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Heat Transfer Research
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ISSN Imprimir: 1064-2285
ISSN En Línea: 2162-6561

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Heat Transfer Research

DOI: 10.1615/HeatTransRes.2017017295
pages 1127-1138


Rogério Martins Saldanha da Gama
Mechanical Engineering Graduate Program (FEN), Rio de Janeiro State University, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, Brazil
Felipe Bastos de Freitas Rachid
Mechanical Engineering Graduate Program (TEM-PGMEC), Universidade Federal Fluminense, Rua Passo da Pátria, 156, 24210-240, Niterói, RJ, Brazil
Maria Laura Martins-Costa
Universidade Federal Fluminense


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.