Lie-group method for unsteady flows in a semi-infinite expanding or contracting pipe with injection or suction through a porous wall. (English) Zbl 1103.37058
The work deals with the solution of Navier-Stokes equations, which describe the unsteady laminar flow of incompressible fluids, in a semi-infinite porous circular pipe with injection or suction through the pipe wall, whose radius varies with time. The authors use the Lie-group method to determine symmetry reductions of this problem, and then they solve the resulted fourth-order nonlinear differential equation using small parameter perturbations. The effects of the cross-flow Reynolds number Re and the dimensionless wall expansion ratio \(\alpha\) on axial and radial velocities, flow streamlines, shear stress, radial and axial pressure drop are studied. By using the shooting method coupled with the Runge-Kutta scheme, the numerical results of the above investigations are presented, too.
Reviewer: Rodica Luca (Iaşi)
MSC:
| 37N10 | Dynamical systems in fluid mechanics, oceanography and meteorology |
| 37L20 | Symmetries of infinite-dimensional dissipative dynamical systems |
| 35B20 | Perturbations in context of PDEs |
| 35Q30 | Navier-Stokes equations |
| 76M60 | Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics |
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