Browse > Article
http://dx.doi.org/10.5666/KMJ.2021.61.2.323

MHD Pulsatile Flow and Heat Transfer of Two Immiscible Couple Stress Fluids Between Permeable Beds  

Kumar, Deepak (Department of Mathematics and Astronomy, University of Lucknow)
Agarwal, Manju (Department of Mathematics and Astronomy, University of Lucknow)
Publication Information
Kyungpook Mathematical Journal / v.61, no.2, 2021 , pp. 323-351 More about this Journal
Abstract
The present paper addresses magnetohydrodynamic pulsating flow and heat transfer of two immiscible, incompressible, and conducting couple stress fluids between two permeable beds. The flow between the permeable beds is assumed to be governed by Stokes' [28] couple stress fluid flow equations, whereas the dynamics of permeable beds is determined by Darcy's law. In this study, matching conditions were used at the fluid-fluid interface, whereas the B-J slip boundary condition was employed at the fluid-porous interface. The governing equations were solved analytically, and the expressions for velocity, temperature, mass flux, skin friction, and rate of heat transfer were obtained. The analytical expressions were numerically evaluated, and the results are presented through graphs and tables.
Keywords
couple stress fluid; permeable bed; Darcy's law; Beaver-Joseph slip condition;
Citations & Related Records
연도 인용수 순위
  • Reference
1 A. A. Elsharkawy and L. H. Guedouar, An inverse solution for finite journal bearings lubricated with couple stress fluids, Tribol. Int., 34(2)(2001), 107-108.   DOI
2 T. T. Ariman and N. D. Sylvester, Microcontinum fluid mechanics-a review, Int. J. Eng. Sci., 11(8)(1973), 905-930.   DOI
3 T. T. Ariman and N. D. Sylvester, Applications of microcontinuum fluid mechanics, Int. J. Eng. Sci., 12(4)(1974), 273-293.   DOI
4 G. Beavers and D. Joseph, Boundary conditions at naturally permeable wall, J. Fluid Mech., 30(1)(1967), 197-207.   DOI
5 N. M. Bujurke and G. Jayaraman, The influence of couple stresses in squeeze films, Int. J. Mech. Sci., 24(6)(1982), 369-376.   DOI
6 M. Farooq et.al., Heat transfer flow of steady couple stress fluids between two parallel plates with variable viscosity, Heat Transfer Res., 42(8)(2011), 737-780.   DOI
7 R. S. Gupta and L. G. Sharma, Analysis of couple stress lubricant in hydrostatic thrust bearings, Wear, 125(3)(1988), 257-270.   DOI
8 D. P. Hochmuth and D. K. Sunada, Ground-water model of two-phase immiscible flow in coarse material, Groundwater, 23(5)(1985), 617-626.   DOI
9 J. R. Lin, Static and dynamic behaviour of externally pressurized circular step thrust bearings lubricated with couple stress fluids, Tribol. Int., 32(4)(1999), 207-216.   DOI
10 U. M. Mokhiamer et.al., A study of a journal bearing lubricated by fluids with couple stress considering the elasticity of the linear, Wear, 224(2)(1999), 194-201.   DOI
11 S. Panda, S. C. Martha and A. Chakrabarti, Three-layer fluid flow over a small obstruction on the bottom of a channel, ANZIAM J., 56(3)(2015), 248-274.   DOI
12 B. G. Prasad and A. Kumar, Flow of a hydromagnetic fluid through porous media between permeable beds under exponentially decaying pressure gradient, Comput. Meth. Sci. Technol., 17(1-2)(2011), 63-74.   DOI
13 B. Punnamchandar and T. K. V. Iyengar, Oscillatory flow of an incompressible couple stress fluid between permeable beds with an imposed uniform magnetic field, Spec. Topics Rev. Porous Media, 4(1)(2013), 23-31.   DOI
14 M. Sharan and A. S. Popel, A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall, Biorheology, 38(5-6)(2001), 415-428.
15 A. M. Siddiqui et al., Couette and Poiseuille flows for non-Newtonian fluids, Int. J. Nonlin. Sci. Num. Sim., 7(1)(2006), 15-26.
16 L. M. Srivastava, Flow of couple stress fluid through stenotic blood vessels, J. Bio-Mech., 18(7)(1985), 479-485.   DOI
17 V. M. Soundalgekar and R. N. Aranake, Effects of couple stresses on MHD Couette flow, Nucl. Eng. Design, 49(3)(1978), 197-203.   DOI
18 J. Srinivas and J. V. R. Murthy, Flow of two immiscible couple stress fluids between two permeable beds, J. Appl. Fluid Mech., 9(1)(2016), 501-507.   DOI
19 T. K. V. Iyengar and B. Punnamchandar, Pulsating flow of an incompressible couple stress fluid between permeable beds, Int. J. Math. Comput. Phys. Elect. Comp. Eng., 5(8)(2011), 1241-1251.
20 G. Ramanaiah, Squeeze films between finite plates lubricated by fluids with couple stress, Wear, 54(2)(1979), 315-320.   DOI
21 D. Jogie and B. Bhatt, Flow of immiscible fluids in a naturally permeable channel, Int. J. Pure Appl. Math., 78(3)(2012), 435-449.
22 C. B. Mehta et.al., Thermal convection of magneto compressible couple stress fluid saturated in a porous medium with hall current, Int. J. Appl. Mech. Eng., 21(1)(2016), 83-93.   DOI
23 V. K. Stokes, Theories of fluids with microstructure, an introduction, Springer Verlag, New York, 1984.
24 K. Vajravelu, P. V. Arunachalam and S. Sreenadh, Unsteady flow of two immiscible conducting fluids between two permeable beds, J. Math. Anal. Appl., 196(3)(1995), 1105-1116.   DOI
25 A. Z. Szeri and K. R. Rajagopal, Flow of a non-Newtonian fluid between heated parallel plates, Int. J. of Nonlin. Mech., 20(2)(1985), 91-101.   DOI
26 P. Chaturani and R. P. Samy, A study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases, Biorheology, 22(6)(1985), 521-531.   DOI
27 A. E. Garcia and D. N. Riahi, Two phase blood flow and heat transfer in an inclined stenosed artery with or without a catheter, Int. J. Fluid Mech. Res., 41(1)(2014), 16-30.   DOI
28 S. Islam and C. Y. Zhou, Exact solutions for two-dimensional flows of couple stress fluids, ZAMP, 58(6)(2007), 1035-1048.
29 L. M. Srivastava, Peristaltic transport of a couple stress fluid, Rheol. Acta, 25(6)(1986), 638-641.   DOI
30 V. K. Stokes, Couple stresses in fluids, Phys. Fluids, 9(9)(1966), 1709-1715.   DOI
31 J. C. Umavathi, I. C. Liu and J. Prathap-Kumar, Unsteady flow and heat transfer of porous media sandwiched between viscous fluids, Appl. Math. Mech. (Engl. Ed.), 31(12)(2010), 1497-1516.   DOI
32 K. Vajravelu, K. Ramesh, S. Sreenadh, and P.V. Arunachalam, Pulsatile flow between permeable beds, Int. J. Non-Linear Mech., 38(7)(2003), 999-1005.   DOI
33 J. Srinivas, Entropy generation analysis of the flow of two immiscible couple stress fluids between two porous beds, Comput. Therm. Sci., 7(2)(2015), 123-137.   DOI