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

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Abstract

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.

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Abbreviations

\({\mu }\) :

Viscosity coefficient

p :

Pressure

t :

Time

\({r_1}\) :

Radius of inner cylinder

\({r_2}\) :

Radius of outer cylinder

I :

Identity vector

\({B_0}\) :

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

v :

Velocity field

\({B_1}\) :

Dimensionless magnetic field parameter

\({\omega }\) :

Dimensionless rotation parameter

\({W_B}\) :

Energy of the magnetic field in a cross section

\({m_0}\) :

Mass of the fluid element

H :

Magnetic field intensity

\({C_{{\mathrm{f}}}}\) :

Skin friction coefficient

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

Cauchy stress tensor

\({\varvec{q}}\) :

Velocity vector

\({\dot{\varvec{D}}}\) :

Deformation tensor

\({\ddot{\varvec{D}}}\) :

Material derivative

\({{\mathbf{J}}}\) :

Electric current density

\({{\mathbf{B}}}\) :

Total magnetic field

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Authors and Affiliations

  1. Department of Mathematics, Lovely Professional University, Jalandhar, 144411, India

    Deepak Kumar & K. Ramesh

  2. Department of Mathematics, IKG Punjab Technical University, Kapurthala, 144603, India

    Deepak Kumar

  3. School of Mathematics, Thapar University, Patiala, 147004, India

    Sumit Chandok

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  1. Deepak Kumar
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  2. K. Ramesh
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  3. Sumit Chandok
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Correspondence to K. Ramesh.

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Technical Editor: Cezar Negrao.

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Kumar, D., Ramesh, K. & Chandok, S. Effectiveness of magnetic field on the flow of Jeffrey fluid in an annulus with rotating concentric cylinders. J Braz. Soc. Mech. Sci. Eng. 40, 305 (2018). https://doi.org/10.1007/s40430-018-1232-3

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  • DOI: https://doi.org/10.1007/s40430-018-1232-3

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