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Study of toroidal magnetic field for the flow past a rotating rigid sphere embedded in the less permeable medium

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Abstract

This paper represents the exact solution for the properties of the conducting fluid that is flowing past a rotating sphere immersed in a porous medium. It’s a continuation of Sharma and Srivastava (Z Angew Math Mech 103:e202200218, 2022), where the sphere is rotating in the clear fluid region. The solution to the problem was found using Stokes’ equation. In this paper the solutions are found using the Brinkman model in terms of special functions- Bessel’s function of the first and second kind. In this problem, the drag force experienced by the rotating sphere is also calculated for the less permeability of the porous medium. The model is solved using the asymptotic expansion method for the prescribed boundary conditions. By this method, the model consisting of partial differential equations is reduced into ordinary differential equations – modified Bessel’s equations. The results for fluid velocity, stream function, and separation parameters are found in terms of Bessel’s functions and these results match with the existing literature in the absence of Reynolds number. The graphs are plotted for the drag force on the rotating sphere and separation parameter. It has been observed that the separation of the particles occurs at the surface of the sphere more often for high permeability and the drag was found to be decreasing for low permeability. Both graphs were plotted for a range of Reynolds numbers.

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Abbreviations

V :

Flow velocity

Ψ :

Stream function

μ :

Dynamic viscosity

\({\mu }_{e}\) :

Effective viscosity

Re:

Reynolds number

\({B}_{T}\) :

Toroidal magnetic field

c :

Darcy’s number

\(\zeta \) :

Taylor number

J :

Current density

\(\Omega \) :

Angular velocity

ρ :

Density

K :

Permeability

\({\mu }_{0}\) :

Magnetic permeability

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Acknowledgements

The work in this paper would not have been done without the constant support of the committee members and Amrita School of Engineering, Bangalore. The authors show their gratitude for the constant encouragement of the committee.

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Work is done in the Lab VGST-GRD787.

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Authors and Affiliations

  1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru, 560035, India

    Bharti Sharma & Neetu Srivastava

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  1. Bharti Sharma
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  2. Neetu Srivastava
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Correspondence to Neetu Srivastava.

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Sharma, B., Srivastava, N. Study of toroidal magnetic field for the flow past a rotating rigid sphere embedded in the less permeable medium. Int J Geomath 15, 5 (2024). https://doi.org/10.1007/s13137-024-00246-z

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