Skip to main content

Advertisement

SpringerLink
Log in

Magneto-Micropolar Flow Over a Stretching Surface Embedded in a Darcian Porous Medium by the Numerical Network Method

  • Research Article - Mechanical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

The present work investigated the 2D steady-state boundary layer flow and heat transfer of an electrically conducting incompressible micropolar fluid over a continuously moving stretching surface embedded in a Darcian porous medium with a uniform magnetic field imposed in the direction normal to the surface. The stretching velocity is assumed to vary linearly with the distance along the sheet. The transformed coupled non-linear ordinary differential equations are solved numerically. The main velocity, transverse velocity, angular velocity and temperature are shown graphically. This study presents a Network Simulation Method solution using the Pspice algorithm database. The present study searched for and determined applications in metallurgical processes involving the cooling of continuous strips or filaments by drawing them through a quiescent fluid, in polymer flows in filtration systems and general non-Newtonian fluid mechanics.

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

Similar content being viewed by others

Abbreviations

B 0 :

Magnetic induction, Tesla

C p :

Specific heat, J kg−1K−1

C :

Positive constant

U :

Velocity of the wall, ms−1

V 0 :

Suction velocity, ms−1

u,v :

Translational velocity components in the (x, y) directions, ms−1

x :

Coordinate parallel to plate, m

y :

Coordinate transverse to plate, m

ν :

Newtonian kinematic viscosity, m2s−1

κ :

Vortex viscosity (rotational viscosity) coefficient

μ :

Dynamic viscosity, Pa s

ρ :

Density of micropolar fluid, kgm−3

N :

Angular velocity (micro-rotation component in the x–y plane), s−1

K :

Permeability of porous medium, m2

j:

Eringen micro-inertia per unit mass (micro-inertia density)

j :

Electrical current, A

β :

Volume expansion coefficient, K−1

σ :

Fluid electrical conductivity, Sm−1

γ :

Spin gradient viscosity (gyroviscosity) coefficient

τ w :

Local wall shear stress, Pa

Γ w :

Local wall couple stress, Pa

q w :

Rate of heat transfer from the wall, Wm−2

C f :

Skin friction coefficient

Da:

Darcy number

Er:

Eringen micropolar number

f :

Dimensionless stream function

Gr:

Grashof number

h :

Variable ∂f/∂η

M :

Magnetic parameter

Nux :

Local Nusselt number

Rex :

Local Reynolds number

α*:

Heat source parameter

β :

Micro-inertia parameter

ψ :

Dimensional stream function

λ :

Constant suction parameter

η :

Transformed y-coordinates

θ :

Dimensionless temperature

δ :

Heat conduction parameter

Ω:

Dimensionless micro-rotation (angular velocity)

References

  1. Eringen A.C.: Theory of micropolar fluids. J. Math. Mech. 16, 1–18 (1966)

    MathSciNet  Google Scholar 

  2. Eringen A.C.: Theory of thermomicro fluids. J. Math. Anal. Appl. 38, 480–492 (1972)

    Article  MATH  Google Scholar 

  3. Lukaszewicz G.: Micropolar Fluids: Theory and Applications. Birkhäuser, Boston (1999)

    Book  MATH  Google Scholar 

  4. Kelson N.A., Farrell T.W.: Micropolar flow over a porous stretching sheet with strong suction or injection. Int. Comm. Heat Mass Transf. 28, 479–488 (2001)

    Article  Google Scholar 

  5. Kumari M., Slaouti A., Takhar H.S., Nakamura S., Nath G.: Unsteady free convection flow over a continuous moving vertical surface. Acta Mechanica, 116, 75–82 (1996)

    Article  MATH  Google Scholar 

  6. Ishak A., Nazar R., Pop I.: Unsteady mixed convection boundary layer flow due to a stretching vertical surface. Arab. J. Sci. Engng. 31, 165–182 (2006)

    MathSciNet  Google Scholar 

  7. Yucel A.: Mixed convection in micropolar flow over a horizontal plate with surface mass transfer. Intern. J. Engi. Sci. 27, 1593–1602 (1989)

    Article  Google Scholar 

  8. Ziabicki A.: Physics of Fiber Formation from Natural and Synthetic Polymers. WNT Press, Poland (1970)

    Google Scholar 

  9. Sakiadis B.C.: Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChemE J. 7(1), 26–28 (1961)

    Google Scholar 

  10. Vajravelu K.: Fluid flow over a nonlinearly stretching sheet. Appl. Math. Comput. 181, 609–618 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Cortell R.: Viscous Flow and heat transfer over a non-linearly stretching sheet. Appl. Math. Comput. 184, 864–873 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Abbas Z., Hayat T.: Radiation effects on MHD flow in porous space. Int. J. Heat Mass Transfer. 51, 1024–1033 (2008)

    Article  MATH  Google Scholar 

  13. Raptis A., Perdikis C.: Viscous flow over a non-linear stretching sheet in the presence of a chemical reaction and magnetic field. Int. J. Non-Lin. Mech. 41, 527–529 (2006)

