(t) = q 0 t , and in the second case, we assume a temperature boundary condition T = Ts < Tf at the fixed face. Solutions of similarity type are obtained in both cases, and the equivalence of the two problems is demonstrated. We also give procedures in order to compute the explicit solution.
Keywords: Stefan problem; free boundary problem; phase-change process; similarity solution Stefan problem; free boundary problem; phase-change process; similarity solution
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
MDPI and ACS Style

Briozzo, A.C.; Natale, M.F. One-Dimensional Nonlinear Stefan Problems in Storm’s Materials. Mathematics 2014, 2, 1-11.

View more citation formats

Related Articles

Article Metrics


Cited By

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert