SOME PROBLEMS IN HYDRODYNAMICS AND MAGNETOHYDRODYNAMICS

Abstract

The thesis has been devoted to the study of flow problems in hydrodynamics and magnetohydrodynamics (MHD). Most of the work is on MHD problems and there is only one chapter on a hydrodynamlc flow* In the first chapter on introduction those aspects of MHD and hydrodynamics have been described which are to be used in the subsequent chapter a. This brings a kind of uniformity in the treatment. This has been uone nlso because it makes the presentation self-contained in a large measure. A brief account of the rel ted studies made by various workers in the field la given at the end of this chapter. The second, third and fourth chapter a deal with problems which are like in character and so have been placed one after another. In the second chapter unsteady flow of conducting fluid in a circular pipe with non-conducting walls snd the magnetic field parallel to a diameter has been uiscusaed. The corresponding steady solution has been investigated by Gold <49> . The third chr.pter consists in the study of unsteady MHD flow in a rectangular channel with non-conducting walls and a uniform initial field existing parallel to a pair of walls. The corresponding steady flow was studied by -hercliff <45> # A rigorous study of the unsteady flows in the second end the third chapters will require the discussion of electro- magnetic phenomena inside the material of the walls of the channel. This has been disregarded m& the equations have been solved only for the flow region. It has been presumed that the flow does not affect the electromagnetic field inside the walls or that it affects negligibly. So restricted the solution is exact in the special esse when the Reynold's number of the flow is the same as the magnetic Reynold's number. The fourth chapter discusses the MHD flow in an elliptic pipe, the aiplied field being parallel to a principal axis of the cross-section. The solution is an exact one and therefore, applicable to all values of Hertmann number. In the fifth chapter is investigated the non-stationary flow of a conducting fluid in an annular tuba in the presence of a field emanating radially from the axis. This time electromagnetic equations have been solved within the flow region (still in the special cnse of Reynold's number being equal to the magnetic Reynold*e number) and also in the interior of the Inner cylinder and of the outer cylinder. The sixth chapter deals with a problem of steady heat transfer by laminar flow In the region between two coaxial circular cylinders when a radial magnetic field exists in the inter - space. The semi infinite cylinder r • a, r * b, «<u are kept at a constant temperature TQ and the cylinders r • a, r » fc, a>G at another constant temperature T§. These ere Joined smoothly at the cross-section a - 0 by imposing physic lly Justifiable continuity conditions. CHI) The seventh chapter discusses the laminar steady state flow (MHU) in an annular channel with suction and injection at the cylindrical boundaries in the presence of a radial magnetic field. The solution appears In a closed fssjeji The Inst chapter deals with an axial unsteady hydrodynamic laminar viscous flow in an annular sector. First the steady solution is derived end to this 88 expo nentially decreasing unsteady part has been added. The solution has been obtained in terms of integrals some of which cm be integrsted in the closed form and the others can either be expressed in series or can be evaluated