STUDIES ON SOME PROBLEMS IN HYDRODYNAMICS AND MAGNETOHYDRODYNAMICS

Abstract

The thesi» deals with problems in ordinary hydrodynamic flow and t-iose involving the flov of an electrically conducting fluid in the presence of a magnetic field (Msgnetohydrcdynamic flow). The problems dealt with are concerred with flows in chan: els which are steady in time. The governing equations become automatically linear and hence are carable of yielding exact ablutions. Almost all the flows discussed tend to well-known simpler flows when some quantities involved in the solution are allowed to take special limiting values for the simpler cases. Tables of numerical res alts and graphs I /ey the results of investigations | family are appended *o every chapter. The work is classical in character. Ths thesis has boon oivided into six chapters. The first chapter is introductory laying down the funda mental aspects of the topics discussed and gives a summary of connected work existing snd to which the author could have access. In Chapter 11 is investigated the i >iseuilie-type flow through the inter-space between two confocal elliptic cylinders. This is obviously an extension of Polseuille flow in the ennulsr space between two coaxial circular cylinders. The motion discussed here tends to the usual classical one when the elliptic cylinders are made circular and coaxial. The temperature distribution in the fluid when the cylinders are fcep* at constant temperatures is also studied. A number of results of interest have been obtained. In Chapter III a similar problem to the one in the second chapter haa been solved. This is concerning two eccentric circular cylinders. The correaponding Polseuilla flow la discussed by the use of Fourier Eorles. Other results, likely to be significant have bean obtained. The temperature distribution when the cylinders are at different constant temperatures has also been investigated. Chapter IV deals with the axial flow of an electrically conducting fluid in an amulus under radial magnetic fiefc which has already been Uacussed by Globe. An alternative approach to the problem reduces the number of boundary conditions necessary and leads to the same solution already obtained. The corresponds ing temperature distribution has also been studied when the cylinders are at distinct steady temperatures. Other interesting aspects have been discussed. A varied problem when the * ;ries are in uniform steady axial motion, is also studied. Chapter V is akin to Chapter IV in its essence, as far as the boundaries and the applied field are concerned. The cylinders are allowed to rotate steadily (with the assumption of a fixed radial field) and the resulting steady magnatohydrodynamic flow is obtaineo. Allied significant quantities have also been calculated. Chapter VI deals with a varied problem in relation to Chapter V. in addition to the conditions of Chapter V, injection and suction at the boundaries of the region have also bean included. Numerical work has been extensively carried out on the l»f 1620 computer available at the structural Engineering Research Centre, Roorkee.