Magnetohydrodynamic Mixed Convection Flow and Entropy Generation of a Hybrid Cu–Al2O3/H2O Nanofluid over a Vertical Cylinder with Joule Heating and Thermal Radiation

This study investigates entropy generation in a steady, laminar, magnetohydrodynamic mixed-convection boundary-layer flow of a hybrid Cu–Al2O3/water nanofluid over a heated, slender vertical cylinder subjected to a transverse magnetic field, Joule heating, viscous dissipation and thermal radiation. The governing partial differential equations are reduced to a non-similar system via a local-Reynolds-number similarity transformation and solved using a finite-difference collocation boundary-value method (bvp4c) combined with ξ-continuation and a second-level local non-similarity formulation. The model is validated against previously published results with deviations of about 2% over the range of curvature considered. Results show that the applied magnetic field decelerates the flow and increases the local entropy generation, while increased buoyancy accelerates the flow and enhances wall heat transfer. Thermal radiation and Joule heating both thicken the thermal boundary layer. Quantitatively, as the radiation parameter Rd increases from 0 to 2, the local Nusselt number rises from 0.9283 to 2.4103 (at Ri=1, M=0.5, ξ=1); as the Richardson number Ri increases from 0 to 2, the skin-friction coefficient rises from 0.9477 to 1.7798. The Brinkman number is identified as the dominant parameter controlling the balance between heat transfer and Joule irreversibility, as quantified through the entropy generation number and the Bejan number. These findings provide guidance for the thermal design and second-law optimization of MHD hybrid-nanofluid systems operating over curved geometries.