An Analysis of Axial Couette Flow in Annular Region of Abruptly Stopped Pipes

Abstract

Aims: Flow in annular regions encounters in many fields such as bio-medical, petroleum, aerospace and chemical industries and among them, the flow between two coaxial pipes has rather become interesting due to its asymmetry nature. Study Design: Theoretical solution and numerical approximation and analysis. Place and Duration of Study: Department of mathematics, Faculty of Science, University of Peradeniya, Sri Lanka, between August 2017 and January 2018. Methodology: Yet it is particularly challenging to obtain theoretical solutions. In this paper, we carried out a comprehensive analysis for unsteady, unidirectional and incompressible Couette flow between annulus, when inner and outer pipes were brought to abrupt stop from constant velocities. The velocity of the field is derived by applying the Laplace transformation method. The analytical work is supported by the numerical approximation using Finite Difference Method for the same fluid, which was implemented in MATLAB programming. We illustrate results varying radii of the outer and inner pipe captured by ratio ( η =0.1, 0.3, 0.5 and 0.5) and for different boundary conditions. Flow field was visualized using FDM approximation for selected parameter regime when the flow was suddenly stopped. Results: Asymmetry of the velocity profile was affected by different radius ratios (η =0.1, 0.3, 0.5 and 0.5 ). Unsteadiness in the flow field was happened due to sudden changes in flow parameters. Conclusion: The results depicted that radii ratio and boundary condition has a strong impact on the role on changing the flow characteristics and flow parameters.