A Moving Boundary Problem in a Finite Domain

Abstract

The heat conduction and the moving solid-liquid interface in a finite region is studied numerically. A Fourier series expansion is used in both phases for spatial temperature distribution, and the differential equations are converted to an infinite number of ordinary differential equations in time. These equations are solved iteratively for the interface location as well as for the temperature distribution. The results are compared with existing solutions for low Stefan numbers. New results are presented for higher Stefan numbers for which solutions are unavailable.