Skip to main content
SpringerLink
Log in

Numerical Solution of Unsteady MHD Couette Flow in the Presence of Uniform Suction and Injection with Hall Effects

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

In this paper, unsteady magnetohydrodynamic Couette flow is studied numerically for a viscous, incompressible and electrically conducting fluid between two infinitely long parallel porous plates, taking Hall current into account. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel and fluid motion is subjected to a uniform suction and injection at upper and lower plates. Magnetic lines of force are assumed to be fixed relative to the fluid. Numerical solutions for primary and secondary velocities are obtained from the governing momentum equation by employing explicit finite difference method. Numerical solutions of the primary and secondary velocities are displayed graphically versus non-dimensional channel width variable \(y\) for various values of Hall current parameter \(m\), magnetic parameter \(M\), suction/injection parameter \(S\) and time \(t\) whereas the numerical values of co-efficient of skin-frictions at the moving plate due to primary and secondary flows are presented in tabular form for different values of \(m\), \(M\), \(S\) and \(t\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Abbas Z, Sajid M, Hayat T (2006) MHD boundary layer flow of an upper convected Maxwell fluid in a porous channel. Theor Comp Fluid Dyn 20:229–238

    Article  Google Scholar 

  • Attia HA (2006) Time varying Hartmann flow with heat transfer of a Power-law fluid with uniform suction and injection under constant pressure gradient. Kragujevac J Sci 28:25–38

    Google Scholar 

  • Bhaskara Reddy N, Bathaiah D (1982) Hall effects on MHD flow through a porous straight channel. Def Sci J 32:313–326

    Article  Google Scholar 

  • Chamkha AJ (2004) Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption. Int J Eng Sci 42:217–230

    Article  Google Scholar 

  • Cowling TG (1957) Magnetohydrodynamics. Inter-Science Inc, New York

    MATH  Google Scholar 

  • Das S, Guchhait SK, Jana RN (2015) Hall effects on unsteady hydromagnetic flow past an accelerated porous plate in a rotating system. J Appl Fluid Mech 8(3):409–417

    Article  Google Scholar 

  • Deka RK (2008) Hall effects on MHD flow past an accelerated plate. Int J Theor Appl Mech 35(4):333–346

    Article  MathSciNet  Google Scholar 

  • Guchhait S, Das S, Jana RN, Ghosh SK (2011) Combined effects of Hall current and rotation on unsteady Couette flow in a porous channel. World J Mech 1:87–99

    Article  Google Scholar 

  • Harisingh Naik S, Ramana Murthy MV, Rama Rao K (2014) The effect of Hall current on an unsteady MHD free convective Couette flow between two permeable plates in the presence of thermal radiation. Int J Comput Eng Res 4(7):2250–3005

    Google Scholar 

  • Hayat T, Ahmed N, Sajid M, Asghar S (2007) On the MHD flow of second grade fluid in a porous channel. Comp Math Appl 54:407–414

    Article  MathSciNet  Google Scholar 

  • Hayat T, Ahmed N, Sajid M (2008) Analytic solution for MHD flow of third order fluid in a porous channel. J Comp Appl Math 214:572–582

    Article  MathSciNet  Google Scholar 

  • Hossain MA (1986) Effect of Hall current on unsteady hydromagnetic free convection flow near an infinite vertical porous plate. J Phys Soc Jpn 55:2183–2190

    Article  Google Scholar 

  • Jana RN, Dutta N (1977) Hall effects on unsteady Couette flow. Int J Eng Sci 15(1):35–43

    Article  Google Scholar 

  • Katagiri M (1962) Flow formation in Couette motion in magnetohydrodynamics. J Phys Soc Jpn 17:393–396

    Article  Google Scholar 

  • Katagiri M (1969) Effect of Hall currents on the magnetohydrodynamic boundary layer flow past a semi- infinite flat plate. J Phys Soc Jpn 27:1051–1059

    Article  Google Scholar 

  • Khan M, Rahman S, Hayat T (2009) Heat transfer analysis and magnetohydrodynamic flow of a non-Newtonian fluid through a porous medium with slip at the walls. J Porous Media 12:277–287

    Article  Google Scholar 

  • Makinde OD, Chinyoka T (2001) Unsteady MHD flow in a porous channel with an exponentially decreasing suction. J Pure Appl Math 1(1):1–13

