An Analytical Solution of Micropolar-Newtonian Fluid Flow Through Annular Porous Regions
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An Analytical Solution of Micropolar-Newtonian Fluid Flow Through Annular Porous Regions Pramod Kumar Yadav1
•
Jaikanth Yadav Puchakatla1 • Sneha Jaiswal1
Received: 9 June 2019 / Revised: 17 December 2019 / Accepted: 11 January 2020 The National Academy of Sciences, India 2020
Abstract This work concerns with an analytical solution of two immiscible fluids flows through an annular porous region. The annular porous regions are composed by three concentric cylinders in which inner cylinder is impermeable and other two cylinders enclosing impermeable cylinder are filled with porous material having different permeability. An analytical solution for flow velocity, micro-rotational velocity, flow rate and shear stress has been found. The variation in velocity and flow rate of fluids flowing in two different porous regions with respect to the different permeability is presented and discussed graphically. Keywords Micropolar fluid Porous medium Immiscible fluids Microrotation velocity
Introduction The problem presented and solved in this research article is an application of fluid flow problem through porous medium. For the interest of readers, authors first tried to explain the basic terms related to this problem. Fluid mechanics is a branch of science which explains the motion of and forces on the fluid, respectively [1]. The classical laws of & Pramod Kumar Yadav [email protected] Jaikanth Yadav Puchakatla [email protected] Sneha Jaiswal [email protected] 1
Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj 211004, India
fluid mechanics explain the motion of Newtonian fluids, which satisfy linear relation between stress and rate of strain (Newton’s law of viscosity). Although several research problems have been solved on the Newtonian fluid flow with various applications, but there is some inadequacy in Newtonian fluid theory to explain the motion of complex fluids such as polymer solution, animal blood, starch solution and paints. The fluid which does not follow Newton’s law of viscosity or having nonlinear relation between stress and rate of strain is known as non-Newtonian fluids. The rheology of non-Newtonian fluids is described by their constitutive equation. A book of Chhabra and Richardson [2] gives a detail review on the rheology of number of non-Newtonian fluids. Some of named non-Newtonian fluids are Casson fluid, Jeffrey fluid, micropolar fluid, Reiner-Rivlin fluid, power-law fluids, etc. In this book, they also discussed the various engineering applications of non-Newtonian fluids. In 1964, Eringen [3] introduced the theory of simple microfluids whose particles undergo micromotion and consist of micro-inertia. Later in 1966, Eringen [4] introduced the theory of micropolar fluid and derived the field equations for it with a smaller number of coefficients. Eringen [5] given a detail explanation on the microcontinuum mechanics, and Lukaszewicz [6] explained the theory of micropolar fluids. Ariman et al. [7] did a review
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