Fluctuating Hydromagnetic Flow of Viscous Incompressible Fluid past a Magnetized Heated Surface

Abstract

The phenomena of convective heat transfer between an ambient fluid and a body immersed in it, stems give a better insights into the nature of underlying physical processes such as processing with high temperature, space technology, engineering and industrial areas such as propulsion devices for missiles, aircraft, satellites and nuclear power plants. With this understanding, in the present work, an immense research effort has been expended in exploring and understanding the convective heat transfer between fluid and submerged vertical plate. In practice, we are interested in the full details of velocity, temperature and transverse component of magnetic field profiles, boundary layer thickness and some other quantities at the surface of the vertical plate such as the heat transfer from liquid to the plate or from plate to the liquid, frictional drag exerted by the fluid on the surface and current density for the case of magnetohydrodynamics (MHD) flow field. For this purpose, the boundary layer equations are transformed into convenient form by introducing independent variables such as primitive variables for finite difference method and stream function formulation for asymptotic series solutions to calculate the above mentioned quantities. For the development of the topic, an extensive literature survey is outlined in Chapter 1 with appropriate references well targeted to the title of the problem. The purpose of the Chapter 2 of this thesis is to introduce the boundary layer concepts and to show how the equations of viscous flow are simplified hereby. The standard boundary layer parameters and boundary layer equations are introduced in more general form in this chapter. Chapter 3 deals with the thermal radiation effects on hydromagnetic mixed convection laminar boundary layer flow of viscous, incompressible, electrically conducting and optically dense grey fluid along a magnetized vertical plate. The solution of transformed boundary layer equations are then simulated by employing two methods (i) finite difference method for entire values of ξ and (ii) asymptotic series solution for small and large values of transpiration parameter ξ . The physical parameters that dominate the flow and other quantities such as the local skin friction, rate of heat transfer and current density at the surface of the plate has been discussed. The effect of magnetic force parameter S, conduction radiation parameter Rd , Prandtl number Pr, magnetic Prandtl number Pm and mixed convection parameter λ with surface temperature θ w in terms of local skin friction, rate of heat transfer and current density at the surface have been shown graphically and in tabular form. The material used in Chapter 3 is modified in Chapter 4 and reformulated to calculate the effects of conduction-radiation on hydromagnetic natural convection flow by using the same numerical techniques as used in Chapter 3. The material has been divided into two parts. The first part Chapters 3 and 4 presents steady part of the problem for mixed and natural convection flow. The second part of the thesis is the Chapters 5 and 6 which is devoted to find the numerical solution of the problem for unsteady part of mixed and natural convection flow. Chapter 5 describes the effect of conduction radiation on fluctuating hydromagnetic mixed convection flow of viscous, incompressible, electrically conducting and optically dense grey fluid past a magnetized vertically plate. The effects of different values of the mixed convection parameter λ , the conduction radiation parameter Rd , Prandtl number Pr, the magnetic Prandtl number Pm , the magnetic force parameter S and the surface temperature θ w , are discussed in terms of amplitudes and phases of shear stress, rate of heat transfer and current density at the surface. The effects of these parameters on the transient shear stress, rate of heat transfer and current density have also been discussed in detail. The finite difference method for the entire values of local frequency parameter ξ and asymptotic series solution for small and large values of local stream wise parameter ξ have been implemented in this study. In Chapter 6, we extended the Chapter 4 into unsteady form and find the numerical solutions of the effects of conduction radiation on fluctuating hydromagnetic natural convection flow of viscous, incompressible, electrically conducting and optically dense grey fluid past a magnetized vertically plate.