Mixture continuum formulation of convection-conduction energy transport in multiconstituent solid-liquid phase change systems for BEM solution techniques

Abstract

This paper describes the two nonlinear boundary-domain integral equations for Fourier heat conduction and convection governed energy transport. The equations are compatible with the mixture continuum formulation of an incompressible multiconstituent solid-liquid phase change system. The equations assume the boundary conditions to be functions of thermal field, and thermal conductivity and specific heat to be functions of temperature and species concentrations. The constitutive enthalpy-temperature relation is assumed to be a function of the species concentrations. The integral equations are derived on the basis of time-domain weighting with the fundamental solutions of the Laplace and Fourier equations and are suitable for boundary element discrete approximative method solution techniques. The nonlinearity that appears in thermal conductivity is treated by the Kirchhoff transform and the nonlinearities of specific heat and specific latent heat phase change are both transformed into the nonlinearity of the source term. The presented equations, in connection with a similar integral description for mass, momentum and species conservation, will be used as a basis for the boundary element method computation of macroscopic transport phenomena characteristics for melting and solidification.