Application of an Integral Numerical Technique for a Temperature-Dependent Thermal Conductivity Fin with Internal Heat Generation

A numerical study of convective heat transfer in a longitudinal fin with temperature-dependent thermal conductivity and internal heat generation is undertaken. Integral calculations are implemented on each generic element of the discretized problem domain. The resulting systems of nonlinear equations are solved efficiently because of the coefficient matrix sparsity to yield both the dependent variable and its flux. In order to validate the formulation, the effects of the thermogeometric parameter, nonlinearity due to the temperature-dependent thermal conductivity, and of the heat transfer coefficient on the fin temperature distribution are investigated. The results are found to be in agreement with those for similar problems described in the literature and with the physics of the problem.