Freezing in a Finite Slab Using Extensive Perturbation Expansions Method

Abstract

In this paper Mathematica is used to solve the moving boundary problem of freezing in a finite slab for higher order perturbations. Mathematica is a new system which makes it possible to do algebra with computer. More specifically, it enables researchers to find the location of the ice at any time for as high order of perturbation as one whishes. Using of Mathematica and outer solution and an inner solution for the quantities involved are developed and then these solutions are matched together using the method of matched asymptotic expansions. At the end the composite solutions are compared to the available low-order solutions.