Effects of Slip and Inclined Magnetic Field on the Flow of Immiscible Fluids (Couple Stress Fluid and Jeffrey Fluid) in a Porous Channel

Abstract

In this paper, we study the flow of two immiscible fluids namely, couple stress fluid and Jeffrey fluid in a porous channel. Instead of the classical no-slip conditions on the boundaries, we used slip boundary conditions, which are more realistic and meaningful. In addition, we used inclined magnetic field effects on the fluid flow. The couple stress fluid and Jeffrey fluid are flowing adjacent to each other in the region I and in the region II, respectively, of the horizontal porous channel. The nondimensionalized governing equations are solved analytically by using slip conditions at the lower and upper boundaries and interface conditions at the fluid-fluid interface. The analytical expressions for the velocity components in both regions are obtained in closed form. The effects of slip parameter, Hartmann number, couple stress parameter, Jeffrey parameter, angle of inclination, and Darcy number on velocity components in both regions are investigated. In the absence of slip, couple stress parameter, and Jeffrey parameters, limiting cases are obtained and discussed.

Hydromagnetic Flow of Two Immiscible Couple Stress Fluids in an Inclined Porous Channel: Effects of Slip Boundary

“…Te law about fow through porous media, as found by Darcy via experimentation, is the corner-stone in the feld of transport in porous media. Darcy's law relates the volume fux u[ms − 1 ] with the force driving the fow [27,39,40], as follows:…”

“…Te behavior of immiscible fuids infuenced by the properties of its components, such as their Newtonian and/ or non-Newtonian characteristics, viscosity, density, size, shape, the fow rate of the components, and the geometry of the system. In immiscible fuid fow, scholars study the nature of the interactions between the fuids, the fow patterns, and the way in which the fuids are distributed by considering Newtonian fuid and Newtonian fuid [7,[12][13][14], Newtonian fuid and Non-Newtonian fuid [15][16][17][18][19][20][21], and Non-Newtonian and Non-Newtonian fuids [18,[22][23][24] in diferent fow geometers; they concluded the second immiscible fuid has an efect on the fow properties of other fuid and very few of these studies have been conducted analytically.…”

“…Tis Navier slip condition for velocity for single phase and two phase fuids is considered by numerous researchers. Abbas et al [25] and Abbas et al [26] used perturbation technique and Punnamchandar and Sitotaw [27] analytically investigated the efects of the slip boundary condition on hydromagnetic two phase Newtonian/non-Newtonian fuids fow in an inclined channel in the presence of velocity slip conditions. Gautam et al [28] and Bhattacharyya et al [29] were motivated by the theory of Navier slip and investigated the efects of slip boundary.…”

Heat transfer effects on the oscillatory MHD flow in a porous channel with two immiscible fluids

“…Soil mechanics, groundwater hydrology, crude oil purification, water-to-oil mixtures in packed rocks, chemical engineering, etc. are fields where immiscible fluid flows occur [2,4,8,12,[15][16][17][18]20,24,27,31,32]. Packham and Shail [16] investigated the problem of two immiscible steady cocurrent viscous liquid flows in a pipe.…”

“…Region I contains the nanofluid whose base fluid is immiscible with the pure fluid flowing through region II. Very recently, Bitla and Sitotaw [4] studied the combined influences of slip and inclined uniform magnetic field on immiscible liquids (couple stress fluid and Jeffrey liquid) flow in a porous channel. Most recently, Yadav et al [32] analyzed the influences of oriented magnetic fields and thermal radiation on the entropy generation of two immiscible electrically conduction micropolar and Newtonian liquids in a rectangular enclosure.…”