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Fluid is a substance that continuously deform under the influence of shear stress. Basically, fluid can be classified into two categories which are Newtonian and non-Newtonian. In reality, most fluids are belongs to the class of non-Newtonian fluids and one of them is Jeffrey fluid. Jeffrey fluid is also known as viscoelastic fluid that exhibits both viscous and elastic characteristics. Recently, this type of fluid have received considerable attention due to their numerous applications in industries especially in polymer industries. Due to this reason, many investigations has been made to study the Jeffrey fluid in various aspects from both theoretical and experimental. However, theoretical work on Jeffrey nanofluid is not much. Therefore, this book is devoted to study analytically the unsteady magnetohydrodynamic free convection flow of Jeffrey nanofluid past an oscillating vertical plate by Laplace transform technique.