A Dual Reciprocity Boundary Element Formulation for Transient Non-Linear Conduction-Radiation Problems

Abstract

A boundary-only formulation for transient temperature fields in bodies of non-linear material properties and arbitrary non-linear boundary conditions has been developed. The option for self-irradiating boundaries has been included in the formulation. Heat conduction equation has been partially linearized by Kirchhoff’s transformation. The result has been discretized by Dual Reciprocity Boundary Element Method. The integral equation of heat radiation has been discretized by standard boundary element method. The coupling of the resulting two sets of equations has been accomplished by eliminating the radiative heat fluxes arising in both sets. The final set of ordinary differential equations has been solved using Runge-Kutta solver with automatic time step adjustment. Another discussed problem is the coupling of transient conduction in a solid with natural convection in the surrounding fluid by discretizing the fluid itself.