S.P Pawar - Department of Mathematics, S. N. Mor College, Tumsar (MS), India
J.J Bikram - Department of Mathematics, R. T. M. Nagpur University, Nagpur (MS), India
G.D Kedar - Department of Mathematics, R. T. M. Nagpur University, Nagpur (MS), India

This paper deals with the mathematical approach to discuss the radially varying transient temperature distribution in a multilayer composite hollow sphere subjected to the time independent volumetric generation of heat in each layer. Initially the layers are at arbitrary temperature and the analysis assumes all the layers of the body are thermally isotropic and having a perfect thermal contact. It is novel to obtain the exact solution for temperature field by the separation of variables by splitting the problem into two parts homogeneous transient and non-homogeneous steady state. The set of equations obtained are solved by using the rigorous applications of analytic techniques with the help of eigen value expansion method. The thermoelastic response is studied in the context of uncoupled Thermoelasticity. The results obtained pointed out that the magnitude and distribution of the temperature and thermal stresses are greatly influenced by the layered heat generation parameter. The accuracy and feasibility of the proposed model is demonstrated by an example of three layered hollow sphere of Aluminium, Copper and Iron subjected to given conditions. The results presented in this article could be found hardly in an open literature despite of extensive search.

Heat conduction, Internal heat generation, Multilayer, Thermal stresses