Nonlinear numerical analysis of convective-radiative fin using MLPG method

Abstract

A mathematical model describing nonlinear and transient heat transfer through a straight insulated tip fin with temperature-dependent heat transfer coefficient has been addressed by the meshless local Petrov-Galekin (MLPG) method. Moving least square approximants are used to approximate the unknown function of temperature T(x) with Th (x).These approximants are constructed by using a linear basis, a weight function and a set of non-constant coefficients. Essential boundary conditions are imposed by penalty method. An iterative predictor-corrector scheme is used to handle nonlinearity and two-level method for temporal discretization. The accuracy of MLPG method is verified by comparing the results for the simplified versions of the present model with an exact analytical solution. Once the accuracy of MLPG method is established, the method is used to generate results for the complex heat transfer problems formulated here. Temperature variation along the fin length over the discrete time range till the attainment of steady state, under convective and convective-radiative environment has been demonstrated.