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Impact of Magnetic Field on the Flow of a Conducting Fluid Past an Impervious Spheroid Embedded in Porous Medium

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Abstract

The majority of the previous studies analyzed the flow of fluid around the perfect sphere however the slight deformations in the shape of the particle are observed in nature. The motivation of the present work is to investigate the impact of MHD flow on slightly deformed sphere embedded in unbounded porous medium. The stream function for the flow field is calculated in terms of Bessel and Gegenbauer functions. As a boundary conditions, vanishing of normal and tangential component of velocity are applied. The resistance force is evaluated past an impermeable spheroid. As a special case, we consider an electrically conducting fluid motion past a rigid oblate spheroid embedded in a porous medium. Also, the expression for non-dimensional drag and dimensionless shearing stress are computed and its variation with Hartmann number, permeability, and deformation parameters are depicted graphically. The flow patterns of the streamline are represented graphically along the axial direction of the spheroidal particles. A number of specific cases are developed and compared to earlier research, demonstrating that our approach is valid. The results show that the magnetic field increases the resistance on the oblate spheroid. The investigation of the current study may be beneficial in the delivery of medications to the desired location, the medical treatment of tumors, cancer, and others.

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Abbreviations

\(\mathbf{q}\) :

Fluid velocity

\(p\) :

Pressure

\(\mathbf{F}\) :

Magnetic force

\(\psi \) :

Stokes stream function of the fluid flow

U:

Uniform flow

\(d\) :

Equatorial radius of oblate spheroid

\(k\) :

Permeability of the fluid

\(\mathbf{J}\) :

Electric current density

\(\mathbf{H}\) :

Magnetic field intensity

\(\mu \) :

Coefficient of viscosity

\(\alpha \) :

Non-negative Hartmann number

\(\epsilon \) :

Deformation parameter

\(\sigma \) :

Electric conductivity of the fluid

\({D}_{N}\) :

Non-dimensional drag

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

Magnetic field component

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

Magnetic permeability

\({\mathrm{F}}_{\mathrm{D}}\) :

Drag force

\({G}_{n}(\zeta )\) :

Gegenbauer function

\({P}_{n}\left(\zeta \right)\) :

Legendre polynomial

\({T}_{r\zeta }\) :

Tangential stress

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

Normal stress

\({q}_{r}, {q}_{\theta }\) :

Component of fluid velocity in spherical coordinates

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  1. Department of Mathematics, Jaypee University of Engineering and Technology, Guna, MP, 473226, India

    Ravendra Prasad Namdeo & Bali Ram Gupta

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  1. Ravendra Prasad Namdeo
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Namdeo, R.P., Gupta, B.R. Impact of Magnetic Field on the Flow of a Conducting Fluid Past an Impervious Spheroid Embedded in Porous Medium. Int. J. Appl. Comput. Math 8, 131 (2022). https://doi.org/10.1007/s40819-022-01321-5

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