HEAT CONDUCTION WITH LINEAR TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY: AN UNCONSTRAINED MATHEMATICAL DESCRIPTION

MARIA LAURA MARTINS-COSTA¹; FELIPE BASTOS DE FREITAS RACHID¹; ROGÉRIO MARTINS SALDANHA DA GAMA²

¹ UNIVERSIDADE FEDERAL FLUMINENSE; ² UNIVERSIDADE DO ESTADO DO RIO DE JANEIRO

doi:10.20906/CPS/COB-2015-2612

Resumo

When dealing with nonlinear heat transfer problems, it is very important is to avoid a physically inadmissible solution. Provided the physical solution exists and is unique, an unrestricted mathematical modeling - without inequalities, are a very valuable tool for computational simulations, minimizing costs and effort. In this work a conduction heat transfer problem in which the thermal conductivity decreases linearly with the temperature in a given interval is considered. A physically equivalent alternative form - valid for any absolute temperature , giving rise to an unrestricted mathematical modeling and circumventing the need of choosing the solution with physical meaning. An equivalent minimum principle of the nonlinear heat transfer problem is presented, showing that the extremum of a proposed functional is a solution of the Euler-Lagrange equation and any boundary condition.

Palavras-chave: Nonlinear heat transfer; Unconstrained mathematical description; Linear temperature-dependent thermal conductivity; Kirchhoff transformation