Numerical modelling of heat transfer and flow efficiency in the stretching process and extrusion of Jeffrey fluid in a heated cylinder

This study presents a numerical investigation of magnetohydrodynamic (MHD) Jeffrey fluid flow over a stretching cylinder, incorporating convective heat transfer and the influence of motile microorganisms. To capture non-Fourier heat conduction effects, the Cattaneo-Christov heat flux model is employed. The governing partial differential equations, formulated in cylindrical coordinates, are transformed into a system of ordinary differential equations using similarity transformations. These equations are solved numerically using MATLAB’s bvp4c solver. The effects of key physical parameters on involved profiles are analysed and visualised. The study also evaluates engineering quantities such as skin friction and Nusselt number. The novelty of this work lies in its integration of Cattaneo-Christov heat conduction and bioconvection due to gyrotactic microorganisms in the context of MHD Jeffrey fluid flow with convective boundary conditions. Magnetic field $M$ diminishes the speed of fluid and raises temperature, while higher $\beta$ drops fluid velocity $f^{\prime }$, making the Jeffrey fluid behave more viscoelastic.