On an integral formulation for moving boundary problems

Abstract

The classical moving boundary problems arising in the freezing or chemical reaction of spheres, cylinders and slabs are considered. An integral method is employed to formally effect the integration of the motion of the moving boundary. This formal integration permits upper and lower bounds to be deduced for the motion and in particular simple upper and lower bounds are established for the time to complete freezing or reaction (that is, when the moving boundary reaches the centre of the sphere or cylinder). In addition an improved second upper bound on the motion is achieved by demonstrating that the dimensionless temperature or concentration is bounded above by the standard pseudo steady state approximation. The use of the integral formulation as an iterative scheme and the generalisations for a time dependent surface condition and a non nlinear diffusivity are also briefly considered.