The solutions for the flow of micropolar fluid through an expanding or contracting channel with porous walls

Boundary value problems

Jianhui Zhou¹  Liancun Zheng²  Lin Li²  Mingyang Pan²  Xinhui Si² 

[1] Qianan College, North China University of Science and Technology, Tangshan, China;School of Mathematics and Physics, University of Science and Technology, Beijing, China

关键词: micropolar fluid;    expansion ratio;    multiple solutions;    Lighthill method;    matching theorem;    boundary value problem;   

DOI  :  10.1186/s13661-016-0686-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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 Berman problem (Berman in J. Appl. Phys. 24:1232-1235, 1953), 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 (Terrill and Thomas in Appl. Sci. Res. 21:37-67, 1969), 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.

【 授权许可】

CC BY