A time-domain precise BEM for solving transient heat conduction problems with variable heat conductivities

Abstract

In this paper, the Green’s function for the Laplace equation is adopted to derive the boundary integral equation for solving transient heat conduction problems with variable heat conductivities and heat sources. As a result, domain integrals are involved in the derived integral equations. Firstly, the radial integration method is used to convert the domain integrals into equivalent boundary integrals. Then, by expanding variables at a discrete time interval, the recursive formulation of the governing equation is derived. Finally, the recursive equation is solved by the radial integration boundary element method. A self-adaptive check technique is carried out to estimate how many expansion terms are needed in a time step size. Numerical results show satisfactory performance.