AI-driven analysis of Darcy-Forchheimer EMHD boundary layer flow in thermal hybrid nanofluids

Abdulaziz H. Alharbi; El Hadi Boussaha; Ali M. Alhartomi; Hicham Salhi; Raed Alrdadi; Mohamed Kezzar; Mohamed Rafik Sari; Abdulaziz H. Alharbi; El Hadi Boussaha; Ali M. Alhartomi; Hicham Salhi; Raed Alrdadi; Mohamed Kezzar; Mohamed Rafik Sari

doi:10.3934/math.20251192

AIMS Mathematics

2025, Volume 10, Issue 11: 27129-27151. doi: 10.3934/math.20251192

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AI-driven analysis of Darcy-Forchheimer EMHD boundary layer flow in thermal hybrid nanofluids

1.
Department of Mathematics, Jamoum University College, Umm Al-Qura University, Makkah 25375, Saudi Arabia
2.
Department of Process Engineering, Faculty of Technology, Universit´e 20 Aout 1955, ElHadaik Road, Skikda 21000, Algeria
3.
Department of Mathematics, Al-Leith University College, Umm Al-Qura University, Makkah 24382, Saudi Arabia
4.
Laboratory of Applied Research in Hydraulics, University of Mustapha Ben Boulaid, Batna2, Batna 05000, Algeria
5.
Materials and Energy Engineering Laboratory (LMGE), Technology Department, Faculty of Technology, 20 Aout 1955 University of Skikda, P. O. Box 26, 21000, Skikda, Algeria
6.
Mechanics of Materials and Plant Maintenance Research Laboratory (LR3MI), Mechanical Engineering Department, Faculty of Technology, Badji Mokhtar-Annaba University, P. O. Box 12, Annaba 23000, Algeria

Received: 23 September 2025 Revised: 29 October 2025 Accepted: 04 November 2025 Published: 21 November 2025
MSC : 35A22, 76A05, 76D05, 76S05, 76W05

This study thoroughly examined the complex electro-magnetohydrodynamic (EMHD) boundary layer flow of ternary hybrid nanofluids (THNP), specifically, Ti 6Al4V-ZnO-Fe₂O₃, over stretching-shrinking and permeable surfaces, and recognized the important impact of the nonlinear Darcy-Forchheimer law and thermal radiation. The THNP, comprised of three distinct nanoparticles including: titanium alloy Ti6Al4V (6% aluminum, 4% vanadium, balance titanium), zinc oxide ZnO, and iron oxide Fe₂O₃ suspended in a base fluid, is used to enhance both thermal and flow properties. The model comprehensively addressed inertial effects in porous media through the Darcy-Forchheimer drag, as well as the electromagnetic forces and thermal radiation. The governing partial differential equations were transformed into nonlinear ordinary differential equations via similarity transformations, which were solved through an intelligent numerical approach using artificial neural networks (ANN). A thorough analysis was conducted on the effect of important parameters such as the Darcy-Forchheimer permeability, nanoparticle volume fractions, stretching/shrinking rates, surface permeability, and radiation intensity on the velocity and temperature profiles. The results are shown graphically and discussed, providing insight related to the fluid dynamics and heat-transfer phenomena in such advanced systems.
- artificial intelligence,
- artificial neural networks,
- Darcy-Forchheimer law,
- THNP,
- EMHD,
- stretching/shrinking,
- intelligent numerical approach
Citation: Abdulaziz H. Alharbi, El Hadi Boussaha, Ali M. Alhartomi, Hicham Salhi, Raed Alrdadi, Mohamed Kezzar, Mohamed Rafik Sari. AI-driven analysis of Darcy-Forchheimer EMHD boundary layer flow in thermal hybrid nanofluids[J]. AIMS Mathematics, 2025, 10(11): 27129-27151. doi: 10.3934/math.20251192

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Abstract

This study thoroughly examined the complex electro-magnetohydrodynamic (EMHD) boundary layer flow of ternary hybrid nanofluids (THNP), specifically, Ti 6Al4V-ZnO-Fe₂O₃, over stretching-shrinking and permeable surfaces, and recognized the important impact of the nonlinear Darcy-Forchheimer law and thermal radiation. The THNP, comprised of three distinct nanoparticles including: titanium alloy Ti6Al4V (6% aluminum, 4% vanadium, balance titanium), zinc oxide ZnO, and iron oxide Fe₂O₃ suspended in a base fluid, is used to enhance both thermal and flow properties. The model comprehensively addressed inertial effects in porous media through the Darcy-Forchheimer drag, as well as the electromagnetic forces and thermal radiation. The governing partial differential equations were transformed into nonlinear ordinary differential equations via similarity transformations, which were solved through an intelligent numerical approach using artificial neural networks (ANN). A thorough analysis was conducted on the effect of important parameters such as the Darcy-Forchheimer permeability, nanoparticle volume fractions, stretching/shrinking rates, surface permeability, and radiation intensity on the velocity and temperature profiles. The results are shown graphically and discussed, providing insight related to the fluid dynamics and heat-transfer phenomena in such advanced systems.

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