The solutions for the flow of micropolar fluid through an expanding or contracting channel with porous walls. (English) Zbl 1352.35123
Summary: The unsteady, two-dimensional laminar flow of an incompressible micropolar fluid in a channel with expanding or contracting porous walls is investigated. The governing equations are transformed into a coupled nonlinear two-points boundary value problem by a suitable similarity transformation. Unlike the classic A. S. Berman problem [J. Appl. Phys. 24, 1232–1235 (1953; Zbl 0050.41101)], three new solutions (totally six solutions) and no-solution interval, which is one of important characteristics for the laminar flow through porous pipe with stationary wall [R. M. Terrill and P. W. Thomas, Appl. Sci. Res. 21, 37–67 (1969; Zbl 0179.56904)], are found numerically for the first time. The multiplicity of the solutions is strictly dependent on the expansion ratio. Furthermore, the asymptotic solutions are constructed by the Lighthill method, which eliminates the singularity of the similarity solution, for large injection and by the matching theorem for the suction Reynolds number, respectively. The analytical solutions also are compared with the numerical ones and the results agree well.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 76S05 | Flows in porous media; filtration; seepage |
| 76A05 | Non-Newtonian fluids |
Keywords:
micropolar fluid; expansion ratio; multiple solutions; Lighthill method; matching theorem; boundary value problemSoftware:
MatlabReferences:
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