Analytical study of magnetothermoelastic wave propagation in media with double porosity and microtemperature under Lord and Shulman heat conduction

This study develops a comprehensive generalized thermoelastic model that uniquely integrates four advanced physical frameworks for analyzing wave propagation in semiconductor materials. The model combines: (i) the Lord-Shulman (LS) theory of finite-speed heat conduction with a single thermal relaxation time; (ii) a double-porosity formulation capturing hierarchical interactions between macro-pore and micro-fissure networks; (iii) a microtemperature vector field accounting for sub-scale thermal gradients and microstructural thermal inertia; and (iv) a magnetic body force acting perpendicular to the direction of wave propagation. Through rigorous analytical treatment using normal mode analysis, the coupled governing equations are reduced to a tenth-order characteristic polynomial and solved using eigenvalue decomposition, yielding closed-form expressions for all field variables. Key findings demonstrate that: (1) the magnetic field introduces additional stiffness through the Lorentz force, modifying wave dispersion and increasing effective wave speeds; (2) the double-porosity structure introduces substantial damping through enhanced internal dissipation between macro-pore and micro-fissure networks; (3) microtemperature effects intensify and prolong the thermoelastic response by adding microstructural thermal degrees of freedom; and (4) the Lord-Shulman framework is validated by finite-speed thermal wave profiles distinct from classical diffusion patterns. The refined theoretical tool developed is essential for predictive accuracy in semiconductor devices, magneto-thermoelastic applications, and porous media where magnetic effects cannot be neglected.