Convective instability of ferromagnetic fluids subjected to magnetic field modulation

Abstract

The thesis deals with an analytic study of the stability of ferroconvection in a horizontal layer of a ferromagnetic fluid under the influence of a time-dependent magnetic field. The applied vertical magnetic field consists of two parts: a constant part and a time-dependent periodic part which varies sinusoidally with time. The effect of porous medium, couple stresses, anisotropies of porous permeability and thermal conductivity, rotation and viscoelasticity on the onset of ferroconvection is considered. The findings of the problems addressed in the thesis may come in handy for heat transfer applications with ferromagnetic fluids as working media. The summary of the problems investigated in the thesis is given below. newline newlineThermomagnetic convection in a magnetic fluid filled sparse permeable structure with modulated magnetic field newlineThe stability of a horizontal layer of a ferromagnetic fluid saturated porous medium heated from below subjected to time-dependent sinusoidal magnetic field is investigated. The fluid flow through porous medium is described by the extended Darcy equation commonly known as Brinkman model. It is responsible for viscous shearing stresses acting on a volume element of the fluid, whereas in Darcy equation, only the damping force of the porous mass has been retained. The porous medium is assumed to be isotropic. The effect of magnetic field modulation is treated by a perturbation expansion in powers of the amplitude of modulation. The stability of the system, characterized by a correction Rayleigh number, is determined as a function of frequency of the modulated magnetic field, porous parameter, Brinkman number, Prandtl number and buoyancy magnetization parameter. It is found that subcritical motion is possible for small frequency magnetic field modulation and that the porous and magnetic field modulation mechanisms work against each other for small and moderate values of frequency of modulation.