Some problems on MHD flow past solid bodies and thermal convection in MHD

Abstract

This thesis can be broadly divided into two parts. In the first part we deal with a few problems of MHD flow past solid bodies. The first problem is concerned with a steady two-dimensional streaming motion of an infinite mass of an incompressible, inviscid and electrically conducting fluid past an elliptic cylinder in presence of an aligned uniform magnetic field. The interaction of the field and the motion is considered to be small; analysis has been carried out by using a kind of perturbation technique. The first order corrections to undisturbed flow and field are obtained and the drag force experienced by the cylinder is also calculated. In the second problem we consider a steady two-dimensional slow motion of an incompressible, viscous and conducting fluid past a circular cylinder placed midway between two parallel planes, the applied field being parallel to the bounding planes. For solution away from the cylinder image methods which are developed by Faxen are used and it is matched with the solution valid in the immediate neighbourhood of the cylinder. Attempt has been made to calculate the drag force on the cylinder. Stream lines and lines of constant molecular rotation are also drawn. In the remaining part of the thesis, we investigate the problem of thermal convection in a non-homogeneous conducting horizontal fluid layer heated from below in presence of a magnetic field, when non-homogeneity is of the exponential type. Analysis has been carried out with respect to infinitesimel disturbances and a linear theory is followed. It is found that the marginal state is of oscillatory character and thermal convection sets in as overstability. The onset of instability as overstability is considered and proper solutions have been obtained when both bounding surfaces are either free or rigid. It is further found that both non-homogeneity and magnetic field have stabilizing influence on the overstable mode of convection.