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Fractional-order Klein-Gordon nonlocal model for thermo-elasto-diffusion in porous medium
Abhik Sur1, Moataz Alosaimi2, Abhinav Singhal3
1Department of Mathematics, Sister Nivedita University, Kolkata, West Bengal, India.
Scientific Reports
|May 27, 2026
Summary
This study introduces a generalized thermo-elasto-diffusion model for porous materials, incorporating fractional-order heat conduction and nonlocal dynamics. The findings reveal that these advanced parameters significantly impact wave propagation and heat transfer in micro/nanoscale materials.
Area of Science:
- Continuum Mechanics
- Materials Science
- Heat Transfer
Background:
- Classical heat conduction and thermoelastic theories fail at micro/nanoscale due to instantaneous propagation assumptions.
- Memory and nonlocal effects are crucial in advanced materials under rapid thermal/chemical loads.
- Existing models like Lord-Shulman lack comprehensive descriptions for complex transport phenomena.
Purpose of the Study:
- To develop a generalized thermo-elasto-diffusion model for porous media.
- To incorporate fractional-order heat conduction and Klein-Gordon-type nonlocal dynamics.
- To analyze the transient response of coupled thermo-mechanical fields in advanced materials.
Main Methods:
- Fractional-order calculus applied to heat conduction and viscoelastic analogies.
- Klein-Gordon-type nonlocal dynamics integrated into the model.
- Analytical solutions derived in the Laplace domain and numerically inverted using Zakian's algorithm.
Main Results:
- Fractional-order parameters and nonlocal effects critically influence wave propagation and heat transfer.
- Significant impact observed near boundaries and in regions with strong microstructural interactions.
- Transient responses of displacement, temperature, chemical potential, and stress fields were evaluated.
Conclusions:
- The proposed fractional-order nonlocal model offers a more realistic description of coupled thermo-mechanical processes.
- The framework provides valuable insights for designing and analyzing advanced porous and semiconductor materials.
- This generalized model enhances understanding of transport phenomena in micro/nanoscale systems under extreme conditions.
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