An Inverse Mathematical Approach for Thermal Stresses in a Solid Sphere

The present work deals with the determination of unknown temperature and thermal stresses in a solid sphere. A solid sphere is subjected to arbitrary known interior temperature under steady state. The Legendre's transform are used for heat transfer analysis to determine temperature change within solid sphere. The solution of Navier's equation in terms of Goodier's thermoelastic displacement potential and the Boussinesq's harmonic function for spherical co-ordinate system have been used for thermal stress analysis. The results for temperature change, displacement and stresses have been computed numerically and illustrated graphically