Insight into the dynamics of non-Newtonian Casson fluid over a rotating non-uniform surface subject to Coriolis force

Abayomi S Oke,Winifred N Mutuku,Mark Kimathi,Isaac L Animasaun

doi:10.1515/nleng-2020-0025

Abstract

AbstractCasson fluid model is the most accurate mathematical expression for investigating the dynamics of fluids with non-zero plastic dynamic viscosity like that of blood. Despite huge number of published articles on the transport phenomenon, there is no report on the increasing effects of the Coriolis force. This report presents the significance of increasing not only the Coriolis force and reducing plastic dynamic viscosity, but also the Prandtl number and buoyancy forces on the motion of non-Newtonian Casson fluid over the rotating non-uniform surface. The relevant body forces are derived and incorporated into the Navier-Stokes equations to obtain appropriate equations for the flow of Newtonian Casson fluid under the action of Coriolis force. The governing equations are non-dimensionalized using Blasius similarity variables to reduce the nonlinear partial differential equations to nonlinear ordinary differential equations. The resulting system of nonlinear ordinary differential equations is solved using the Runge-Kutta-Gills method with the Shooting technique, and the results depicted graphically. An increase in Coriolis force and non-Newtonian parameter decreases the velocity profile in the x-direction, causes a dual effect on the shear stress, increases the temperature profiles, and increases the velocity profile in the z-direction.

Highlights

The centrifugal force, the Azimuthal force, and the Coriolis force are the three forces experienced in a rotating frame of reference; Debnath [1]
Models used include Bingham, Carreau, Casson, modi ed Casson, Cross, Kuang-Luo (K-L), Powell-Erying, Power-law, and Walburn-Schneck models and the results show that the time-averaged velocity at the center of the arteries produced in the CFD simulations that uses the Carreau, modi ed Casson or Quemada blood viscosity models corresponded exceptionally well with the clinical measurements regardless of stenosis severities and highlights the usefulness of these models to determine the potential determinants of blood vessel wall integrity such as dynamic blood viscosity, blood velocity, and wall shear stress
No attempt has been made to investigate the e ect of Coriolis force on the ow of Casson uid over a surface with non-uniform thickness whose importance cannot be overlooked in energy production, nuclear reactor cooling, biomedical applications, etc

Summary

Introduction

The centrifugal force (acting radially outward from the axis of rotation), the Azimuthal force (parallel but opposite to the velocity, known as the Euler force), and the Coriolis force (outward and perpendicular to angular velocity) are the three forces experienced in a rotating frame of reference; Debnath [1]. Koriko [28] explored the e ect of Coriolis force on the ow of Newtonian uid over a rotating surface with non-uniform thickness. No attempt has been made to investigate the e ect of Coriolis force on the ow of Casson uid over a surface with non-uniform thickness whose importance cannot be overlooked in energy production, nuclear reactor cooling, biomedical applications, etc. Such a study is important in the design of turbines and turbo-machines, in estimating the ight path of rotating wheels and spin, stabilized missiles, and in the modeling of many geophysical vortices.

Numerical Procedure

Findings

Conclusion