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ISSN Imprimir: 1064-2285
ISSN En Línea: 2162-6561

# Heat Transfer Research

DOI: 10.1615/HeatTransRes.2018019450
pages 413-422

## A GENERAL MINIMUM PRINCIPLE FOR STEADY-STATE CONDUCTION HEAT TRANSFER PROBLEMS WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY SUBJECTED TO LINEAR ROBIN BOUNDARY CONDITIONS

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

### SINOPSIS

In this paper, a mathematical model is presented for describing the conduction heat transfer process in rigid, isotropic, and homogeneous bodies, with temperature-dependent thermal conductivity and a linear Robin (convection) boundary conditions. The nonlinear partial differential equation, describing the conduction heat transfer inside the body, is rewritten with the aid of a Kirchhoff transformation. The conductivity is regarded as a piecewise constant function of the temperature in such a way that the transformation is easily invertible and may be employed for any material. In addition, a suitable minimum principle is presented for describing the problems considered.

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