An Analytical Solution for Transient Asymmetric Heat Conduction in a Multilayer Elliptic Annulus and its Associated Thermal Stresses

Abstract

A closed-form solution is presented for the transient heat conduction problem in the elliptic annulus with multiple layers in the radial direction, but time-independent volumetric heat sources in each layer. The solution is obtained applying an integral transform technique analogous to Vodicka's approach considering series expansion function in terms of an eigenfunction to solve the heat conduction partial differential equation in elliptical coordinates. The results are obtained as a series solution in terms of Mathieu functions and hold convergence test. The temperature and thermal stresses for the three-layer elliptic region have been computed numerically and exhibited in a graphical form, by using dimensionless values and therefore discussed.