On the dual solutions assoclated with boundary-layer equations in a corner

✍ Scribed by A. Ridha

• Book ID: 104620172
• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 600 KB
• Volume: 26
• Category: Article
• ISSN: 0022-0833
• DOI: 10.1007/bf00042768

✦ Synopsis

The dual solutions of two coupled third degree non-linear ordinary differential equations associated with the incompressible viscous laminar flow along a corner are considered. It is shown (through the numerical solution) that dual solutions occur in the interval /3 b ~</3 ~< 1.1211 for the Falkner-Skan parameter /3 with the bifurcation taking place at the regular turning point/3 b. In the neighbourhood of the latter it is also shown that in such a case it is appropriate to expand the solution in powers of (/3 -/3b) 1/2 with the dual solutions branching out from the single solution at /3b. Then, on considering a simple transient problem (which provides an exact solution of the Navier-Stokes equations when/3 = 1.0) it is found that the branch having the greatest value of the wall shear stress (for a given 13) is stable while the other is unstable, the bifurcation point being the point of exchange of stability.