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This book has been devoted to the study of some fluid dynamics problems with or without magnetic field. The hydrodynamic & hydro-magnetic flows of non-conducting & electrically conducting fluids in different geometries and some problems on a dusty fluid have been studied in this book. The unsteady Couette flow between two infinite horizontal plates induced by non-torsional oscillation and flow due to a porous oscillating disk and a fluid at infinity have been studied in Chapter 2 & 3. Unsteady hydro-magnetic flow in a rotating channel in the presence of uniform magnetic field has been analyzed in Chapter 4. Chapter 5 deals the hydro-magnetic flow of an in-compressible viscous electrically conducting fluid past a porous plate. The problem in chapter 6 can be re-investigated on taking viscous and Joule dissipation into account. The problems in chapter 7-9 can be extended to an unsteady flow problems. Chapter 10 deals with the effect of dust particles on the flow caused by torsionaloscillation of a disk. Chapter 11 deals with the unsteady motion of a dusty fluid occupying the semi-infinite region. The effect of volume fraction has been neglected in chapter 10 & 11.