An alternative mathematical modelling for coupled conduction/radiation energy transfer phenomenon in a system of N gray bodies surrounded by a vacuum

Abstract

In this work the energy transfer process among N rigid, opaque and gray bodies is considered. The energy transfer phenomenon takes place by conduction (inside each body) and by thermal radiation (among the boundaries of the bodies). All the bodies can emit and reflect thermal radiant energy and, hence, at each point of each boundary, the reflected and the emitted thermal radiant energy coming from the N bodies of the system must be taken into account. This complex phenomenon, with infinitely many practical applications, is described by a set of N partial differential equations coupled by a set of 2N non-linear equations defined on the boundaries of the bodies. A new mathematical modelling for the phenomenon is proposed that allows the construction of the solution in an easy way and provides proofs of existence and uniqueness of the solution. Some inconveniences of the classical modelling are presented, providing an expressive support for the proposed new modelling.