Isotherm migration along orthogonal flow lines in two dimensions

Abstract

A novel approach to the solution of transient heat flow problems in two dimensions is described. The movements of isotherms along orthogonal flow lines are tracked in successive small intervals of time by solving a locally one-dimensional IMM form of radial heat equation. The determination of the new orientation of the orthogonal system at the end of each time interval is based on geometrical considerations. The method is applied to the moving boundary problem presented by the solidification of a square prism of fluid and the results compared with those obtained by the enthalpy method.