Magnetophoretic Jeffrey Nanofluid Flow Over a Stretching Cylinder: Heat Transfer Enhancement and Entropy Generation

The primary goal of this research is to develop a comprehensive thermodynamic optimization framework that quantifies the competing effects of magnetic field manipulation and viscoelastic memory on heat transfer efficiency. To the best of the authors’ knowledge, this study introduces a novel mathematical paradigm by being the first to simultaneously integrate Jeffrey viscoelastic rheology, susceptibility-based magnetophoretic forcing, and magnetohydrodynamic (MHD) Lorentz damping over a curved surface. The study addresses the synergistic effects of magnetophoretic nanoparticle transport and non-Newtonian behaviour on the convective thermal characteristics of nanofluids along a stretching cylinder. The mathematical model utilizes the Jeffrey fluid constitutive relationship—accounting for stress relaxation and retardation—combined with Buongiorno's dual-slip transport formulation for nanoparticle diffusion. The thermal energy balance incorporates Joule heating, viscous dissipation, and nanoparticle-enhanced thermal conductivity. Thermodynamic performance is quantified via a second-law entropy production analysis. The governing coupled partial differential equations are transformed and solved using the Spectral Quasilinearization Method with Chebyshev-Gauss-Lobatto collocation points for high computational accuracy. Parametric investigations reveal that increasing magnetophoretic intensity enhances axial fluid acceleration and near-surface nanoparticle enrichment, boosting convective heat transfer. Conversely, the viscoelastic Deborah number dampens velocity gradients and reduces thermodynamic irreversibility. The Hartmann number elevates fluid temperatures via resistive heating, while surface curvature broadens the thermal diffusion zone. Entropy production rises with magnetophoretic intensity, electromagnetic strength, and viscous dissipation. The Bejan ratio demarcates regions dominated by thermal gradients versus viscous and magnetic friction. Crucially, these findings reveal a previously unreported thermodynamic transition zone where the Hartmann number optimally balances convective heat transfer enhancement against electromagnetic energy degradation. These results confirm magnetophoresis as a viable strategy for thermal transport optimization in magnetic-based thermal management, microfluidic drug delivery, and polymer processing.