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

Jerome Monnier (1, 2) , Jean-Paul Vila (3)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul
2 IDOPT - System identification and optimization in physics and environment
3 MIP - Mathématiques pour l'Industrie et la Physique

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 twodimensional numerical results of thermal exchanges under a car bonnet are presented.

Domaines: Analyse fonctionnelle [math.FA]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Jerome Monnier, Jean-Paul Vila. Convective and radiative thermal transfer with multiple reflections. Analysis and approximation by a finite element method. Mathematical Models and Methods in Applied Sciences, 2001, 11 (2), pp.229-262. ⟨10.1142/S0218202501000854⟩. ⟨inria-00256540⟩