The Lie-group shooting method for boundary-layer problems with suction/injection/reverse flow conditions for power-law fluids
Resource
International Journal of Non-Linear Mechanics, 46(8), 1001-1008
Journal
International Journal of Non-Linear Mechanics
Pages
1001-1008
Date Issued
2011
Date
2011
Author(s)
Liu, Chein-Shan
Abstract
For power-law fluids we propose a Lie-group shooting method to tackle the boundary-layer problems under a suction/injection as well as a reverse flow boundary conditions. The Crocco transformation is employed to reduce the third-order equation to a second-order ordinary differential equation, and then through a symmetric extension to a boundary value problem with constant boundary conditions, which can be solved numerically by the Lie-group shooting method. However, the resulting equation is singular, which might be difficult to solve, and we propose a technique to overcome the initial impulse caused by the singularity using a very small time-step integration at the first few time steps. Because we can express the missing initial condition through a closed-form formula in terms of the weighting factor r∈(0,1), the Lie-group shooting method is very effective for searching the multiple-solutions of a reverse flow boundary condition. © 2011 Elsevier Ltd. All rights reserved.
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