Proposta de estratégia para discretização aplicada ao método de diferenças finitas para um problema de transferência de calor em geometria circular com geração de calor no centro

Abstract

The determination of temperature gradients in objects has been increasingly studied by the mathematics, since its application in engineering projects has become more frequent and essential, given its relevance for design quality assurance. In this scenario, this work aims to adapt a strategy, already present in literature, to describe temperature gradients in circular geometry using the Finite Difference Method. Giving the difficulty that Cartesian meshes have in discretizing geometries with irregular contours, the proposal of the new strategy is the development of a nodal network that is based on the polar coordinate system. Through the development of the equations, subsequent application to the problem and comparison with the general analytical solution, it was found that the polar mesh has a good fit to the geometric shapes of the plate and, when used in the proposed discretization strategy, presents convergence to the exact solution .