Fractional-order Hall-current magneto-photothermal waves in microtemperature hydro-poroelastic semiconductor media subjected to ramp-type heating and variable thermal conductivity

Abstract

This work presents an advanced theoretical model for magneto-photothermal wave propagation in microtemperature hydro-poroelastic semiconductor media subjected to ramp-type thermal heating, explicitly accounting for fractional-order non-Fourier heat conduction, Hall current effects, and variable thermal conductivity. Unlike classical formulations that assume constant thermal properties, the present model incorporates a temperature-dependent thermal conductivity via the Kirchhoff transformation, enabling a realistic description of nonlinear heat diffusion under rapid thermal loading. A fractional-order time derivative is introduced in the heat conduction equation to capture thermal memory and anomalous diffusion, while Hall current effects are included in the electromagnetic coupling, leading to modified current density and Lorentz force expressions under strong magnetic fields. The governing system couples elastic deformation, microtemperature evolution, pore-fluid pressure, carrier density, and electromagnetic fields within a unified framework. Analytical solutions are obtained using the normal mode analysis technique, yielding closed-form expressions for the primary field variables and associated stresses. Numerical simulations are performed for porous silicon (PSi) as a representative hydro-poroelastic semiconductor material, using thermophysical, mechanical, electrical, and microtemperature properties reported in the literature. The parametric analysis spans physically relevant ranges of the fractional thermal order (0 < α≤ 1), Hall parameter, and thermal conductivity variation coefficient, allowing systematic investigation of memory effects, electromagnetic coupling, and nonlinear heat transport. The Hall parameter introduces additional damping and directional coupling, whereas ramp-type heating intensifies near-surface transient responses. The model reduces to the classical magneto-photothermal hydro-poroelastic theory in the limiting cases of constant thermal conductivity, integer-order heat conduction, and vanishing Hall current, confirming its generality. The proposed framework provides new physical insight into coupled wave phenomena in semiconductor materials and is relevant to the design of advanced optoelectronic, sensing, and energy-harvesting devices operating under rapid thermal loading and strong magnetic environments.