Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient

This research endeavors to conduct an examination of the thermal characteristics within the duct filled with the copper nanoparticles and water as base fluid. In exhaust systems, like car exhausts, chimneys, and kitchen hoods, duct flows are crucial. These systems safely discharge odors, smoke, and contaminants into the atmosphere after removing them from enclosed places. The study focuses on a laminar flow regime that is both hydrodynamically and thermally developed, with a specified constraints at any cross-sectional plane. To address this, we employ the finite volume method as it stands as a judicious choice, offering a balance between computational efficiency and solution accuracy. Notably, we have observed that the deceleration of flow induced by elevated Rayleigh numbers can be effectively regulated by the application of an appropriately calibrated external magnetic field. The prime parameters of the problem with ranges are: pressure gradient (1 ≤ p 0 ≤ 100) (1\le {p}_{0}\le 100), Hartmann number (0 ≤ Ha ≤ 50) (0\le \text{Ha}\le 50), Rayleigh number (1, 000 ≤ Ra ≤ 40, 000) (1,000\le \text{Ra}\le 40,000), and magnetic parameter (0 ≤ M ≤ 50) (0\le M\le 50). Furthermore, our analysis reveals that the Nusselt number exhibits a nearly linear correlation with the nanoparticle volume fraction parameter, a trend observed across a range of Rayleigh numbers and magnetic parameter values. We have noted that a mere 20% nanoparticle volume fraction can result in up to 62% rise in the Nusselt number while causing an almost 50% decrease in the factor f Re. This research framework serves as a robust foundation for understanding the intricate interplay between magnetic influences and thermal-hydraulic behavior within the delineated system.