| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 785010 | International Journal of Non-Linear Mechanics | 2011 | 8 Pages |
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)r∈(0,1), the Lie-group shooting method is very effective for searching the multiple-solutions of a reverse flow boundary condition.
► Boundary layer problems of power-law fluids were treated by a Lie-group shooting method. ► Singularity appears by using the Crocco transformation. ► A new technique was developed to overcome the initial impulse. ► The missing initial condition could be expressed in terms of a weighting factor. ► Multiple solutions of a reverse flow were found.
