Linear and nonlinear convection in magnetic fluids

Abstract

The thesis deals with linear and nonlinear Rayleigh-Bénard ferroconvection in a horizontal porous layer. Modified Darcy law is used to describe the fluid motion. The effect of chemical reaction, temperature newlinemodulation, gravity modulation and finite amplitudes on the onset of Darcy ferrroconvection is considered. The findings of the problems addressed in the thesis may come in handy for heat transfer application newlinesituations with ferromagnetic fluids as working medium. The summary of the problems investigated in the thesis is given below.Effect of chemical reaction on the onset of ferroconvection in a porous medium The problem of the effect of chemical reaction on the onset of Darcy newlineferrroconvection in a horizontal porous layer heated from below is investigated by means of the classical linear stability analysis. It is assumed that the fluid undergoes a zero-order exothermic chemical reaction and that there exists a local thermal equilibrium between the fluid and the solid phases. It is proved that stationary convection is preferred to the oscillatory mode. The Galerkin method is employed to determine the eigenvalues.The effect of Frank-Kamenetskii number and magnetic parameters on the stability of the system is discussed. It is newlinefound that the basic temperature profile turns out to be more and more nonlinear and asymmetric as the Frank-Kamenetskii number increases and that the effect of both chemical reaction and magnetic forces is to newlinehasten the onset of Darcy ferrroconvection. Further, it is shown that when there is very strong nonlinearity of magnetization, the fluid layer is destabilized slightly. Effect of temperature modulation on the onset of ferroconvection in a porous medium The effect of temperature modulation on the onset of Darcy ferroconvection in a horizontal porous layer heated from below is considered. The analysis is based on the assumption that the amplitude of the temperature modulation is small enough compared with the imposed newlinesteady temperature difference. newline