Influence of Magnetic Field on Micropolar Fluid Flow in a Cylindrical Tube Enclosing an Impermeable Core Coated with Por
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nfluence of Magnetic Field on Micropolar Fluid Flow in a Cylindrical Tube Enclosing an Impermeable Core Coated with Porous Layer Satya Deoa, Deepak Kumar Mauryaa, b, and A. N. Filippovc, * aDepartment
of Mathematics, University of Allahabad, Prayagraj, 211002 (U.P.) India of Mathematics, Prof. Rajendra Singh (Rajju Bhaiya) Institute of Physical Sciences for Study and Research, V. B. S. Purvanchal University, Jaunpur, 222003 (U.P.) India c Department of Higher Mathematics, National University of Oil and Gas “Gubkin University”, Moscow, 119991 Russia *e-mail: [email protected]
bDepartment
Received June 3, 2020; revised June 23, 2020; accepted June 25, 2020
Abstract—In this research work, we have investigated the Stokesian flow of a micropolar fluid in a cylindrical tube enclosing an impermeable core coated with porous layer in the presence of magnetic field. The axis of the cylinder is taken along the direction of fluid flow and the uniform magnetic field is applied in the direction perpendicular to the axis of the cylinder. Using appropriate boundary conditions, fluid velocities, microrotational velocities and stresses are evaluated for corresponding fluid flow regions. Expressions for volumetric flow rate through the annulus and the filtration velocity are obtained. Graphs of linear velocities, microrotational velocities and flow rate for various values of different parameters are plotted and discussed. DOI: 10.1134/S1061933X20060022
INTRODUCTION Micropolar fluids are the fluids consisting of rigid, randomly oriented particles suspended in a viscous medium, where the deformation of fluid particles is ignored. However, in animal blood, polymeric suspensions, liquid crystals, and other such complex fluids, particles may be of different shape, may shrink or expand, or change their shape, or they may rotate. The most applications of micropolar fluids are in the theory of lubrication and porous media [1]. Micropolar fluids are a subclass of microfluids with microstructure, termed as micromorphic fluids. A class of theories in which both the effects of couple stresses and microstructure are simultaneously taken into account in a systematic manner has developed by Eringen [2]. The ideas and results of the classical theory of micropolar-elasticity which constitutes one of particular cases of Cosserats’ theory, investigated by Nowacki [3]. The micropolar theory is of the current and emerging interest of mechanicians, physicians, materials scientists as well as engineers as its limits and possibilities are not fully established that is a serious constraint for applications [4]. Eringen and Okada [5] reported a nonlocal lubrication theory of fluids with microstructure to present a fundamental concept for calculating the rate at which a thin film of liquid drains. Magnetohydrodynamics (MHD) is concerned with the interactions of free currents and magnetic fields with fluid matter, liquids and gases [6]. Eringen and Suhubi [7] formulated the boundary value prob-
lem with the state of stress in two normally intersecting ci
