SOLUTION OF THE STEFAN TWO-PHASE PROBLEM WITH AN INTERNAL SOURCE AND OF HEAT CONDUCTION PROBLEMS BY THE METHOD OF RAPID EXPANSIONS

The Stefan two-phase problem with an internal source, as well as the heat conduction problem for rectangular and curvilinear regions, has been solved by the method of rapid sine-expansion, which involves the Fourier series. The problem of heat conduction in a body of rectangular form was solved in a general form with the Dirichlet conditions and an internal heat source by the method of rapid expansion, and thereafter the problem for a body of curvilinear shape. The solutions obtained were used in considering the Stefan problem with unknown curvilinear interface. Expressions are presented for matching the input data of the problem, on satisfaction of which the solution will be universally continuous everywhere in the region of the rectangle together with derivatives up to the sixth order inclusive. The nonfulfi llment of these conditions leads to the discontinuity of the solution at the corner points. The algorithms of the solution of problems in rectangular and curvilinear regions, as well as of the Stefan twophase problem, are written. The solution for the rectangular region is represented in an explicit form, whereas the solution for the curvilinear region and the solution of the Stefan problem are reduced to a closed algebraic system of equations of small volume
   
Author:  A. D. Chernyshov
Keywords:  heat conduction problem, Stefan two-phase problem, rapid sine-expansion, Fourier series
Page:  95