THERMAL AND MHD EFFECTS ON THE STABILITY OF COUETTE FLOW BETWEEN TWO ROTATING CYLINDERS

Abstract

Abstract : The effects of heating and an applied axial magnetic field on the stability of viscous incompressible flow between two concentric rotating cylinders (Couette flow) are examined. The equations governing the marginal stability state of the flow are solved numerically, and the results are presented in both tabular and graphical forms. Our predictions for some special cases of the problems considered exhibit good agreement with those previously reported by various authors. In chapter one, a general introduction to the topic of hydrodynamic stability is given. The introduction describes: (i) The first systematic experiments in this field. (ii)The assumptions employed to simplify the mathematical treatment of a stability problem. (iii)The patterns of flow observed at the onset of instability. (iv)The numerical methods used to solve different types of stability equations. (v) The practical importance of these studies in the field of hydrodynamic stability. (vi)The problems investigated in this thesis In chapter two, the stability of Couette flow in the presence of a radial temperature gradient due to a constant heat flux at the inner cylinders is studied. In formulating the stability equations, we assume that the gap between the two cylinders is small and arbitrary. All three types of rotation of the two cylinders are considered. The two cylinders may rotate in the same or opposite directions, or only the inner cylinder is rotating. In chapter three, we examine the combined effect of a radial temperature gradient and an axial magnetic field on the stability of an electrically conducting Couette flow. The narrow gap annulus is assumed, and the critical angular velocities are calculated for all types of rotation of the two cylinders. It is found that while the magnetic field always stabilizes the flow, the temperature gradient, depending on the direction of heat flow, may stabilize or destabilize the flow. In chapter four, we explore, in the presence of various gap sizes between the cylinders, the stability effect of (i) a radial temperature gradient, (ii) an axial magnetic field, and (iii) the type of rotation of the two cylinders. The important role that different gap sizes play in the stability of Couette flow is manifested through the strong dependence of the critical velocity on their values