<p>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 electroconductive 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 pseudospectral method (RBFPS) 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 grayscale image fuzzy profiles of velocity and temperature for both fluids and particles, providing valuable information for designing and optimizing nanofluid systems.</p>