Enhanced Thermophysical Analysis of Unsteady MHD Jeffrey Nanofluid Flow with Microorganisms: Incorporating Forchheimer Drag, Variable Thermal Properties, and Double-Diffusive Effects

This study presents an extended numerical investigation of the unsteady magnetohydrodynamic (MHD) flow of a Jeffrey nanofluid containing motile microorganisms past a vertically stretching cylinder. The model incorporates nonlinear Forchheimer drag to simulate non-Darcian porous resistance, variable thermal conductivity and viscosity for realistic material behavior, and the Dufour—Soret effects to account for double-diffusive convection. Buongiorno’s two-component model is used to characterize nanoparticle dynamics, including Brownian motion and thermophoresis. The nonlinear partial differential equations system receives solution through an implicit finite difference method which achieves second-order spatial accuracy. The simulation investigates how different parameters including Hartmann number and Deborah number and Forchheimer number and Eckert number and thermophoresis and Brownian motion and bioconvection-related parameters affect the velocity and temperature and concentration and microorganism distributions. The research findings provide essential knowledge about how to enhance transport and control flows in systems used for thermal management and bio-reactors and porous media processing.

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