Magneto–thermal instability in Rivlin–Ericksen nanofluids for hyperthermia therapy and polymer processing

This study investigates thermal convection in a Rivlin–Ericksen nanofluid subjected to a vertical magnetic field, incorporating Brownian motion and thermophoresis under passive nanoparticle boundary conditions. A Galerkin-type method is employed to analyze the onset of stationary and oscillatory convection. Stationary convection occurs for both heavier and lighter nanoparticles, whereas oscillatory convection arises only for lighter nanoparticles due to the combined effects of viscoelasticity, magnetic damping, and diffusivity ratios. Sensitivity analysis reveals that for stationary convection (Rn>0), hyperthermia exhibits minimal sensitivity (Δ(Ra)st