Waves reflection in porous thermoelastic media with spatial–temporal nonlocality under hyperbolic two-temperature effects
5 affiliations
- 1Mathematics, 1277 Harrow Cres, Yardley, PA, 19067, USA
- 2Department of Mathematics, Kishan Lal Public College, Rewari, Haryana, 123401, India
- 3Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, 136119, India
- 4Mathematics Department, Faculty of Science, Sohag University, Sohag, Egypt
- 5Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O.Box 84428, Riyadh11671, Saudi Arabia
Abstract
The present work examines how plane waves are reflected within an isotropic, homogeneous, incompressible porous thermoelastic plane incorporating a spatial-temporal nonlocal elastic formulation together with hyperbolic two-temperatures (HTT) effects under impedance boundary conditions. The primary objective is to examine how nonlocal interactions and generalized heat conduction influence wave propagation and energy partition in porous thermoelastic media. The mathematical formulation is developed within the generalized Lord–Shulman thermoelastic framework combined with Klein–Gordon-type nonlocal elasticity. By employing Helmholtz decomposition and normal mode analysis, the governing equations are reduced, from which closed-form relations for the reflection coefficients and associated energy ratios are obtained. Numerical simulations demonstrate that the HTT parameter and both spatial and temporal nonlocal parameters significantly modify the distribution of reflected wave energy while satisfying the law of energy conservation. In particular, temporal nonlocality exerts a stronger influence on energy partition than spatial nonlocality, and the HTT model exhibits marked deviations from the classical one-temperature and two-temperature formulations. These findings provide a comprehensive multiscale framework for accurately characterizing wave reflection phenomena in porous thermoelastic media and offer valuable insights for applications in geomechanics, seismology, ocean engineering, petroleum engineering, biomedical imaging, and nanoscale thermoelastic analysis.
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BibTeX
@article{saurav2026waves,
title = {{Waves reflection in porous thermoelastic media with spatial–temporal nonlocality under hyperbolic two-temperature effects}},
author = {Sharma Saurav and Batra Divya and Kumar Rajneesh and Abbas Ibrahim and Almuneef Areej},
journal = {Open Physics},
year = {2026},
month = oct,
doi = {10.1515/phys-2025-0319},
url = {https://doi.org/10.1515/phys-2025-0319},
note = {CC BY},
}
RIS
TY - JOUR
TI - Waves reflection in porous thermoelastic media with spatial–temporal nonlocality under hyperbolic two-temperature effects
AU - Sharma Saurav
AU - Batra Divya
AU - Kumar Rajneesh
AU - Abbas Ibrahim
AU - Almuneef Areej
PY - 2026
DA - 2026/10/26
JO - Open Physics
DO - 10.1515/phys-2025-0319
UR - https://doi.org/10.1515/phys-2025-0319
AB - The present work examines how plane waves are reflected within an isotropic, homogeneous, incompressible porous thermoelastic plane incorporating a spatial-temporal nonlocal elastic formulation together with hyperbolic two-temperatures (HTT) effects under impedance boundary conditions. The primary objective is to examine how nonlocal interactions and generalized heat conduction influence wave propagation and energy partition in porous thermoelastic media. The mathematical formulation is developed within the generalized Lord–Shulman thermoelastic framework combined with Klein–Gordon-type nonlocal elasticity. By employing Helmholtz decomposition and normal mode analysis, the governing equations are reduced, from which closed-form relations for the reflection coefficients and associated energy ratios are obtained. Numerical simulations demonstrate that the HTT parameter and both spatial and temporal nonlocal parameters significantly modify the distribution of reflected wave energy while satisfying the law of energy conservation. In particular, temporal nonlocality exerts a stronger influence on energy partition than spatial nonlocality, and the HTT model exhibits marked deviations from the classical one-temperature and two-temperature formulations. These findings provide a comprehensive multiscale framework for accurately characterizing wave reflection phenomena in porous thermoelastic media and offer valuable insights for applications in geomechanics, seismology, ocean engineering, petroleum engineering, biomedical imaging, and nanoscale thermoelastic analysis.
SN - 2391-5471
ER -