Effectiveness of magnetic field on the flow of Jeffrey fluid in an annulus with rotating concentric cylinders

  • Deepak Kumar
  • K. Ramesh
  • Sumit Chandok
Technical Paper


In the present article, the flow of an incompressible Jeffrey fluid in the annulus of rotating concentric cylinders in the presence of magnetic field has been investigated. The governing equations for Jeffrey fluid model are formulated considering cylindrical coordinates system. The constitutive equations for the fluid flow have been simplified under the choice of velocity. The existence of the solution to the momentum equation is established using Schauder’s fixed point theorem. The analytical solutions for the velocity and skin friction coefficient are presented using modified Bessel functions. The effect of various parameters of interest such as the rotating speed of the cylinders, magnetic field parameter, non-Newtonian fluid parameter and the aspect ratio of cylinders on the velocity field and skin friction coefficient have been studied. It is observed that, the velocity decreases with increase in magnetic field parameter and aspect ratio of the cylinders. It is also depicted that, the higher velocities are seen in Newtonian fluid model as compared to the Jeffrey fluid model. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study of the effects of rotation on the flow characteristics.


Non-Newtonian fluid Magnetic field Schauder’s fixed point theorem Banach space Modified Bessel functions 

List of symbols

\({\mu }\)

Viscosity coefficient






Radius of inner cylinder


Radius of outer cylinder


Identity vector


Strength of the magnetic field

\({\lambda _1}\)

Ratio of relaxation and retardation times

\({\lambda _2}\)

Retardation time

\({\Omega _1,\Omega _2}\)

Angular velocities

\({\sigma }\)

Electrical conductivity of the fluid


Velocity field


Dimensionless magnetic field parameter

\({\omega }\)

Dimensionless rotation parameter


Energy of the magnetic field in a cross section


Mass of the fluid element


Magnetic field intensity


Skin friction coefficient

\({\varvec{\tau }}\)

Cauchy stress tensor


Velocity vector


Deformation tensor


Material derivative


Electric current density


Total magnetic field


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Department of MathematicsLovely Professional UniversityJalandharIndia
  2. 2.Department of MathematicsIKG Punjab Technical UniversityKapurthalaIndia
  3. 3.School of MathematicsThapar UniversityPatialaIndia

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