Generalized magneto-thermoelasticity problem in an orthotropic hollow sphere under thermal shock

Abstract

This article addresses the magneto-thermoelasticity problem within an orthotropic hollow sphere. The governing equations are formulated based on the Lord-Shulman coupled theory of thermoelasticity. Time-dependent thermal and mechanical boundary conditions are imposed on the inner and outer surfaces of the hollow sphere. The analytical solution is obtained using the finite Hankel transform. A thermal shock in the form of heat flux is prescribed on the sphere’s inner surface, and subsequently, the transient thermal response of the sphere, along with radial displacement and radial, tangential, and circumferential stresses, are derived. The influence of different magnetic field values, orthotropic material properties, and relaxation time is investigated and presented graphically. The obtained results exhibit excellent agreement with existing literature, validating the robustness of the proposed model. The findings not only contribute to the fundamental understanding of magneto-thermoelasticity but also offer practical insights for engineering applications involving orthotropic materials in complex thermal and magnetic environments. The availability of an exact solution facilitates the validation of numerical models, ensuring their accuracy and reliability in capturing the intricate behavior of orthotropic materials under coupled fields.