Effect of magnetic field dependent viscosity on darcy brinkman ferroconvection

Abstract

Theoretical investigation of the convective instability of a Boussinesq ferrofluid saturating a porous medium with magnetic field dependent viscosity heated from below under the influence of additional constraints such as Maxwell-Cattaneo law, variable gravity, couple stress effect, anisotropic porous medium and rotation is presented in the thesis. Darcy-Brinkman law is employed to describe the fluid motion. Magnetorheological effects are given attention by treating the effective viscosity as a function of temperature and magnitude of magnetic field. The work reported in this thesis is primarily based on linear stability analysis based on the normal mode technique. The higher order Galerkin method is used to study the various modes of disturbances. The problems investigated in the thesis find intensive applications in fields such as chemical engineering, geothermal energy devices, nuclear reactors, oil reservoirs, polymer industries, crystal growth, utilization, solidification of molten alloys, bio mechanics, food processing and production of pure medication and so on. newlineWith this motivation, we investigate five problems in the thesis. The brief summary of each problem is given below. newline1) Effect of Magnetic field dependent viscosity on Darcy-Brinkman ferroconvection with Maxwell-Cattaneo law newlineThe problem of buoyancy-driven convection in a ferromagnetic fluid saturated porous medium with the Maxwell-Cattaneo law and MFD viscosity is investigated by the method of small perturbation. The fluid motion is described using the Brinkman model. It is assumed that the fluid and solid matrices are in local thermal equilibrium. The non-classical Maxwell-Cattaneo heat flux law involves a wave type of heat transport and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. For simplified boundary conditions, the eigenvalue problem is solved exactly and closed form solutions for stationary instability are obtained.