Analysis of the Effects of Time Periods and Fractal Patterns on Heat Flow in Porous Materials

Document Type : Research Paper

Authors
A.M. Al Khulayf 1
A.N. Abdalla 2
F.A. Alshehri 3
A. Alasmari 4
A. Ismail 5
A.A. Kilany 6
1 Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
2 Department of Mathematics, Faculty of Science, Sohag University, 82425 Sohag, Egypt
3 Department of Mathematics, College of Sciences, University of Bisha, P.O Box 8154, 67398-5644 Alnamas, Saudi Arabia
4 Department of Physics, College of Science, University of Bisha, Bisha 61922, Saudi Arabia
5 Department of Physics, Al-Azhar University, 71524 Asyut, Egypt
6 Ministry of Higher Education, Higher Institute of Management Sciences, Beni Suef, Egypt
10.22055/jacm.2025.48309.5135
Abstract
The proposed mathematical model applies non-integer derivative orders to study how porosity influences a generalized thermoelastic medium while utilizing improved multi-phase delays framework. The system consists of a porous homogenous isotropic domain where the volume percent shows two-dimensional variations. The modified couple stress theory enables transformation of controlling differential equations into ordinary differential equations. Declining to the normal mode approach allows analysis of these equations' mathematical solutions. The calculation of precise solutions for displacement, temperature change, shear and perpendicular loads and volume fraction parameter depends on harmonic wave analysis. The research outcomes present graphical illustrations which present the influence of complex derivative orders together with material porosity levels. The paper demonstrates how models that use fractal differentiation differ from standard models through comparison studies. The research findings enhance thermoelastic behavior understanding in porous media while facilitating the creation of improved performance materials. The study provides significant ramifications for materials science and offers solutions to multi-physics problems as well as enables the development of high-precision industrial technologies.
Keywords
Generalized thermoelasticity
Non-integer derivative order
Refined multi-phase lags model
Porous media
Harmonic wave analysis
Subjects

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Journal of Applied and Computational Mechanics
Volume 12, Issue 1
Winter 2026
Pages 202-211