The solution of the nonlinear heat transfer problems having mixed and nonlinear boundary conditions using optimization principles

Abstract

In this work, the equation for obtaining the transient temperature distribution within a solid are derived using the nonlinear finite element analysis. The mixed boundary conditions in this formulation can be made up of four different forms which are: (a) the specified heat flux, (b) the convective heat flux, (c) the radiative heat flux and (d) the specified surface temperature distribution. The nonlinear set of equations are solved using a method based on optimization principles as well as three other numerical techniques. The results show that the methods based on the optimization principles can be successfully used in solving such problems.