Heat Production in a Simply Supported Multilayer Elliptic Annulus Composite Plate and Its Associated Thermal Stresses

This paper is concerned with the theoretical treatment of thermoelastic problem in multilayer elliptical composite plate and the generation of heat in the body as well as at the interfaces with imperfect thermal contact under arbitrary initial temperature distribution. In order to obtain a closed-form solution of transient heat conduction problem, an alternative approach using a new Sturm-Liouville integral transform is presented that considers the series expansion using the eigenfunction expansion method for Sturm-Liouville boundary value problem. Any particular case of special interest can be
derived from assigning suitable values to the parameters and functions of the temperature field and its associated stresses. As a particular case, the quandary on the heat conduction and its stresses on a two-layered elliptical plate were solved.