The Method of Lines with Event Location Applied to the Stefan Problem

Abstract

This paper describes the method of lines with event location applied to one-dimensional Stefan problem. Stefan problems arise in many physical processes, such as, freezing and thawing of foods, solidification of steel and chemical reaction. Mathematically, those problems are special cases of moving boundary problems. The solution of such problems requires solving the transient heat conduction equation in a unknown region which has to be determined as part of the solution. The model experiences structural changes in the definition of the ordinary differential equation. To overcome these difficulties,
the model was implemented in MATLAB and the event-function in the Ordinary Differential Equation (ODE) solver was activated. To validate the present method, the results for a test case with known analytical solution are compared. The results for a wide spectrum of Stefan numbers indicate that the method of lines with event location is able to accurately track the moving liquid-solid interface and temperature history.