Conductive-radiative heat transfer in grey materials

We study the well-posedness of a class of models describing heat transfer b y conduction and radiation. For that purpose we propose an abstract mathema tical framework that allows us to prove existence, uniqueness and the compa rison principle for the weak solution with minimal or almost minimal a prio ri assumptions for the data. The theory covers different types of grey mate rials, that is, both semitransparent and opaque bodies as well as isotropic or nonisotropic scattering/reflection provided that the material propertie s do not depend on the wavelength of the radiation. To demonstrate the use of the abstract theory we consider in detail two examples, heat transfer be tween opaque bodies with diffuse-grey surfaces and a model with semitranspa rent material and specularly reflecting surfaces.