Numerical solution of one-phase Stefan problems by the heat balance integral method, Part I?cylindrical and spherical geometries

This paper considers the numerical solution of one-dimensional Stefan problems. The basic method used is the heat balance integral method (HBIM). The method is applied to one-phase melting/solidification problems. Both cylindrical and spherical geometries are considered and a special starting procedure is used for small times to overcome the singularity at t=0. The method can also deal with heat transfer problems with temperature-dependent thermal properties. Numerical results are obtained for both cylindrical and spherical geometries and conclusions are drawn. Full details of the special starting procedure for both cylindrical and spherical geometries are discussed in a companion paper, Part II. This includes the derivation of the systems of non-linear algebraic equations for the coefficients in the small time series.