Eur. Phys. J. Plus (2019) 134: 236
https://doi.org/10.1140/epjp/i2019-12593-2

Regular Article

Circular flow around a turning point in an annular area between two coaxial porous cylinders

¹ Applied Mechanics Laboratory, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
² Department of Mathematics and Physical Science, National Advanced School of Engineering, University of Yaoundé I, P.O. Box 8390, Yaoundé, Cameroon

^* e-mail: honajacques@yahoo.fr

Received: 13 November 2018
Accepted: 22 February 2019
Published online: 28 May 2019

Abstract

In order to investigate a suction-driven circular flow within an annular tube formed by two coaxial porous cylinders, a mathematical model expressed as a nonlinear two-point boundary-value problem is achieved. In seeking solutions of the problem, the results obtained reveal the existence of a hydrodynamic turning point among the main physical settings of the study. The dynamics of the fluid is examined through three solution branches Fr, S₁ and S₂ that form this turning point. By increasing the Reynolds number above the turning point, regions where the fluid moves in the counterclockwise direction are observed through the first branch Fr and the secondary branch of type S₂ near the inner and the outer cylinders, respectively. Due to this described behavior, solutions of types Fr and S₂ seem to be mirror images of each other. A flow of the boundary layer type takes place through the secondary branch of type S₁ for great values of the Reynolds number. This boundary layer causes the radial velocity to approach a linear profile at the same constant curve for different Reynolds numbers.