Journal of Engineering Physics and Thermophysics

, Volume 85, Issue 6, pp 1441–1452

Analytical solution of the Stefan problem with account for the ablation and the temperature-disturbance front


DOI: 10.1007/s10891-012-0794-7

Cite this article as:
Kudinov, V.A., Eremin, A.V. & Kudinov, I.V. J Eng Phys Thermophy (2012) 85: 1441. doi:10.1007/s10891-012-0794-7

An approximate analytical solution of the problem on the heat conduction of an infinite plate has been obtained on the basis of the determination of the temperature-disturbance front and the introduction of additional boundary conditions with account for the movement of the melting front in the case where the melted substance is completely removed (Stefan problem with ablation). A method for construction of additional boundary conditions, which allows one to obtain solutions of the indicated problem for engineering applications in the form of simple algebraic polynomials free of special functions, is proposed. The accuracy of these solutions is determined by the number of approximations, which is not limited in the case where additional boundary conditions are used.


integral methodsStefan problemtemperature-disturbance frontmelting frontheat of phase transition;ablationadditional boundary conditions

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Samara State Technical UniversitySamaraRussia