Computational method for 1-D one phase problem

Abstract

In this paper a simple but an efficient Computational algorithm is developed to solve one dimensional single phase Stefan problems. The Stefan problem describes the distribution of temperature on the boundary when the position of the interface is known. The main difficulty to find interface is that there is no domain at the initial time in addition to find the solution of the problem. The procedure outlined in literature to solve such problems is messy and laborious. Such difficulty is handled intuitively using Green’s theorem of vector calculus and finite difference discretization. Hence, the idea outlined in this manuscript and the algorithm developed is applied on two cases of the problem and validated the computational method by comparing the results for trivial cases. Hence the approach is applicable in the field of materials science through major fields of applications. Here, we discuss Stefan problem that includes a moving phase change of materials and a material shape or size-dependent thermal conductivity.