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European Journal of Applied Sciences – Vol. 12, No. 5

Publication Date: October 25, 2024

DOI:10.14738/aivp.125.17580.

Islam, M. R. & Nasrin, S. (2024). Hall and Ion-Slip Current Effects on Micropolar Fluid Flow over a Vertical Plate with an Inclined

Magnetic Field. European Journal of Applied Sciences, Vol - 12(5). 169-187.

Services for Science and Education – United Kingdom

Hall and Ion-Slip Current Effects on Micropolar Fluid Flow over a

Vertical Plate with an Inclined Magnetic Field

Md. Rafiqul Islam

Department of Mathematics,

Bangabandhu Sheikh Mujibur Rahman Science and

Technology University, Gopalganj-8100, Bangladesh

Sonia Nasrin

Department of Mathematics,

Jagannath University, Dhaka-1100, Bangladesh

ABSTRACT

In this study, we explore how Hall and Ion-slip currents influence the flow of

micropolar fluid over a vertical plate in the presence of an inclined magnetic field.

To simplify the analysis, we consider a small magnetic Reynolds number, allowing

us to exclude the magnetic induction equation. The equations governing the flow

are derived from principles of linear momentum equation, angular momentum

equation, and energy equation which are made dimensionless through similarity

analysis. Then these non-linear, dimensionless equations are solved by using the

explicit finite difference method for finding the primary velocity, secondary

velocity, microrotation, and temperature. This investigation extensively examines

the impact of key parameters on velocity, microrotation, and temperature

distributions. It also provided concise graphical explanations of skin friction and

heat transfer rate at the plate.

Keywords: Micropolar Fluid, Heat Transfer, Inclined Magnetic Field, Hall Current, Ion- slip.

INTRODUCTION

Micropolar fluids are characterized by their micro-structured composition, consisting of rigid

spherical particles endowed with spin inertia, dispersed within a viscous medium. These

fluids deviate from the behavior of traditional Newtonian fluids due to the presence of

suspended particles. Examples of micropolar fluids abound in various non-Newtonian fluid

systems such as blood flow, fluids traversing neural networks and the brain, polymer

solutions, and liquid crystals, all of which exhibit inherent polarities. Micropolar fluid

dynamics finds applications in modeling phenomena involving the presence of dust or

particulate matter in gases, especially in environments where traditional fluid dynamics fail to

capture the complexities. This framework enables the description of physical phenomena at

micro and nanoscales, providing an additional degree of freedom for rotational motion.

Understanding the influence of magnetic fields on micropolar fluid flows, particularly in the

context of Hall and Ion-slip currents, holds significant practical and theoretical importance

across diverse fields including magnetic material processing, astrophysics, nuclear

engineering, geophysics, and industrial processes.

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European Journal of Applied Sciences (EJAS) Vol. 12, Issue 5, October-2024

Eringen [1,2] first proposed the general theory, which illustrates specific microscopic effects

arising from the microstructure and micro motions of flow are micropolar fluids that exhibit

the microrotational effects and micro-rotational inertia so that clench body couples and

couple stress. Whereas the Navier-Stokes theory cannot express the phenomena at micro and

nanoscales, but MFD can explain. After that, many authors investigated and developed the

MHD micropolar fluid flow with or without hall current and ion slip effect. The extensive

developments on micropolar fluids, their behavior, and applications in engineering and

technology are studied by Ariman et al. [3,4]. Rees and Pop [5] discussed the characteristics

and nature of a micropolar fluid flow that is set in a vertical plate with steady free convection.

Hsu and Wang [6] represented the laminar micropolar fluids flow with mixed convection in a

square dent with an induced stream influenced by temperature. Olajuwon et al. [7] have

analyzed the unsteady viscoelastic micropolar fluid flow upon an infinite moving plate in a

porous medium in a magnetic field with Hall effect and thermal radiation. Zakaria [8]

explained the nature of an electrically conducting micropolar fluid flows with the presence of

a transverse magnetic field over a porous medium in one-dimensional and used the Laplace

transformation with e –algorithm technique to find its key with the Laplace transformation

domain numerically. Nadeem et al. [9] are obtained the effect of heat and mass transfer with

thermal radiation on magneto-hydrodynamic micropolar fluids flow over an oscillating plate

set in a porous media. Seddeek and Abdelmeguid [10] have been explained the mixed

convection boundary layer flow of viscous, incompressible, and electrically conducting

micropolar fluids with Hall current and Ion-slip effect along with a horizontal plate. Gorla [11,

12] analyzed the mixed convection of a micropolar fluid from a semi-infinite vertical plate

with the heat transfer rate and showed the comparison of Newtonian and micropolar fluids.

Jha and Malgwi [13] studied the free convection viscous incompressible fluid flow within a

vertical microchannel with an induced magnetic field with hall current and ion-slip effect.

Ram [14] considered a free convective heat-generating on a rarefied gas in a rotating frame

with a strong magnetic field attributed perpendicular to the plate with the effects of Hall and

ion-slip current that has various industrial applications, tangential filtration, crystallization,

turbo machinery, petroleum industry, bio-reaction, and liquid-liquid extraction. Uddin and

Kumar [15] investigated the micropolar fluids flow over a non-conducting wedge with hall

and ion-slip effects with a strong magnetic field. Singh [16] expressed the joint effect of Joule

heating and thermal diffusion on MHD free convection viscous fluid flow with the Hall current

of an electrically conducting fluid. The influence of the Hall current effect in a viscous and

conducting fluid with the generalized Couette flow under an inclined magnetic field is

analyzed by Prasada et al. [17]. Seth et al. [18] investigated a steady, incompressible, and

rotational Couette flow along an inclined magnetic field. It has significant use in geophysics,

agriculture, astrophysics, and chemical, mechanical and fluid engineering. Krishna et al. [19]

investigated the angle of inclination of an unsteady magneto-hydrodynamic free convective

flow with hall and ion slip current effects in a rotational system through an accelerated

inclined plate entrenched in a porous medium. Opanuga et al. [20] considered Hall current

and ion-slip effects on the rate of entropy generation of couple stress fluid with velocity slip

and temperature wall. Hanvey et al. [21] examined the flow of a viscoelastic, electrically

conducting fluid between two parallel plates filled with a porous medium, positioned in an

inclined magnetic field. Initially, the flow is driven by a pressure gradient parallel to the

bounding fluid. However, once the system reaches a steady state, the pressure gradient

diminishes, and a magnetic field inclined simultaneously is applied to ascertain the velocity