Thermoelastic response to an internal heat source and an electromagnetic field in solids using a refined Lord–Shulman framework with reference temperature

An extended Lord–Shulman thermoelastic formulation has been developed to investigate the coupled effects of an external magnetic field, internal heat source, and non-zero reference temperature on the behavior of magneto-thermoelastic materials. Analytical expressions for the temperature variation, displacement, dilatation, stress components, and induced magnetic field are obtained using the normal mode analysis method. The resulting formulation enables the effects of the newly introduced physical parameters to be identified separately and their contributions to the coupled response to be quantified. Numerical computations and graphical simulations are performed using MATLAB R2013a. The results demonstrate that the applied magnetic field significantly modifies the mechanical and thermal responses through magnetoelastic coupling, while the internal heat source produces a pronounced alteration in the temperature and associated stress and displacement fields. The reference temperature also affects the thermoelastic response by modifying the thermal–mechanical coupling terms, whereas the vertical distance governs the spatial attenuation and propagation of the coupled fields. In particular, the numerical results reveal sign changes in the temperature variation and induced magnetic field under certain parameter combinations, indicating a reversal in the corresponding local thermal and electromagnetic perturbations rather than an unphysical behavior. These findings constitute clear outcomes of the present refined Lord–Shulman framework. The developed model is relevant to engineering and applied-science problems involving coupled thermal, mechanical, and electromagnetic effects, including magnetoelastic components, electromagnetic heating and sensing systems, geophysical materials subjected to geomagnetic fields and thermal disturbances, and thermally affected electromagnetic devices. Thus, the proposed formulation provides an analytical framework for predicting coupled wave propagation and field distributions in magneto-thermoelastic media under simultaneous magnetic, thermal, and mechanical influences.