an exact solution for kelvin-voigt model classic coupled thermo viscoelasticity in spherical coordinates

In this paper, the classic kelvin-voigt model coupled thermo-viscoelasticity model of hollow and solid spheres under radial symmetric loading condition is considered. a full analytical method is used and an exact unique solution of the classic coupled equations is presented. the thermal and mechanical boundary conditions, the body force, and the heat source are considered in the most general forms and where no limiting assumption is used. this generality allows simulate varieties of applicable problems. at the end, numerical results are presented and compared with classic theory of thermoelasticity.