This is a new perspective where the radiation process is represented by a nonlinear time-dependent partial differential equation, originally derived using Fourier and heat energy conservation laws. The two equations in the model are linked by the heat energy surface loss relation

where n is the normal to the surface G.

When the model represents radiation in terms of the
Stefan-Boltzmann Law, with k representing the Stefan-Boltzmann constant. This case is discussed in [4]. In this paper, we derive the nonlinear time-dependent variational form for the problem, which is then descretized using triangular elements. The descretization leads to the derivation of an FEM algorithm that simultaneously calculates both the body and surface temperatures during the cooling process. The algorithm is the computational form of the 2-D version of the cooling model we proposed in [2], for an isotropic 3-D solid.

Of particular interest about the algorithm is that, a suitable choice for may speed up the cooling process to the attainment of the desired temperature in a single iteration, of course, depending on how high the initial body temperature is, relative to the environmental temperature