We employ the Heat Balance Integral Method (HBIM) to solve a number of thermal and phase change problems which occur in a multitude of industrial contexts. As part of our analysis, we propose a new error measure for the HBIM that combines the least-squares error with a boundary immobilisation method. We describe how to determine this error for three basic thermal problems and show how it can be used to determine an optimal heat balance formulation. We then show how the HBIM, with the new error measure, may be used to approximate the solution of an aircraft deicing problem. Finally we apply the new method to two industrially important phase change problems.
S. L. Mitchell. T. G. Myers. "Application of Heat Balance Integral Methods to One-Dimensional Phase Change Problems." Int. J. Differ. Equ. 2012 (SI1) 1 - 22, 2012. https://doi.org/10.1155/2012/187902