Heat balance integral method for the heat conduction problems with phase change

Abstract

Heat conduction problems with phase change occur naturally in many physical and industrial processes. A moving boundary of these problems results in strong nonlinear. Very few analytical solutions to these problems are obtained. Numerical methods and approximate methods are two kinds of methods solving these problems. Heat Balance Integral Method (HBIM) is an approximate method to effectively solve these problems. There is not a systematic principle for the selection of an approximate solution profile in original HBIM, and the calculation accuracy is not as good as expected. This paper provides a general rule to select the approximate solution profile in HBIM. A new method for determining the parameters in approximate solution is proposed. The results show that the new method improves accuracy greatly.