Some Aspects of MHD Flows with Hall and Ion-Slip Currents
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The purpose of this thesis is to give the basic assumption and the formulation of the theory of the flow problems of megnetohydrodynamics (MHD), as well as to the various methods of solving these problems. ''An explicit finite- difference method is used to analyse megnetohydrodynamics (MHD) stokes problem for a heat generating fluid with Hall effect'' And '' Perturbation method is also applied to study the effects of both Hall and Ion-slip currents on convective flow in a rotating fluid with wall temperature oscillations.'' Velocity and temperature profiles have been interpreted graphically before the conclusions are drawn as a result of applying the above stated methods to solve the highly non- linear differential equations. The present thesis consists of four chapters followed by bibliography. Before the beginning of Chapter 1 the nomenclature of the various symbols used in the thesis is given for easy reference. Chapter 1 contains the general introduction the basic assumptions and the formulation of the theory of the flow problems. The important non-dimensional parameters for the flow problems in magnetohynamics have been given. A brief description of the survey of the applications is also given. In chapter 11 the work done by the previous workers in the field of MHD has been reviewed. The last two chapters (III and IV) specifically deal with the study of the effects of Hall and ion- slip current on convective flow in the presence of strong magnetic field. Analytical expression for the velocity and temperature fields are obtained. The velocity and temperature profiles have been shown on graphs and the results are discussed in terms of the parameters me or be (the Hall parameter), mi or bi (their ion-slip parameter) and Grashof number Gr. Both the cases when Gr<O (in the presence of heating of the plate by free convection currents) and Gr>O (in the presence of heating of the plate by free convection currents) have been discussed extensively. One of the most important applications of such problems are in the studies of coronal plasma flows in the configuration of plasma sheet formation in the active region of the sun or in the magnetic tail region. Further trends are discussed at the end of Chapter IV. The validity for the results and conclusions of the work done together with brief details of computational fluid dynamics codes for computerization is also added towards the end of Chapter IV. Bibliography of the research papers and books, concerning the subject matter of the present work is given at the end of the thesis arranged in the alphabetical order by names of the authors.