MIXTURE CONTINUUM FORMULATION OF CONVECTION-CONDUCTION ENERGY-TRANSPORT IN MULTICONSTITUENT SOLID-LIQUID PHASE-CHANGE SYSTEMS FOR BEM SOLUTION TECHNIQUES

This paper describes the two nonlinear boundary-domain integral equati ons for Fourier heat conduction and convection governed energy transpo rt. The equations are compatible with the mixture continuum formulatio n of an incompressible multiconstituent solid-liquid phase change syst em. The equations assume the boundary conditions to be functions of th ermal field, and thermal conductivity and specific heat to be function s of temperature and species concentrations. The constitutive enthalpy -temperature relation is assumed to be a function of the species conce ntrations. The integral equations are derived on the basis of time-dom ain weighting with the fundamental solutions of the Laplace and Fourie r equations and are suitable for boundary element discrete approximati ve method solution techniques. The nonlinearity that appears in therma l conductivity is treated by the Kirchhoff transform and the nonlinear ities of specific heat and specific latent heat of phase change are bo th 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 b oundary element method computation of macroscopic transport phenomena characteristic for melting and solidification.