Finite amplitude oscillatory convection in a rotating Rivlin–Ericksen ferrofluid layer with variable viscosity

This study explores the onset of oscillatory convection, bifurcation structure, and heat transport in a rotating viscoelastic ferrofluid layer, where the viscoelastic model is described by Rivlin–Ericksen (RE) constitutive equations, and the viscosity varies with applied magnetic field. Motivated by applications such as magnetic drug targeting using ferrofluid carriers in a viscoelastic bloodstream under an external magnetic field, as well as in aerospace and thermal management systems, the present analysis determines the critical Rayleigh numbers and wavenumbers for both stationary and oscillatory instabilities, with the latter identified as the preferred mode. Weakly nonlinear theory is employed to analyze bifurcation behavior, leading to a complex Ginzburg–Landau amplitude equation solved numerically. Heat transport is quantified via the Nusselt number, expressed in terms of the nonlinear convection amplitude. The results reveal that the Coriolis force significantly alters the flow structure and stabilizes the system. The viscoelasticity parameter exhibits a twofold influence, as it does not affect the stationary onset threshold, but it significantly impacts the nature of the bifurcation, which can be either supercritical or subcritical, depending strongly on its value. Compared to the non-rotating, constant-viscosity case, the combined action of viscoelasticity, magnetization, and rotation amplifies convective strength and heat transfer, whereas stronger magnetic field-dependent (MFD) viscosity reduces thermal transport efficiency. The evolution of heat transport is further examined through isotherm plots. The formulation is validated through excellent agreement with classical limiting cases and existing results from prior studies.