Transient non-linear heat conduction-radiation problems - A boundary element formulation

A novel 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 the dual reciprocity boundary element method. The integral equation of heat radiation has been discretized by the standard boundary element method. The coupling of the resulting two sets of equations has been accomplished by static condensation of the radiative heat fluxes arising in both sets. The final set of ordinary differential equations has been solved using the Runge-Kutta solver with automatic time step adjustment. The algorithm proved to be robust and stable. Numerical examples are included.