Skip to main content
SpringerLink
Log in

Ion slip effect on unsteady Couette flow of a dusty fluid in the presence of uniform suction and injection with heat transfer

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

The combined effects of Hall current, ion slip, viscous dissipation, and Joule heating on unsteady magnetohydrodynamic Couette flow with heat transfer of a dusty viscous incompressible electrically conducting fluid are studied under a constant pressure gradient. The fluid is subjected to an external uniform magnetic field and a uniform suction and injection perpendicular to the plates (y-direction). Numerical solutions for the constitutive equations are obtained using the method of finite differences. The effects of the magnetic field, Hall parameter, and ion slip parameter on the velocity and temperature distributions for both the fluid and particle phases are investigated in details and shown graphically. It is found that, the Hall current and ion slip parameters have a great effect on the fluid and dust velocities and temperature.

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
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Lohrabi J (1980) Investigation of magnetohydrodynamic heat transfer in two-phase flow. Ph.D. Thesis, Tennessee Technological University, P. I

  2. Saffman PG (1962) On the stability of a laminar flow of a dusty gas. J Fluid Mech 13:120–128

    Article  MathSciNet  MATH  Google Scholar 

  3. Michael DH, Miller DA (1966) Plane parallel flow of a dusty gas. Mathematika 13:97–109

    Article  MATH  Google Scholar 

  4. Peddieson JJR (1976) Some unsteady parallel flows of particulate suspension. App Sci Res 32:239–268

    Article  MATH  Google Scholar 

  5. Mitra P (1981) Flow of a dusty gas between two parallel plate’s one stationary and other oscillating. Def Sci J 31:211–223

    Article  MATH  Google Scholar 

  6. Mitra P (1982) On the steady flow of a dusty gas between two parallel plates, one being at rest and the other oscillating. Erevueroumaine de Sciences Technique, Eerie de Micamque applique 27:57–68

    MATH  Google Scholar 

  7. Madhura KR, Gireesha BJ, Bagewadi CS (2009) Exact solutions of unsteady dusty fluid flow through porous media in an open rectangular channel. Adv Theor Appl Mech 2:1–17

    MATH  Google Scholar 

  8. Attia HA, Abbas W, Abdeen MAM, Emam MS (2014) Effect of porosity on the flow of a dusty fluid between parallel plates with heat transfer and uniform suction and injection. Eur J Environ Civil Eng 18:241–251

    Article  Google Scholar 

  9. Attia HA (2002) Unsteady MHD flow and heat transfer of dusty fluid between parallel plates with variable physical properties. Appl Math Model 26:863–875

    Article  MATH  Google Scholar 

  10. Singh V, Singh G (2011) Unsteady magnetohydrodynamic flow of a dusty fluid between two oscillating plates under varying constant pressure gradient. Novi Sad J Math 41:123–129

    MathSciNet  MATH  Google Scholar 

  11. Basant KJ, Apere CA (2013) Unsteady MHD two-phase Couette flow of fluid–particle suspension. Applied Math Model 37:1920–1931

    Article  MathSciNet  Google Scholar 

  12. Attia HA (2008) Unsteady hydro magnetic Couette flow of dusty fluid with temperature dependent viscosity and thermal conductivity under exponential decaying pressure gradient. Commun Nonlinear Sci Numer Simul 13:1077–1088

    Article  MathSciNet  MATH  Google Scholar 

  13. Ezzat MA, El-Bary AA, Morsey MM (2010) Space approach to the hydro-magnetic flow of a dusty fluid through a porous medium. Comput Math Appl 59:2868–2879

    Article  MathSciNet  MATH  Google Scholar 

  14. Anurag D, Singh UR (2012) Effect of dusty viscous fluid on unsteady laminar free convective flow through porous medium along a moving porous hot vertical plate with thermal diffusion. Appl Math Sci 6:6109–6124

    MathSciNet  MATH  Google Scholar 

  15. Attia HA, Aboul-Hassan AL, Abdeen MAM, Abdin AE (2014) MHD flow of a dusty fluid between two infinite parallel plates with temperature dependent physical properties under exponentially decaying pressure gradient. Bulg Chem Commun 46:320–329

    Google Scholar 

  16. Parul S, Manju A (2014) Unsteady flow of a dusty fluid between two parallel plates bounded above by porous medium. Int J Eng Sci Technol 6:27–33

    Article  Google Scholar 

  17. Hatami M, Hosseinzadeh KH, Domairry G, Behnamfar MT (2014) Numerical study of MHD two-phase Couette flow analysis for fluid-particle suspension between moving parallel plates. J Taiwan Inst Chem Eng (in press, corrected proof, available online 11 June 2014)

  18. Attia HA (2005) Effect of the ion slip on the MHD flow of a dusty fluid with heat transfer under exponential decaying pressure gradient. Cent Eur J Phys 3:484–507

    Google Scholar 

  19. Attia HA (2007) Analytical solution for flow of a dusty fluid in a circular pipe with Hall and ion slip effect. Chem Eng Commun 194:1287–1296

    Article  Google Scholar 

  20. Golovanov AN, Ruleva EV, Yakimov AS (2011) Modeling the heat and mass exchange process in the systems of porous cooling with gas flow pulsations. High Temp 49:917–921

    Article  Google Scholar 

  21. Terekhov VV, Terekhov VI (2012) Free-convective heat transfer within a differentially heated vertical plane during additional heat supply through a bottom wall. High Temp 50:91–97

    Article  Google Scholar 

  22. Valueva EP (2012) Numerical modeling of heat exchange and turbulent flow of fluid within tubes at supercritical pressure. High Temp 50:278–285

    Article  Google Scholar 

  23. Marble FE (1970) Ann Rev Fluid Mech 2:397

    Article  Google Scholar 

  24. Aboul-Hassan AL, Sharaf El-Din H, Megahed AA (1991) Temperature due to the motion of one of them. First International Conference of Engineering Mathematics and Physics, Cairo, Egypt

  25. Schlichting H (1968) Boundary layer theory. McGraw-Hill, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Engineering Mathematics and Physics Department, Faculty of Engineering, El-Fayoum University, El Fayoum, 63514, Egypt

    Hazem Ali Attia

  2. Basic and Applied Science Department, College of Engineering and Technology, Arab Academy for Science Technology and Maritime Transport, Cairo, Egypt

    W. Abbas

  3. Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza, 12211, Egypt

    Mostafa A. M. Abdeen

Authors
  1. Hazem Ali Attia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Abbas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mostafa A. M. Abdeen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mostafa A. M. Abdeen.

Additional information

Technical Editor: Francisco Ricardo Cunha.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Attia, H.A., Abbas, W. & Abdeen, M.A.M. Ion slip effect on unsteady Couette flow of a dusty fluid in the presence of uniform suction and injection with heat transfer. J Braz. Soc. Mech. Sci. Eng. 38, 2381–2391 (2016). https://doi.org/10.1007/s40430-015-0311-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-015-0311-y

Keywords

Search

Navigation