A 3-D anisotropic solid is heated uniformly and subsequently placed in a vacuum, which is at a lower temperature. Due to difference in the temperature of the solid and its environment, the solid starts radiatively cooling down. The aim of this paper is to propose a mathematical model for that cooling phenomenon.

Based on the radiative cooling model, we proposed in [1] for an isotropic 3-D solid, in this paper, we propose a similar model, but for an anisotropic 3-D solid. The main challenge is the modeling (in terms of the relevant laws) of radiative heat transfer in an anisotropic solid, for both the body and surface of the 3-D solid. We subsequently obtain a vectorial cooling problem, whose analysis is effected component-wise. In the mathematical analysis, we show that, component-wise, the model has a unique solution which then extends to its vectorial version.