Investigating Hall Effect and Viscous Dissipation in Saffman/Nanofluid MHD Duct Flow: A Combined RBF and Fuzzy Logic Approach

Singh Bhatia, Gurpreet; Kumar Chandrawat, Rajesh; Anwar Bég, O; Kuharat, S; Dang, B C; Kumar, Deepak

Abstract

Nano-energetic materials are recognized for their exceptional ability to release high amounts of energy at the nanoscale, making them promising elements for thermal management and energy storage applications. These materials are increasingly utilized in modern fuel cells, hybrid heat exchangers, and power generation systems. The use of electro-conductive working liquids in advanced smart thermal energy systems is also gaining popularity. Such complex media respond to external electrical and magnetic fields and require the application of magnetohydrodynamics (MHD). These systems may exhibit multiple magneto-physical phenomena, including Maxwell displacements, Landau damping (for plasmas), electromagnetic induction, Ohmic dissipation (heat generation due to electrical resistance), oblique magnetic fields, and alternating magnetic field intensity. Motivated by these advancements, the present study aims
to develop a robust mathematical model to analyze the effectiveness of incorporating 𝐴𝑙2𝑂3 nanoparticles into an Ethylene-Glycol (EG)-water base fluid mixture for enhancing heat transfer in magnetohydrodynamic pumping systems. The study specifically examines a horizontal thermal duct containing two immiscible layers: an upper Saffman dusty fluid (fluid-particle suspension) layer and a lower viscous nanofluid layer. The behavior of nanofluids in thermal duct applications is often influenced by uncertain pressure gradients, which can significantly impact their flow and heat transfer characteristics. To address this issue, a fuzzy differential equation approach is employed to model the uncertainty in the immiscible fluid flow characteristics, including velocity and temperature profiles. The relevant energy and momentum balance equations for these immiscible fluids are formulated to include fuzzy pressure gradient forces, as well as magnetic body force, ion slip, and Hall current parameters. A radial basis function pseudo-spectral method (RBF-PS) is utilized to solve the transformed fuzzy dimensionless boundary value problem. The findings reveal that the presence of 𝐴𝑙2𝑂3 nanoparticles, although limited to the lower region of the duct, significantly influences energy and momentum transfer across both regions. The study offers valuable insights into the behavior of nanofluids under varying external pressure forces and demonstrates the utility of fuzzy differential equations in capturing uncertainties in pressure gradients. The results of the study include grey scale image fuzzy profiles of velocity and temperature for both fluids and particles, providing valuable information for designing and optimizing nanofluid systems.

• Journal Article Type: Article
• Acceptance Date: Aug 1, 2025
• Deposit Date: Aug 3, 2025
• Print ISSN: 1678-5878
• Electronic ISSN: 1806-3691
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Additional Information: SET STATEMENT: This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/[insert DOI]