Coupled heat equation in thermoelasticity with temperature dependent moduli

Abstract

New and consistent expressions for the coupled heat equation are developed within the framework of small-strain thermoelasticity for both Fourier and Cattaneo–Vernotte conduction models. These expressions place no restrictions on the changes in temperature, allow for the temperature dependence of the thermoelastic moduli, and include all the coupling terms as functions of the thermoelastic moduli and their derivatives. As applications, (i) an extended Lord–Shulman-type model is derived that takes into account the temperature dependence of the thermoelastic moduli, and (ii) the equations underpinning the experimental technique of thermoelastic stress analysis are revisited.

Keywords:

• Cattaneo–Vernotte heat conduction equation
• generalized thermoelasticity
• Lord–Shulman model
• thermoelastic stress analysis
• temperature dependent properties