A refinement of the heat balance integral method applied to a melting problem

Abstract A mode of refinement of the heat balance integral method which is particularly suited to problems involving melting or freezing is presented. The dependent variable temperature is sub-divided into equal intervals and a system of first order, non-linear, differential equations is produced for a set of penetration variables. The penetration variables define the position of each isotherm created by the sub-division. The system of equations is then solved numerically. The improvement produced by this type of refinement is illustrated by results obtained for an idealised melting problem.