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The analysis of non-Newtonian fluids has gained the attention of engineers and scientist in recent times due to their important application in various branches of science and engineering. The flow of such non-Newtonian fluids with heat transfer over a stretching surface has tremendous applications in many industrial processes like manufacturing of plastic sheets, artificial fibers and polymeric sheets, plastic foam processing, extrusion of polymer sheet from a die, heat materials traveling between a feed roll and many others. The literature survey indicates that in the general, the stretching sheet is assumed non-oscillatory. However, the situation can arise where sheet may stretch and oscillate at the same time. The flow induced by such stretching surface is inherently unsteady. Moreover, the governing equations of problems are highly nonlinear partial differential equations which always pose challenges for mathematicians to compute analytic and numerical solutions of these equations. In this book, we investigate the unsteady flow of various non-Newtonian fluids with various reheological features. Some interesting analytical and numerical solutions has also been proposed.