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2012 | OriginalPaper | Chapter
Application of the Homotopy Analysis Method to Fluid Flow Problems
Authors : Kuppalapalle Vajravelu, Robert A. van Gorder
Published in: Nonlinear Flow Phenomena and Homotopy Analysis
Publisher: Springer Berlin Heidelberg
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The equations of viscous flow have been known for more than 100 years. In their complete form, these equations are very difficult to solve, even on modern digital computers. In fact, at high Reynolds numbers (turbulent flow), the equations are impossible to solve with present mathematical techniques, because the boundary conditions become randomly time-dependent. Nevertheless, it is very instructive to present and discuss these fundamental equations because they give many insights, yield several particular solutions, and can be examined for modeling purposes. Also, these equations can then be simplified, using Prandtl boundary-layer approximations. The resulting simpler system is very practical and yields many fruitful engineering solutions.