Analytical solution of a two-dimensional stagnation flow in the vicinity of a shrinking sheet by means of the homotopy analysis method

Abstract In this article, stagnation flow in the vicinity of a shrinking sheet is studied. A similarity transformation is employed to reduce the Navier—Stokes equations to a set of non-linear ordinary differential equations. These equations are then solved analytically by means of the homotopy analy...

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Bibliographic Details
Published in:Proceedings of the Institution of Mechanical Engineers. Part E, Journal of process mechanical engineering Journal of process mechanical engineering, 2009-08, Vol.223 (3), p.133-143
Main Authors: Kimiaeifar, A, Bagheri, G H, Rahimpour, M, Mehrabian, M A
Format: Article
Language:English
Subjects:
Differential equations
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
Inelasticity (thermoplasticity, viscoplasticity...)
Mechanical engineering
Physics
Solid mechanics
Structural and continuum mechanics
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Summary:Abstract In this article, stagnation flow in the vicinity of a shrinking sheet is studied. A similarity transformation is employed to reduce the Navier—Stokes equations to a set of non-linear ordinary differential equations. These equations are then solved analytically by means of the homotopy analysis method (HAM). The results obtained were shown to compare well with the numerical results available in the literature for the same problem. Close agreement between the two sets of results indicates the accuracy of the HAM. The method can predict the flow field in all vertical distances from the sheet, and is also able to control the convergence of the solution. The numerical solution of the similarity equations is also developed and the results are in good agreement with the analytical results based on the HAM.
ISSN:0954-4089
2041-3009
DOI:10.1243/09544089JPME231