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The book principally investigates a steady and unsteady laminar flow of a dusty fluid through a rectangular channel. Couette and hydromagnetic flow through a porous medium between parallel plates, permeable beds and eccentric rotating disks are discussed for different unsteady pressure gradient chapterwise. The book consists of six chapters in which the first chapter permeates the introduction part as fundamental equations. Chapter 2 models a laminar flow of an unsteady viscous incompressible fluid with uniform distribution of dust particles through a rectangular channel. Differential geometry technique has been introduced to describe the structure of the curve and corresponding flow regime. An exact solution of the governing equations for the fluid velocity and the velocity of dust particles are obtained by applying Laplace transform method. Chapters 3 and 4 present analytical descriptions of the flow and MHD flow respectively through a porous medium between permeable beds underexponentially decaying pressure gradient. Two governing equations Navier-Stokes equations and Darcy's law have been employed for the flow between and through the permeable beds respectively.