Unsteady Magnetohydrodynamics Heat‐Generating Oldroyd‐B Nanofluid Flow in a Stretching Power Generator Duct Using the Crank–Nicolson Method

Abstract

ABSTRACT Designing efficient hydromagnetic power generators demands a careful understanding of magnetohydrodynamic flows in annular ducts, especially with viscoelastic nanofluids. This work numerically investigates unsteady, heat‐generating Oldroyd‐B nanofluid flow in such a duct, where the inner cylinder stretches radially. The model captures mass, momentum, energy, magnetic induction, and nanoparticle transport, incorporating temperature‐dependent thermal conductivity and Arrhenius nanoparticle accumulation kinetics. We transformed the governing partial differential equations into nonlinear ordinary differential equations using similarity transformations, and then solved them numerically with the Crank–Nicolson method with , , second‐order accuracy, and errors below . The study aims to clarify how viscoelasticity, magnetic field, curvature, unsteadiness, and buoyancy jointly affect transport. Results show that raising the relaxation Deborah number from 0.1 to 0.5 cuts radial and axial velocities by 18% and 22%, while the retardation Deborah number boosts velocities up to 15%. The magnetic parameter suppresses velocities by 30% but elevates temperature by 12% through Joule heating. Curvature enhances radial flow by 20% yet weakens the axial magnetic field by 15%; unsteadiness shrinks the thermal boundary layer thickness by 25%. The skin friction coefficient grows 35% with magnetic parameter, 22% with Reynolds number, and 8% with curvature, but falls 15% with activation energy, 18% with unsteadiness, and 12% with buoyancy ratio. Heat transfer improves 45% with Prandtl number and 30% with Reynolds number, whereas heat generation reduces it 18%. Mass transfer grows up to 54% with activation energy and 40% with magnetic parameter, and drops 18% with unsteadiness. These results provide predictive insights for designing viscoelastic nanofluid‐based hydromagnetic power systems.