%0 Journal Article %A da Gama, Rogério Martins Saldanha %A Freitas Rachid, Felipe Bastos de %A Martins-Costa, Maria Laura %D 2017 %I Begell House %K conductive heat transfer, flat plate, Kirchhoff transformation, variational formulation, solution existence and uniqueness %N 12 %P 1127-1138 %R 10.1615/HeatTransRes.2017017295 %T MATHEMATICAL MODELING OF HEAT TRANSFER PROBLEMS FOR THIN PLATES WITH TEMPERATURE-DEPENDENT CONDUCTIVITY %U https://www.dl.begellhouse.com/journals/46784ef93dddff27,5284b92411fbd139,6b128a61396d5f9f.html %V 48 %X 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. %8 2017-10-18