Thermoelastic behavior of infinite porous media with voids subjected to instantaneous heat Sources: A Spatio-Temporal nonlocal and fractional heat transfer approach

Abstract

This paper presents a novel nonlocal thermoelastic model designed to capture the behavior of porous materials containing voids, effectively addressing the limitations of prior thermoelastic frameworks. The enhanced dual-phase lag (DPL) thermoelastic theory is extended by integrating the Rabotnov fractional differential operator, providing a more accurate representation of equations involving memory effects and nonlocal interactions. Additionally, a poro-thermoelastic model is formulated to account for both spatial and temporal nonlocal effects, enabling the analysis of microscale phenomena and memory-dependent behaviors in porous structures. This advanced mathematical framework offers a more refined and accurate depiction of the dynamic thermomechanical responses of elastic materials with voids. The proposed model is subsequently employed to investigate transient wave propagation in an infinite thermoelastic porous medium containing voids, subjected to time-dependent instantaneous heat supply distributed over the free surface area. To derive the solution in the transformed domain, the Laplace transform method is combined with the eigenvalue approach. Numerical results are presented for specific cases, providing a clear visual representation of the outcomes, which are analyzed in depth. Additionally, various scenarios are compared to enable a thorough evaluation of the results. These comparisons offer valuable insights into the system’s behavior under different conditions.