    Google Scholar 

  • Makinde OD, Osalusi E (2006) MHD steady flow in a channel with slip at permeable boundaries. Rom J Phys 51:319–328

    Google Scholar 

  • Mathews JH, Fink KD (2009) Numerical method using matlab. PHI Learning Private Limited, New Delhi

    Google Scholar 

  • Meyer RC (1958) On reducing aerodynamic heat transfer rates by magnetohydrodynamic techniques. J Aerosp Sci 25:561–572

    Article  Google Scholar 

  • Mohapatra P, Tripathi A (1981) Hall effect on Couette flow. Wear 73(1):79–86

    Article  Google Scholar 

  • Muhuri PK (1963) Flow formation in Couette motion in magnetohydrodynamics with suction. J Phys Soc Jpn 18:1671–1675

    Article  MathSciNet  Google Scholar 

  • Onyango ER, Kinyanjui MN, Uppal SM (2015) Unsteady hydromagnetic Couette flow with magnetic field lines fixed relative to the moving upper plate. Am J Appl Math 3(5):206–214

    Article  Google Scholar 

  • Prasad Rao DRV, Krishna DV, Debnath L (1982) Combined effect of free and forced convection on MHD flow in a rotating porous channel. Int J Math Math Sci 5:165–182

    Article  MathSciNet  Google Scholar 

  • Seth GS, Hussain SM (2011) Hall effects on hydromagnetic Couette flow of class-II in a rotating system in the presence of an inclined magnetic field with asymmetric heating/cooling of the walls. Int J Eng Sci Technol 3(8):234–247

    Google Scholar 

  • Seth GS, Singh JK (2011) Effects of Hall current and rotation on unsteady MHD Couette flow in a porous channel in the presence of a moving magnetic field. J Nat Sci Sustain Technol 5(4):263–283

    Google Scholar 

  • Seth GS, Singh JK (2013) Effects of Hall current on unsteady MHD Couette flow of class-II in a rotating system. JAppl Fluid Mech 6(4):473–484

    Google Scholar 

  • Seth GS, Ansari MdS, Nandkeolyar R (2011a) Unsteady hydromagnetic Couette flow within a porous channel. Tamkang J Sci Eng 14(1):7–14

    Google Scholar 

  • Seth GS, Singh JK, Mahato GK (2011b) Unsteady hydromagnetic Couette flow within a porous channel with Hall effects. Int J Eng Sci Technol 3(6):172–183

    Google Scholar 

  • Seth GS, Nandkeolyar R, Ansari MS (2011c) Effects of Hall current on unsteady hydromagnetic Couette flow in a rotating system induced by an accelerated movement of one of the plates of the channel in the presence of an inclined magnetic field. Int J Appl Mech Eng 16(3):835–849

    Google Scholar 

  • Seth GS, Nandkeolyar R, Ansari MdS (2012a) Effects of Hall current and rotation on unsteady MHD Couette flow in the presence of an inclined magnetic field. J Appl Fluid Mech 5(2):67–74

    Google Scholar 

  • Seth GS, Singh JK, Mahoto GK (2012b) Effects of Hall current and rotation on unsteady hydromagnetic Couette flow within a porous channel. Int J Appl Mech 4(2):1250015 (25 pages)

    Article  Google Scholar 

  • Seth GS, Singh JK, Mahato GK (2013) Hall effects on unsteady magnetohydrodynamic Couette flow within a porous channel due to accelerated movement of one of its plates. J Nat Sci Sustain Technol 7(3):271–290

    Google Scholar 

  • Singh AK, Kumar N (1983) Unsteady magnetohydrodynamic Couette flow. Wear 89:125–129

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Mariani College, Mariani, Assam, 785634, India

    Muhim Chutia

  2. Department of Mathematics, Dibrugarh Unversity, Dibrugarh, Assam, 786004, India

    P. N. Deka

Authors
  1. Muhim Chutia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. N. Deka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhim Chutia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chutia, M., Deka, P.N. Numerical Solution of Unsteady MHD Couette Flow in the Presence of Uniform Suction and Injection with Hall Effects. Iran J Sci Technol Trans Mech Eng 45, 503–514 (2021). https://doi.org/10.1007/s40997-020-00369-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40997-020-00369-2

Keywords

Search

Navigation