Asymptotic solutions for the asymmetric flow in a channel with porous retractable walls under a transverse magnetic field
- 38 Downloads
The self-similarity solutions of the Navier-Stokes equations are constructed for an incompressible laminar flow through a uniformly porous channel with retractable walls under a transverse magnetic field. The flow is driven by the expanding or contracting walls with different permeability. The velocities of the asymmetric flow at the upper and lower walls are different in not only the magnitude but also the direction. The asymptotic solutions are well constructed with the method of boundary layer correction in two cases with large Reynolds numbers, i.e., both walls of the channel are with suction, and one of the walls is with injection while the other one is with suction. For small Reynolds number cases, the double perturbation method is used to construct the asymptotic solution. All the asymptotic results are finally verified by numerical results.
Key wordslaminar flow asymmetric flow asymptotic solution porous and retractable channel magnetic field
Chinese Library ClassificationO175.8 O357.1
2000 Mathematics Subject Classification76M45 76D10
Unable to display preview. Download preview PDF.
The authors would like to thank the editors and reviewers for the valuable comments.
- HIGASHI, T., YAMAGISHI, A., TAKEUCHI, T., KAWAGUCHI, N., SAGAWA, S., ONISHI, S., and DATE, M. Orientation of erythrocytes in a strong static magnetic field. Journal of Blood, 82, 1328–1334 (1993)Google Scholar
- GOTO, M. and UCHIDA, S. Unsteady flows in a semi-infinite expanding pipe with injection through wall. Japan Society for Aeronautical and Space Sciences, 33, 14–27 (1990)Google Scholar
- TERRILL, R. M. and SHRESTHA, G. M. Laminar flow in a uniformly porous channel with an applied transverse magnetic field. Applied Scientific Research, B, 12, 203–211 (1965)Google Scholar
- SU, Y. C. Boundary Layer Correction Method for Singular Perturbation Problems (in Chinese), Shanghai Science and Technology, Shanghai (1983)Google Scholar