Solution for One-Dimensional Transient Heat Conduction And Thermoelasticity in a Multilayer Hollow Sphere

Abstract

An analytical solution is obtained for the problem of one dimensional transient heat conduction and thermo elasticity in the multilayered hollow sphere. The sphere has multiple layers in the radial direction and each layer is time dependent and spatially without heat sources are considered. To obtain the temperature distribution The eigen value problem is solved by use of separation of variables method. At $t> 0$ homogenous boundary conditions of the first kind are set on the inner radial surface ($i = 1$, $r=r_{0}$) and third kind are set on the outer ($i= n$, $r= r_n$) radial surfaces (Convection).