On Estimating the Growth Rate of Perturbations in Rivlin-Ericksen Ferromagnetic Convection with Magnetic Field Dependent Viscosity

Abstract

The unique viscoelastic properties and the consideration of MFD (magnetic field dependent) viscosity in the Viscoelastic ferrofluid model render it highly suitable for the accurate modeling of complex biological fluids, such as blood. The present research comprises the study of perturbation growth rate in a case of Rivlin-Ericksen Ferrofluid layer with viscosity depending on a vertically acting magnetic field. The complex growth rate of an arbitrary oscillatory motion with growing amplitude in Rivlin-Ericksen ferromagnetic convection for free-free boundaries has been analytically proven to be located within a semicircle in the right half of the σiσr-plane and (radius)² = [RM₁/P_r(1+2(1+δM₃)π²F_ν)]. Bounds are also obtained for situation involving rigid boundaries. For stress-free boundaries, the sufficient condition for PES validity is derived as [RM₁P_r/π⁴(1+(1+δM₃)π²F_ν)] ≤ 1, where R represents the Rayleigh number, P_r is the Prandtl number, F_ν characterizes viscoelasticity of Rivlin- Ericksen ferrofluid, M₃ > 0 is the measure of the nonlinearity of magnetization and M₁ is the magnetic number. The mathematical derivation of these results is presented in detail. Thus the analysis presented here reveals that the oscillations in Rivlin-Ericksen ferromagnetic convection can be regulated or halted by taking into account the viscosity dependent on the magnetic field and the viscoelasticity of the fluid.