MATHEMATICAL MODELING OF HEAT TRANSFER PROBLEMS FOR THIN PLATES WITH TEMPERATURE-DEPENDENT CONDUCTIVITY

摘要

In this paper, the steady-state heat transfer phenomenon in a flat plate with temperature-dependent thermal conductivity is considered. The plate thickness is small enough in order to allow a two-dimensional description involving only the mean value of temperature over the plate thickness. A nonuniform, but known, internal heat supply and a convective heat exchange between the plate and the environment according to Newton's law of cooling are assumed. The resulting mathematical description consists of a nonlinear partial differential equation subjected to a Neumann boundary condition. The thermal conductivity is assumed to be a piecewise constant function of the temperature, and the Kirchhoff transformation is employed for constructing a new mathematical approach with an equivalent minimum principle. Proofs of existence and uniqueness of the solution are presented.