SOLUTION OF THE CLASSICAL STEFAN PROBLEM: NEUMANN CONDITION

A polynomial solution of the classical one-phase Stefan problem with a Neumann boundary condition is presented. As a result of the multiple integration of the heat-conduction equation, a sequence of identical equalities has been obtained. On the basis of these equalities, solutions were constructed in the form of the second-, third-, fourth-, and fi fth-degree polynomials. It is shown by test examples that the approach proposed is highly effi cient and that the approximation errors of the solutions in the form of the fourth- and fi fth-degree polynomials are negligible small, which allows them to be considered in fact as exact. The polynomial solutions obtained substantially surpass the analogous numerical solutions in the accuracy of determining the position of the moving interphase boundary in a body and are in approximate parity with them in the accuracy of determining the temperature profi le in it
   
Author:  V. A. Kot
Keywords:  Stefan problem, Neumann boundary condition, interphase front, free boundary, integral method of boundary characteristics, heat balance integral method.
Page:  889