Initial stress effects on fractional thermoelastic wave propagation in semiconductor media under three thermoelasticity theories

Abstract

This work examines the impact of initial stress on the spread of coupled thermo-mechanical waves in a semiconductor thermo-elastic medium using a β -order fractional derivative model. The study is undertaken utilizing three generalized thermo-elastic theories: Dual-Phase-Lag (DPL) model, Lord-Shulman (L-S) theory, and Refined Dual-Phase-Lag (RDPL) model. To accurately reflect the underlying physical processes, the governing equations for heat conduction, elastic deformation, and semiconductor carrier dynamics are fully coupled, taking into account both finite-speed thermal transport and carrier density effects. To simplify the mathematical treatment, a suitable nondimensionalization strategy is adopted, lowering the number of governing parameters and clarifying the structure of the problem. A transform technique is then utilized to transform the resulting system of coupled partial differential equations (PDEs) into an analogous system of ordinary differential equations (ODEs) that can be solved analytically. This approach produces solution for displacement, temperature, carrier density, and stress tensor components, allowing for a complete investigation of wave propagation properties inside the medium. Numerical simulations using graphical representations are used to investigate the physical significance of the theoretical concept. These computations provide a comparative examination of physical quantities with and without initial stress across the three thermo-elastic theories. The β -fractional derivative and initial stress significantly impact wave behavior, including propagation velocity, amplitude evolution, and attenuation characteristics. Furthermore, the analysis sheds further light on the interplay between thermal processes and carrier density effects in thermo-elastic materials, emphasizing the significance of these elements in precisely forecasting the dynamic response of modern semiconductor media.