Análise de problemas não lineares de transferência de calor pelo método dos elementos de contorno

Abstract

The present work discusses the numerical solution of non-linear heat conduction problems by the boundary element method (B.E.M.); non linearities here considered refer to the temperature dependence of the conductivity and to the non-linear boundary and interface conditions. The B.E.M. is employed together with the Kirchhoff transform. By introducing the integral of conductivity as a new variable, the equation governing the transformed problem becomes linear and the convection boundary conditions become non-linear. The B.E.M. consists, basically, in recasting the differential equation of the problem into an integral equation relating only boundary values, and the numerical discretization of this equation. To solve the system of equations resulting from the discretization process we present two direct iteration schemes and introduce one efficient Newton-Raphson algorithm. Results of applications are given in order to prove the validity of the techniques here proposed.