Convective Instability of Ferromagnetic Fluids in A Porous Medium
The thesis is concerned with the study of Rayleigh-Bard ferroconvection in a horizontal porous layer. Darcy-Brinkman law is employed to describe the fluid motion. The effect of second sound,thermal radiation, internal heat generation, variable viscosity and surface tension on the onset of Darcy-Brinkman ferroconvection is considered. newlineThe findings of the problems investigated in the thesis have implications for heat transfer applications wherein magnetic fluids serve as working media. The summary of the problems addressed in the thesis is given newlinebelow. Ferroconvection in a horizontal layer of porous medium with second sound The problem of Rayleigh-Bard convection in a ferromagnetic fluid saturated porous medium with the Maxwell-Cattaneo law is studied by newlinethe method of small perturbation. Modified Darcy-Brinkman model is used to describe the fluid motion. The horizontal porous layer is cooled from the upper boundary, while an isothermal boundary condition is imposed at the lower boundary. The fluid and solid matrix are assumed to be in local thermal equilibrium. The non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport and does not suffer from the newlinephysically unacceptable drawback of infinite heat propagation speed. The resulting eigenvalue problem is solved exactly for simplified boundary conditions and closed form solutions for both stationary and oscillatory instability are obtained. Some of the known cases have been deduced as newlinelimiting cases of the present study. The influence of porous, magnetic, and non-magnetic parameters on the onset of ferroconvection has been analyzed. It is found that magnetic stresses and second sound hasten the onset of Darcy-Brinkman ferroconvection. As the magnetic equation of newlinestate becomes more and more nonlinear, ferroconvection in a porous layer in the presence of second sound is advanced. However, it is delayed when the porous parameters are increased.