Skip to main content
Log in

Transient Generalized Couette Flow of Viscoelastic Fluid Through a Porous Medium with Variable Viscosity and Pressure Gradient

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

Abstract

The transient generalized Couette flow through a porous medium of a non-Newtonian viscoelastic fluid between two parallel porous plates is studied with heat transfer. A uniform suction from above and injection from below are applied perpendicular to the plates which are maintained at two fixed, but different, temperatures while the viscosity of the fluid is assumed to vary exponentially with temperature. The fluid is driven by a uniform horizontal exponential decaying pressure gradient. The coupled set of equations of motion and the energy equation is solved numerically using finite differences. The influence of the different physical parameters of the model on the velocity and temperature fields is investigated and presented.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Abbreviations

a :

Viscosity exponent (K−1)

c p :

Specific heat at constant pressure (J kg−1 K−1)

Ec:

Eckert number

f b :

Body force (kg m−2 s−2)

G :

Pressure gradient (kg m−2 s−2)

h :

Separation between the two plates (m)

k :

Thermal conductivity (J s−1 m−1 K−1)

k 1 :

Modulus of rigidity (kg m−1 s−2)

K :

Darcy permeability (m2 s)

Pr:

Prandtl number

M :

Porosity parameter,

N :

Viscosity exponent

Q :

Viscoelastic parameter

Re :

Reynolds number

S :

Suction parameter

t :

Time (s)

T :

Temperature of the fluid (K)

T 1 :

Temperature of the lower plate (K)

T 2 :

Temperature of the upper plate (K)

V :

Velocity component of the fluid in the x-direction (m s−1)

U o :

Suction velocity (m  s−1)

x :

Axial direction (m)

y :

Distance in the vertical direction (m)

z :

Longitudinal direction (m)

α :

Pressure gradient exponent (s−1)

μ :

Coefficient of viscosity of the fluid (kg m−1 s−1)

ρ :

Density of the fluid (kg m−3)

τ :

Shear stress (kg m−1 s−2)

References

  1. Hartmann, J.; Lazarus, F.: Kgl. Danske Videnskab, Selskab. Mat.-Fys. Medd. 15, 6–7 (1937)

  2. Orhan A., Mete A.: Laminar forced convection with viscous dissipation in a Couette–Poiseuille flow between parallel plates. Appl. Energy 83, 856–867 (2006)

    Article  Google Scholar 

  3. Boaca T., Boaca I.: An unified numerical approach of steady convection between two parallel plates. Appl. Math. Comp. 215, 2673–2685 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Alpher R.A.: Heat transfer in magnetohydrodynamic flow between parallel plates. Int. J. Heat Mass Trans. 3, 108–115 (1961)

    Article  Google Scholar 

  5. Nigam S.D., Singh S.N.: Heat transfer by laminar flow between parallel plates under the action of transverse magnetic field. Q. J. Mech. Appl. Math. 13, 85–97 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  6. Attia H.A.: Hall effect on Couette flow with heat transfer of a dusty conducting fluid in the presence of uniform suction and injection. Afr. J. Math. Phys. 2(1), 97–110 (2005)

    MATH  Google Scholar 

  7. Erik S., Vajravelu K., Robert A., Van G., Pop I.: Analytical solution for the unsteady MHD flow of a viscous fluid between moving parallel plates. Comm. Non. Sci. Num. Sim. 16, 266–273 (2011)

    Article  MATH  Google Scholar 

  8. Herwig H., Wicken G.: The effect of variable properties on laminar boundary layer flow. Warme-und Stoffubertragung 20, 47–57 (1986)

    Article  Google Scholar 

  9. Klemp, K.; Herwig, H.; Selmann, M.: Entrance flow in channel with temperature dependent viscosity including viscous dissipation effects. Proc. of 3rd Int. Con. Fluid Mech. Cairo 3, 1257-1270 (1990)

    Google Scholar 

  10. Attia H.A.: On the effectiveness of variable physical properties on the transient hydromagnetic couette-poiseulle flow. Afr. J. Math. Phys. 4(1), 117–123 (2007)

    MathSciNet  Google Scholar 

  11. Attia, H.A.: The effect of variable properties on the unsteady Couette flow with heat transfer considering the Hall effect. Comm. Nonlinear Sci. Num. Sim. 13(9), 1596–1604 (2008a)

