Finite element framework for modeling conducto-radiative transfers within heterogeneous media at both discrete and continuous scales

Abstract

The paper compares three distinct conducto-radiative models that can be used for modeling heat transfer at high temperature in view of being integrated within a topology optimization process. Finite elements are extensively used. Non-linearities are handled using a fixed-point method coupled with a Newton–Raphson linearization method. A three-dimensional square lattice is sandwiched between a hot and a cold plate. The discrete mesoscopic scale is the reference model. At all conduction-to-radiation regimes, and even when radiation predominates, it appears that the continuous-scale approach, which has been set-up thanks to proper homogenization laws, gives satisfactory results, which is not the case for the Rosseland approximation model. The homogenized continuous-scale model appears to be a good candidate for being used in the future in topology optimization problems.