Simulação de problemas de transferência de calor em regime permanente com uma relação entre condutividade térmica e temperatura constante por partes.

Abstract

This work studies conduction heat transfer considering thermal conductivity as a piecewise constant function of temperature. This relationship, although physically more realistic than assuming constant thermal conductivity, provides a simple explicit form for the inverse of Kirchhoff transformation (employed to deal with the problem non-linearity). An exact solution for a problem with spherical symmetry is presented, as an example. In the sequence, a variational formulation (with demonstrated uniqueness) is proposed. This formulation introduces a functional whose minimization is equivalent to the solution of the problem in the strong form. Finally an exact solution obtained using the inverse of Kirchhoff transformation is compared with the solution obtained via variational formulation.