Transient Conductive–radiative Heat Transfer: Discrete Existence and Uniqueness for a Finite Volume Scheme

This article presents a 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. Proving a maximum principle as well as existence and uniqueness for roots to a class of discrete nonlinear operators that can be decomposed into a scalar-dependent sufficiently increasing part and a benign rest, we establish a discrete maximum principle for the finite volume scheme, yielding discrete L ∞ -L ∞ a priori bounds as well as a unique discrete solution to the finite volume scheme. We present results of numerical experiments to illustrate the effectiveness of the considered scheme.