HIGH-ACCURACY POLYNOMIAL SOLUTIONS OF THE CLASSICAL STEFAN PROBLEM
Abstract
The Stefan problem is of extreme importance in investigating many physical processes and technologies. Solving the Stefan problem reduces to calculating a temperature (concentration) profile when an interphase boundary is to be determined. High-accuracy polynomial solutions of the Stefan problem for a semi-infinite medium with Dirichlet/Neumann boundary conditions and general conditions are presented. An initial medium temperature is assumed to be equal to a phase change temperature. With the use of the integral method of boundary characteristics, based on multiple integration of the heat conduction equation, sequences of identical equalities with different boundary conditions are obtained and, as a result, polynomial solutions are constructed. The high efficiency of the approach proposed is illustrated with various examples. The solutions based on the 2nd and 3rd degree polynomials are more exact in comparison to the known solutions. The accuracy of calculating the position of the interphase boundary by means of 4th and 5th degree polynomials is several orders of magnitude higher than that of numerical methods. The solutions obtained can be considered as conditionally exact because of negligibly small errors in determining the interphase boundary and the temperature profile.
About the Author
Valery A. Kot
A. V. Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of Belarus, Minsk
Belarus
Belarus
Ph. D. (Engineering), Senior researcher
15, P. Brovka Str., 220072
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