New traveling wave solutions of MHD micropolar fluid in porous medium

Abstract

This paper aims to determine the exact solutions of non-Newtonian fluid namely micropolar fluid with MHD in a porous medium by traveling wave method. The governing equations of incompressible micropolar fluid with MHD in a porous medium are non-linear PDEs reduced to ODEs through wave parameter ξ=mx+ny+Ut. The set of new exact solutions are determined for five different cases. In special cases, the solution for micropolar fluid with and without MHD and porous effects can also be obtained from general solutions. Furthermore, these solution reduces to a Newtonian solution if we put vortex viscosity κ→0. Finally, the influence of the material and other parameters of interest on the fluid motion, as well as a comparison among micropolar and Newtonian fluids is also analyzed by 2D and 3D graphical illustrations.

Vortex Model of Plane Couette Flow

“…The considered model predicts several types of stationary laminar Couette flow. As can be seen from solutions ( 9)- (10), the laminar motion without vortex tubes rotation is realized only in a narrow region near the plates. This regime can be important in tribology at low Re, in case of supersmooth plates sliding relative to each other, when a narrow gap between them is filled with a viscous lubricant.…”

“…The schematic distribution of velocity over the channel cross section is shown in Figure 5. Note that in the case of α = 0, the solutions ( 22)-( 24) are reduced to ( 9)- (10), and in the case of α = 1, these solutions are reduced to ( 15)-( 17).…”

“…To describe vortex flows, many authors construct Maxwell-type symmetric equations for the local velocity and vorticity vectors [1][2][3][4][5][6]. In particular, these equations are used for the description of turbulent flows [4] and electron-ion plasma in the framework of a hydrodynamic two-fluid model [7][8][9][10][11][12][13][14][15]. However, in all mentioned papers, the additional equation for vortex motion is obtained by taking the "curl" operator from the Euler equation, hence the resulting equation is not independent.…”

Flow of MHD micropolar fluid through porous medium: a hodograhic approach for exact solution

“…Research on MHD has become increasingly important over the years as it has got various applications in liquid metal cooling of nuclear reactors, electromagnetic casting, MHD pumps, MHD flow meters, MHD power generation among others. The liquid metal cleansing from non-metals by the use of attractive magnetic field is another basic component of application of MHD [29,1,28]. Also, researchers have paid lots of attention in the study and research on non-Newtonian fluids [63] as these fluids have various applications in psychology, biology, technology and industry like blood flow through arteries, vasomotion of small blood vessels, drilling of oil and gas wells, production of synthetic fibers, food stuffs, clay coating and emulsions etc.…”

“…The study of the flow and behavior of micropolar fluids have become prominent field of research with notable number of research papers devoted to micropolar fluid flow investigations [24,25,40,70,18,2,54]. In addition, study of the flow of micropolar fluid in the presence of magnetic field under various conditions and different physical parameters have been carried out by many researchers [3,30,62,8,9,10,13,12,7,41,31,29,32].…”