A New Way of Solving Transient Radiative-Conductive Heat Transfer Problems

One-dimensional transient energy transfer by conduction and radiation is solved for a finite medium. The semitransparent layer emits, absorbs, and scatters radiation (participating medium). The coupled transfer is solved analytically by considering the well-known two-flux approximation, assuming linear transfer and using the Laplace transform. The semitransparent layer can then be modeled by a matrix transfer function. The accuracy of the solution is verified in the case of sharp thermal excitation by a heat pulse on the front face. It is shown that this general model is very accurate for simulating both the limiting cases of purely scattering and purely absorbing media. In the latter case, the same modeling is derived using the kernel substitution technique, and very good agreement is achieved compared with numerical simulations. The resulting computation times are very small, and suggest that such a model can be used in the inverse approach of thermal problems involving semitransparent materials.