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The idea behind writing this book is to give researchers a concise and basic concept about Hall current and its effect on fluid under different physical condition. The effects of Hall current are very important in the presence of strong magnetic field because for strong magnetic field electromagnetic force is prominent. That's why in recent research for the applications of MHD towards a strong magnetic field, the study of Hall current is very important. The book consists of two chapters and both chapters dedicated to explain the effect of Hall current on fluid under different physical condition. Chapter-1 describes how Hall current affects the motion of fluid when it passes through an accelerated vertical plate through a uniform porous medium in a rotating system in presence of Soret number. Chapter-2 describes the effect of Hall current over an unsteady MHD free convection flow past a vertical plate through a porous medium. For practical application of the problem the plate under consideration were kept under different types of motion viz. plate moving with uniform velocity, plate moving with uniform acceleration and plate moving with periodic acceleration.