Convective and radiative thermal transfer with multiple reflections. Analysis and approximation by a finite element method

We study a 3D steady-state thermal model taking into account heat transfer by convection, diffusion and radiation with multiple reflections (grey bodies). This model is a nonlinear integrodifferential system which we solve numerically by a finite element method. Some results of existence and uniqueness of the solution are proved, the numerical analysis is detailed, error estimates are given and two-dimensional numerical results of thermal exchanges under a car bonnet are presented.