Fully Implicit Finite Volume Scheme for Transient Conductive-Radiative Heat Transfer: Discrete Existence, Uniqueness, Maximum Principle

This article studies a fully implicit finite volume scheme for transient nonlinear heat transport equations coupled by nonlocal interface conditions modeling diffuse-gray radiation between the surfaces of (both open and closed) cavities. The model is considered in three space dimensions; modifications for the axisymmetric case are indicated. Extending previous results, where a similar, but not fully implicit, finite volume scheme was considered, a discrete maximum principle is established, yielding discrete $L^\infty$-$L^\infty$ a priori bounds as well as a unique discrete solution to the finite volume scheme.