    Article  MATH  Google Scholar 

  14. Awang Kechil S., Hashim I.: Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field. Phys. Lett. A 372, 2258–2263 (2008)

    Article  MATH  Google Scholar 

  15. Magyari E., Keller B.: Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. J. Phys. D 32, 577–585 (1999)

    Article  Google Scholar 

  16. Ali M.E.: Heat transfer characteristics of a continuous stretching surface. Warme Stoffuberttragung 29, 227–234 (1994)

    Article  Google Scholar 

  17. Nield D.A., Bejan A.: Convection in Porous Media. Springer, New York (1999)

    Book  MATH  Google Scholar 

  18. Ingham D.B., Pop I.: Transport Phenomena in Porous Media. Pergamon, Oxford (1998)

    MATH  Google Scholar 

  19. Jaiswal B.S., Soundalgekar V.M.: Oscillating plate temperature effects on a flow past an infinite vertical porous plate with constant suction and embedded in a porous medium. Heat Mass Transf. 37, 125–131 (2001)

    Article  Google Scholar 

  20. Kim Y.J., Fedorov A.G.: Transiet mixed radiative convection flow of a micropolar fluid past a moving, semi-infinite vertical porous plate. Int. J. Heat Mass Transf. 46, 1751–1758 (2003)

    Article  MATH  Google Scholar 

  21. Peddieson, J.; McNitt, P.R.: Boundary-layer theory for a micropolar fluid. In: Eringen, A.C.: Recent Advances in Engineering Science. vol. 5(1), 405–426, Gordon and Breach, New York (1968)

  22. Gorla R.S.R., Hassanien I.A.: Boundary layer flow of a micropolar fluid near an axisymmetric stagnation point on a moving cylinder. Int. J. Eng. Sci. 28, 323–329 (1990)

    Article  Google Scholar 

  23. Soundalgekar V.M., Takhar H.S.: Flow of micropolar fluid past a continuously moving plate. Int. J. Eng. Sci. 21, 961–965 (1983)

    Article  Google Scholar 

  24. Bernardy T.: The filtration of micropolar liquid through a porous medium. Vodohospod. Cas. 28, 319–326 (1980)

    Google Scholar 

  25. Hassanien I.A., Essawy A.H., Moursy N.M.: Natural convection flow of micropolar fluid from a permeable uniform heat flux surface in porous medium. Appl. Math. Comput. 152, 323–335 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  26. Kozicki W.: Filtration in non-Newtonian media. Encycl. Fluid Mech. 5, 965–985 (1986)

    Google Scholar 

  27. Christopher R.H., Middleman S.: Power-law flow through a packed tube. I & EC Fund. 4, 422–426 (1965)

    Article  Google Scholar 

  28. Kim Y.J.: Heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium. Trans. Porous Media 56, 17–37 (2004)

    Article  Google Scholar 

  29. El-Amin M.F.: Combined effect of internal heat generation and magnetic field on free convection and mass transfer flow in a micropolar fluid with constant suction. J. Magnet. Magn. Mater. 270, 130–135 (2004)

    Article  Google Scholar 

  30. Ishak A., Nazar R., Pop I.: Boundary-layer flow of a micropolar fluid on a continuously moving or fixed permeable surface. Intern. J. Heat Mass Transf. 50, 4743–4748 (2007)

    Article  MATH  Google Scholar 

  31. Tadmor A., Klein I.: Engineering Principles of Plasticating Extrusion, Polymer Science and Engineering Series. Van Nostrand Reinhold, New York (1970)

    Google Scholar 

  32. Pspice 6.0. Irvine, California 92718. Microsim Corporation, 20 Fairbanks (1994)

  33. Takhar H.S., Agarwal R.S., Bhargava R., Jain S.: Mixed convection flow of a micropolar fluid over a stretching sheet. Heat Mass Transf. 34, 213–219 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Industrial Engineering ETS, Campus Muralla del Mar, Department of Thermal and Fluid Engineering, Universidad Politécnica de Cartagena, 30202, Cartagena, Murcia, Spain

    Joaquín Zueco

  2. Department of Mathematics and Computing, Rajiv Gandhi University, Rono Hills, Itanagar, 791112, Arunachal Pradesh, India

    Sahin Ahmed

  3. Department of Mechanical Engineering, Universidad de La Rioja, C/Luís de Ulloa, 20.26004, Logroño, La Rioja, Spain

    L. M. López-Ochoa

Authors
  1. Joaquín Zueco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sahin Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. M. López-Ochoa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joaquín Zueco.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zueco, J., Ahmed, S. & López-Ochoa, L.M. Magneto-Micropolar Flow Over a Stretching Surface Embedded in a Darcian Porous Medium by the Numerical Network Method. Arab J Sci Eng 39, 5141–5151 (2014). https://doi.org/10.1007/s13369-014-1175-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-014-1175-7

Keywords

Search

Navigation