Application of the Homotopy Analysis Method to Fluid Flow Problems

Kuppalapalle Vajravelu () and Robert A. van Gorder ()
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Kuppalapalle Vajravelu: University of Central Florida, Department of Mathematics
Robert A. van Gorder: University of Central Florida, Department of Mathematics

Chapter Chapter 5 in Nonlinear Flow Phenomena and Homotopy Analysis, 2012, pp 101-155 from Springer

Abstract: Abstract 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.

Keywords: Porous Channel; Power Index; Homotopy Analysis Method; Porous Plate; Auxiliary Parameter (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-32102-3_5

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DOI: 10.1007/978-3-642-32102-3_5

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