Skip to main content
SpringerLink
Log in

On Thermal Radiation and Joule Heating Effects in MHD Flow of an Oldroyd-B Fluid with Thermophoresis

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

Abstract

In this article we investigate heat and mass transfer effects in the magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid in a porous space. In addition, thermal radiation, Joule heating and thermophoresis are considered. The relevant equations are first developed and then computed by the homotopy analysis method. The local Nusselt and Sherwood numbers are also analyzed. The dimensionless velocity, temperature and concentration fields are displayed and discussed for various emerging parameters of interest.

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

References

  1. Abbasbandy S.: Solitary wave solutions to the modified form of Camassa–Holm equation by means of the homotopy analysis method. Chaos. Solitons & Fractals 39, 428–435 (2009)

    Article  MATH  Google Scholar 

  2. Abbasbandy S.: Homotopy analysis method for the Kawahara equation. Nonlinear Anal. Real World Appl 11, 307–312 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Abbasbandy S., Shivanian E.: Prediction of multiplicity of solutions of nonlinear boundary value problems: novel application of homotopy analysis method. Commun. Nonlinear Sci. Numer. Simulat 15, 3830–3846 (2010)

    Article  MathSciNet  Google Scholar 

  4. Abbas Z., Hayat T., Sajid M., Asghar S.: Unsteady flow of a second grade fluid film over an unsteady stretching sheet. Math. Comput. Model 48, 518–526 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fetecau C., Fetecau C., Khan M., Vieru D.: Decay of a potential vortex in a generalized Oldroyd-B fluid. Appl. Math. Comput 205, 497–506 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fetecau C., Mahmood A., Fetecau C., Vieru D.: Some exact solutions for the helical flow of a generalized Oldroyd-B fluid in a circular cylinder. Comput. Math. Appl 56, 3096–3108 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fetecau C., Hayat T., Fetecau C., Ali N.: Unsteady flow of a second grade fluid between two side walls perpendicular to a plate. Nonlinear Anal.: Real World Appl 9(1236–1252), 9, 1236–1252 (2008)

    Google Scholar 

  8. Fetecau C., Nazar M., Fetecau C.: Unsteady flow of an Oldroyd-B fluid generated by a constantly accelerating plate between two side walls perpendicular to the plate. Int. J. Non-Linear Mech 44, 1039–1047 (2009)

    Article  MATH  Google Scholar 

  9. Gorder R.A.V., Vajravelu K.: Hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet. Mech. Res. Commun 37, 113–118 (2010)

    Article  Google Scholar 

  10. Hayat, T.; Awais, M.: Simultaneous effects of heat and mass transfer on time-dependent flow over a stretching surface. Int. J. Numer. Methods Fluids. doi:10.1002/fld.2414

  11. Hayat, T.; Awais, M.: Three-dimensional flow of upper-convected Maxwell (UCM) fluid. Int. J. Numer. Methods Fluids. doi:10.1002/fld.2289

  12. Hayat T., Nadeem S., Asghar S.: Hydromagnetic couette flow of an Oldroyd-B fluid in a rotating system. Int. J. Eng. Sci 42, 65–78 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hayat T., Abbas Z., Sajid M.: MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface. Chaos. Solitons & Fractals 39, 840–848 (2009)

    Article  MATH  Google Scholar 

  14. Hayat T., Nawaz M., Sajid M., Asghar S.: The effect of thermal radiation on the flow of a second grade fluid. Comput. Math. Appl 58, 369–379 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Hayat T., Iram S., Javed T., Asghar S.: Shrinking flow of second grade fluid in a rotating frame: an analytic solution. Commun. Nonlinear Sci. Numer. Simul 15, 2932–2941 (2010)

    Article  Google Scholar 

  16. Hayat T., Qasim M.: Influence of thermal radiation and Joule heating on MHD flow of a Maxwell fluid in the presence of thermophoresis. Int. J. Heat Mass Transf 53, 4780–4788 (2010)

    Article  MATH  Google Scholar 

  17. Hayat T., Awais M., Sajid M.: Similar solutions of stretching flow with mass transfer. Int. J. Numer. Methods Fluids 64, 908–921 (2010)

    MathSciNet  MATH  Google Scholar 

  18. Hayat T., Sajjad R., Asghar S.: Series solution for MHD channel flow of a Jeffery fluid. Commun. Nonlinear Sci. Numer. Simulat 15, 2400–2406 (2010)

    Article  MathSciNet  Google Scholar 

  19. Hayat T., Iram S., Javed T., Asghar S.: Flow by a porous shrinking surface in a rotating frame. Z. Naturforsch 65a, 45–52 (2010)

    Google Scholar 

  20. Hayat, T.; Mustafa, M.; Sajid, M.: On mass transfer in three-dimensional flow of a viscoelastic fluid. Numer. Methods Partial Differ. Equ. doi:10.1002/num.20561

