Two-dimensional unsteady heat conduction analysis by improved multiple-reciprocity boundary element method

If initial temperature is assumed to be constant, a domain integral is not required for solution of unsteady heat conduction problems without heat generation using the boundary element method (BEM). However, under heat generation or nonuniform initial temperature distribution, the domain integral is necessary. In this report it is shown that the problem of unsteady heat conduction with heat generation and initial temperature can approximately be solved without use of the domain integral by an improved multiple-reciprocity boundary element method. In this method, the domain integral in each step is divided into point, line and area integrals in the case of a two-dimensional body.