Magneto-Bioconvection Dynamics of Synovial Nanofluids: Consequences of Porosity, Rheology, and Heat Generation

The primary objective of this study is to analyze the thermal processes, nanoparticle concentration, and bioconvection mechanisms in a synovial fluid model using numerical methods. Two fluid models are considered: Model (1), representing a shear-thinning fluid, and Model (2), representing a shear-thickening fluid. The influences of magnetic field, porosity, Joule heating, and viscous dissipation are incorporated into the analysis. The governing equations for momentum, energy, nanoparticle concentration, and motile microorganism density are formulated using the lubrication approximation. The resulting nonlinear differential equations are solved numerically using the Runge–Kutta–Merson method and the finite difference scheme. The effects of key parameters on velocity, temperature, nanoparticle concentration, and motile microorganism density are systematically explored. The study reveals that the magnetic field significantly alters the fluid motion, reducing velocity as magnetic intensity increases, whereas higher velocities are observed in the shear-thinning model. The synovial fluid achieves its maximum velocity near the knee cartilage surface. The temperature profile is higher in Model (1) than in Model (2), primarily due to heat generation effects. The concentration production parameter also affects the thermal field, leading to lower nanoparticle concentrations in Model (1). Moreover, the thermophoretic parameter decreases nanoparticle concentration, while the Brownian motion parameter enhances it. Heat-source-driven fluid motion ultimately reduces the density of motile microorganisms.