  12. Attia, H.A.: Unsteady hydromagnetic couette flow of dusty fluid with temperature dependent viscosity and thermal conductivity. Int. J. Non-Linear Mech. 43(9), 707–715 (2008b)

  13. Joaquín Z., Pablo E., Enrique G., José L.M., Osman A.B.: An electrical network for the numerical solution of transient mhd couette flow of a dusty fluid: Effects of variable properties and hall current. Int. Comm. Heat Mass Trans. 37, 1432–1439 (2010)

    Article  Google Scholar 

  14. Eguia P., Zueco J., Granada E., Patio D.: NSM solution for unsteady MHD Couette flow of a dusty conducting fluid with variable viscosity and electric conductivity. Appl. Math. Model. 35, 303–316 (2011)

    Article  MATH  Google Scholar 

  15. Abdalla I.A., Attia H.A., Ahmed M.E.S.: Adomian’s polynomial solution of unsteady non-newtonian MHD flow. Int. J. Appl. Math. Inf. Sci. 1(3), 227–245 (2007)

    MATH  Google Scholar 

  16. Attia H.A., Ahmed M.E.S.: Transient MHD Couette flow of a Casson fluid between parallel plates with heat transfer. Italian J. Pure Appl. Math. 27, 19–38 (2010)

    MATH  Google Scholar 

  17. Ahmed M.E.S., Attia H.A., Ewis K.M.: Time dependent pressure gradient effect on unsteady mhd Couette flow and heat transfer of a Casson fluid. J. Engg. 3, 38–49 (2011)

    Google Scholar 

  18. Cho Y.I., Hartnett J.P.: Non-Newtonian fluids. Handbook of Heat Transfer Applications. McGraw-Hill Book Co., New York (1985)

    Google Scholar 

  19. Magno R.N.O., Macêdo E.N., Quaresma J.N.N.: Couette–Poiseuille flow of Bingham fluids between two porous parallel plates with slip conditions. J. Non-Newtonian Fluid Mech. 153, 1–11 (2008)

    Article  Google Scholar 

  20. Tso C.P., Sheela-Francisca J., Hung Y.-M.: Viscous dissipation effects of power-law fluid flow within parallel plates with constant heat fluxes. J. Non-New. Fluid Mech. 165, 625–630 (2010)

    Article  MATH  Google Scholar 

  21. Hartnett J.P.: Viscoelastic fluids: a new challenge in heat transfer. ASME Trans. 114, 296–311 (1992)

    Article  Google Scholar 

  22. Abel M.S., Adress K.M.: Dusty viscoelastic fluid under the influence of time dependent tangential stress applied at the surface. Indian J. Theor. Phys. 41(1), 13–28 (1993)

    Google Scholar 

  23. Hashemabadi S.H., Etemad S.Gh., Thibault J.: Forced convection heat transfer of Couette–Poiseuille flow of nonlinear viscoelastic fluids between parallel plates. Int. J. Heat Mass Trans. 47, 3985–3991 (2004)

    Article  MATH  Google Scholar 

  24. Joseph D.D., Nield D.A., Papanicolaou G.: Nonlinear equation governing flow in a staturated porous media. Water Resour. Res. 18(4), 1049–1052 (1982)

    Article  Google Scholar 

  25. Ingham D.B., Pop I.: Transport Phenomena in Porous Media. Pergamon, Oxford (2002)

    MATH  Google Scholar 

  26. Khaled A.R.A., Vafai K.: The role of porous media in modeling flow and heat transfer in biological tissues, Int. J. Heat Mass Trans. 46, 4989–5003 (2003)

    Article  MATH  Google Scholar 

  27. Mitchell A.R., Griffiths D.F.: The Finite Difference Method in Partial Differential Equations. Wiley, New York (1980)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mostafa A. M. Abdeen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Attia, H.A., Abdeen, M.A.M. & El-Meged, W.A. Transient Generalized Couette Flow of Viscoelastic Fluid Through a Porous Medium with Variable Viscosity and Pressure Gradient. Arab J Sci Eng 38, 3451–3458 (2013). https://doi.org/10.1007/s13369-013-0668-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-013-0668-0

Keywords

Navigation