  21. Hayat, T.; Hina, S.; Ali, N.: Effect of wall properties on the magnetohydrodynamic peristaltic flow of a Maxwell fluid with heat transfer and porous medium. Numer. Methods Partial Differ. Equ. doi:10.1002/num.20477

  22. Jamil M., Fetecau C., Imran M.: Unsteady helical flows of Oldroyd-B fluids. Commun. Nonlinear Sci. Numer. Simulat 16, 1378–1386 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Khan M., Ali S.H., Qi H.: Some accelerated flows for a generalized Oldroyd-B fluid. Nonlinear Anal. Real World Appl 10, 980–991 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Kumari M., Nath G.: Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field. Int. J. Non-Linear Mech 44, 1048–1055 (2009)

    Article  MATH  Google Scholar 

  25. Labropulu F., Li D., Pop I.: Non-orthogonal stagnation-point flow towards a stretching surface in a non-Newtonian fluid with heat transfer. Int. J. Thermal Sci 49, 1042–1050 (2010)

    Article  Google Scholar 

  26. Liao S.J.: A general approach to get series solution of non-similarity boundary layer flows. Commun. Nonlinear Sci. Numer. Simulat 14, 2144–2159 (2009)

    Article  Google Scholar 

  27. Liao, S.J.: Notes on the homotopy analysis method: some definitions and theorems. Commun. Nonlinear Sci. Numer. Simulat. 14, 983–997 (2009)

    Google Scholar 

  28. Liu, Y.; Zheng, L.; Zhang, X.: Unsteady MHD Couette flow of a generalized Oldroyd-B fluid with fractional derivative. Comput. Math. Appl. (2010, in Press)

  29. Nazar, M.; Sultan, Q.; Athar, M.; Kamran, M.: Unsteady longitudinal flow of a generalized Oldroyd-B fluid in cylindrical domains. Commun. Nonlinear Sci. Numer. Simulat. (2010, in Press)

  30. Niu J., Fu C., Tan W.C.: Stability of thermal convection of an Oldroyd-B fluid in a porous medium with Newtonian heating. Phys. Lett. A 374, 4607–4613 (2010)

    Article  Google Scholar 

  31. Pahlavan A.A., Aliakbar V., Farahani F.V., Sadeghy K.: MHD flows of UCM fluids above porous stretching sheets using two-auxiliary-parameter homotopy analysis method. Commun. Nonlinear Sci. Numer. Simulat 14, 473–488 (2009)

    Article  Google Scholar 

  32. Prasad K.V., Vajravelu K.: Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet. Int. J. Heat Mass Transf 52, 4956–4965 (2009)

    Article  MATH  Google Scholar 

  33. Qi H., Jin H.: Unsteady helical flows of a generalized Oldroyd-B fluid with fractional derivative. Nonlinear Anal. Real World Appl 10, 2700–2708 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  34. Renardy M.: On the high Weissenberg number limit of the upper convected Maxwell fluid. J. Non-Newtonian Fluid Mech 165, 70–74 (2010)

    Article  Google Scholar 

  35. Sajid M., Abbas Z., Javed T., Ali N.: Boundary layer flow of an Oldroyd-B fluid in the region of a stagnation point over a stretching sheet. Can. J. Phys 88(9), 635–640 (2010)

    Article  Google Scholar 

  36. Shah H.A.M.: Some accelerated flows of generalized Oldroyd-B fluid between two side walls perpendicular to the plate. Nonlinear Anal. Real World Appl 10, 2146–2150 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  37. Tan W.C., Masuoka T.: Stokes first problem for a second grade fluid in a porous half space with heated boundary. Int. J. Non-Linear Mech 40, 515–522 (2005)

    Article  MATH  Google Scholar 

  38. Tan W.C., Xu M.Y.: Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model. Acta Mech. Sin 18, 342–349 (2002)

    Article  MathSciNet  Google Scholar 

  39. Tong D., Zhang X., Zhang X.: Unsteady helical flows of a generalized Oldroyd-B fluid. J. Non-Newtonian Fluid Mech 156, 75–83 (2009)

    Article  Google Scholar 

  40. Zhang M.K., Shen X.R., Ma J.F., Zhang B.Z.: Flow of Oldroyd-B fluid in rotating curved square ducts. J. Hydrodynamics B 19, 36–41 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan

    T. Hayat

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia

    T. Hayat & Ahmed Alsaedi

Authors
  1. T. Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmed Alsaedi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Hayat.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hayat, T., Alsaedi, A. On Thermal Radiation and Joule Heating Effects in MHD Flow of an Oldroyd-B Fluid with Thermophoresis. Arab J Sci Eng 36, 1113–1124 (2011). https://doi.org/10.1007/s13369-011-0066-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-011-0066-4

Keywords

Mathematics Subject Classification (2000)

Search

Navigation