Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel

• Published in: Applied mathematics and mechanics Vol. 39; no. 7; pp. 993 - 1006
• Main Authors: Yadav, P. K., Jaiswal, S., Sharma, B. D.
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.07.2018; Springer Nature B.V; Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Allahabad 211004, India
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Computational fluid dynamics; Flow velocity; Fluid flow; Fluid- and Aerodynamics; Fluids; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Micropolar fluids; Miscibility; Parameters; Partial Differential Equations; Physical properties; Porous materials; Rotation; Shear stress; Velocity; Velocity distribution; Viscosity ratio; Viscous fluids; Wall shear stresses; immiscible fluid; micropolarity parameter; micropolar fluid; 76T99; porous medium; 76S05; 76E05; O357.3; couple stress
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-018-2351-8

This paper is concerned with the flow of two immiscible fluids through a porous horizontal channel. The fluid in the upper region is the micropolar fluid/the Eringen fluid, and the fluid in the lower region is the Newtonian viscous fluid. The flow is driven by a constant pressure gradient. The presence of micropolar fluids introduces additional rotational parameters. Also, the porous material considered in both regions has two different permeabilities. A direct method is used to obtain the analytical solution of the concerned problem. In the present problem, the effects of the couple stress, the micropolarity parameter, the viscosity ratio, and the permeability on the velocity profile and the microrotational velocity are discussed. It is found that all the physical parameters play an important role in controlling the translational velocity profile and the microrotational velocity. In addition, numerical values of the different flow parameters are computed. The effects of the different flow parameters on the flow rate and the wall shear stress are also discussed graphically.