Nonlinear and Transient Heat Transfer in the Fin by a Truly Meshless Method

In this article, Meshless Local Petrov- Galerkin (MLPG) method is used to solve the nonlinear and transient one- dimensional heat transfer equation of a fin with the power- law temperature- dependent heat transfer coefficient. 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 enforced by direct method of interpolation and Penalty Method (PM) respectively. Temperature variation along the fin length over the different time range till the attainment of steady state has been demonstrated for the convective and insulated tip conditions.