Abstract
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.
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Abbreviations
- K i :
-
non-dimensional permeability of the porous medium
- pi :
-
non-dimensional pressure
- \(\bar x\), \(\bar y\) :
-
coordinates along the channel
- \(\bar u\) i , \(\bar v\) i :
-
velocities in the x-direction
- Re i :
-
Reynolds number
- c :
-
micropolarity parameter
- c 0, c a, c d :
-
coefficients of angular viscosities
- s :
-
couple stress
- ρi :
-
density of the fluid
- \(\overline {{\mu _i}} \) :
-
viscosity of the fluid
- \(\overline {{\omega _i}} \) :
-
microrotational velocity of the fluid
- \(\overline {{\mu _r}} \) :
-
dynamic microrotation viscosity of the micropolar fluid
- λ:
-
viscosity ratio
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Citation: YADAV, P. K., JAISWAL, S., and SHARMA, B. D. Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel. Applied Mathematics and Mechanics (English Edition), 39(7), 993–1006 (2018) https://doi.org/10.1007/s10483-018-2351-8
Project supported by the Science and Engineering Research Board, New Delhi (No. SR/FTP/MS- 47/2012)
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Yadav, P.K., Jaiswal, S. & Sharma, B.D. Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel. Appl. Math. Mech.-Engl. Ed. 39, 993–1006 (2018). https://doi.org/10.1007/s10483-018-2351-8
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DOI: https://doi.org/10.1007/s10483-018-2351-8