Analysis of some important fluid flow problems using differential geometry based methods

Abstract

In this thesis we have studied MHD and EMFD flow of viscous and inviscid fluid for different cases when magnetic field and velocity are variably or constantly inclined. In particular magnetic and velocity vector are orthogonal. The pattern of streamlines and magnetic lines are derived in every problem and the effect of density and magnetic permeability on the variation of pressure is studied. The problems studied in this thesis give further investigation on the analytical solution of magnetohydrodynamic and electromagnetic fluid dynamic flow. The problems that studied analytically in this thesis have possible application in theoretical analysis of fluid dynamics and the analytical findings in this thesis can be applied in engineering fields such as aeronautics, plasmas, liquid metals and salt water or electrolytes. We have studied five problems here in this thesis. These problems are to find analytical solution of different types of fluid flows in the presence of magnetic field. Here we give a brief summary about the problems discussed in detail in this research work. (i) GEOMETRY OF CONSTANTLY INCLINED VISCOUS MHD FLOWS newlineProblems on incompressible MHD flow of viscous and inviscid fluids having newlinefinite or infinite electrical conductivity have been investigated by many researchers newlineusing different transformation methods. Transformation method is applied from newlineone plane to another plane for studying the flows by reducing the order of the equation. In this problem we have studied a viscous MHD flow having infinite electrical conductivity when the magnetic field is inclined to the velocity vector in a constant angle. Hodograph transformation is applied to shift variables from the physical plane to the hodograph plane. Streamlines and magnetic lines are analyzed along with determining the solutions to the flow problems. Finally the newlinepressure variation is analyzed graphically. Flow pattern along with pressure variation, also studied in this problem for an orthogonal MHD flow. newline