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<3.2%, |S|<1), while polymer-processing conditions display strong destabilization, with reductions in (Ra)st, up to 92% and sensitivity indices |S|>2 driven primarily by variations in Rn, NA, and Le. For stationary convection with (Rn<0), both regimes remain weakly sensitive (Δ(Ra)st<7.3%, |S|≪1). In oscillatory convection, hyperthermia exhibits strong stabilization with increasing viscoelastic parameter F and magnetic number Q, leading to increases in (Ra)osc up to 848%. In polymer-processing regimes, variations in F, Q and Pr produce stabilization up to 923%, while cross-diffusion parameters cause destabilization up to 96% (|S|≫1). Magnetic effects are weak in stationary convection but play a critical role in regulating oscillatory behavior. The large percentage variations arise from the proximity of the system to marginal stability, where competing magnetic, viscoelastic, and double-diffusive mechanisms produce steep stability boundaries. From an applications perspective, destabilizing mechanisms enhance nanoparticle mixing and heat transfer in polymer-processing flows, while magnetic and viscoelastic stabilization enables precise control of convective instabilities. In biomedical applications such as magnetic hyperthermia, controlled oscillatory convection supports localized thermal delivery, improving treatment efficacy through externally modulated convection control.