A new study develops a thermoelastic framework based on the Lord-Shulman theory that simultaneously incorporates an internal heat source, an external electromagnetic field and a variable reference temperature in solids. The model refines the classical formulation of thermoelasticity with finite propagation speeds for heat, avoiding the paradox of instantaneous conduction that the Fourier law entails in transient problems.

The Lord-Shulman theory, proposed in the 1960s, introduces a relaxation time into the heat conduction equation to ensure that thermal disturbances propagate at a finite speed. The version presented here extends that scheme by coupling the thermal field with the electromagnetic one and by including a heat source distributed throughout the volume of the solid, while also taking into account the reference temperature with respect to which deformations and thermal gradients are measured.

The mathematical treatment leads to a coupled system of wave equations for the displacement field, the temperature and the electromagnetic components. Including the reference temperature allows a more faithful description of processes in which the solid starts from a non-uniform state, something common in microelectromechanical applications, coatings exposed to intense fields and manufacturing processes with localized heating.

The practical motivation of the model is twofold. On the one hand, solids subjected to intense electromagnetic fields —as in induction furnaces, shielding or fusion components— experience volumetric heat sources whose thermomechanical effect is not always well captured by isothermal-reference formulations. On the other hand, having an explicit reference temperature improves the comparability between simulations and experimental measurements.

The work fits into the line of generalized thermoelastic models seeking to accurately describe thermo-mechano-electromagnetic coupling in real materials. Experimental validation and the extension to anisotropic materials or those with thermal memory remain natural steps for future research.