Skip to main content
Log in

MHD flow and heat transfer from continuous surface in uniform free stream of non-Newtonian fluid

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

An analysis is carried out to study the steady flow and heat transfer characteristics from a continuous flat surface moving in a parallel free stream of an electrically conducting non-Newtonian viscoelastic fluid. The flow is subjected to a transverse uniform magnetic field. The constitutive equation of the fluid is modeled by that for a second grade fluid. Numerical results are obtained for the distribution of velocity and temperature profiles. The effects of various physical parameters like viscoelastic parameter, magnetic parameter and Prandtl number on various momentum and heat transfer characteristics are discussed in detail and shown graphically.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Papanastasiou T C, Georgiou G C, Alexandrou A N. Viscous fluid flow[M]. Boca Raton: CRC Press, 2000.

    Google Scholar 

  2. Sakiadis B C. Boundary-layer behavior on continuous solid surfaces: I. Boundary layer equations for two dimensional and axisymmetric flow[J]. American Institute of Chemical Engineers Journal, 1961, 7:26–28.

    Google Scholar 

  3. Sakiadis B C. Boundary layer behavior on continuous solid surface: the boundary layer on a continuous flat surface[J]. American Institute of Chemical Engineers Journal, 1961, 7:221–224.

    Google Scholar 

  4. Crane L J. Flow past a stretching sheet[J]. Journal of Applied Mathematics and Physics, ZAMP, 1970, 21:645–647.

    Article  Google Scholar 

  5. Gupta P S, Gupta A S. Heat and mass transfer on a stretching sheet with suction or blowing[J]. Canadian Journal Chemical Engineering, 1977, 55:744–746.

    Google Scholar 

  6. Rivlin R S, Ericksen J L. Stress deformation relations for isotropic materials[J]. Journal of Rational Mechanics and Analysis, 1955, 4:323–425.

    MathSciNet  Google Scholar 

  7. Dunn J E, Fosdick R L. Thermodynamics, stability and boundedness of fluids of complexity 2 and fluids of second grade[J]. Archive for Rational Mechanics and Analysis, 1974, 56:191–252.

    Article  MATH  MathSciNet  Google Scholar 

  8. Dunn J E, Rajagopal K R. Fluids of differential type, critical review and thermodynamic analysis[J]. International Journal of Engineering Science, 1995, 33:689–729.

    Article  MATH  MathSciNet  Google Scholar 

  9. Fosdick R L, Rajagopal K R. Anomalous feature in the model of “second order fluids”[J]. Archive for Rational Mechanics and Analysis, 1979, 70:145–152.

    Article  MATH  MathSciNet  Google Scholar 

  10. Galdi G P, Padula M, Rajagopal K R. On the conditional stability of the rest state of a fluid of second grade in unbounded domains[J]. Archive for Rational Mechanics and Analysis, 1990, 109:173–182.

    Article  MATH  MathSciNet  Google Scholar 

  11. Fox V G, Ericksen L E, Fan L T. The laminar boundary layer on a moving continuous flat sheet immersed in a non-Newtonian fluid[J]. American Institute of Chemical Engineers Journal, 1969, 15:327–333.

    Google Scholar 

  12. Rajagopal K R, Na T Y, Gupta A S. Flow of a viscoelastic fluid over a stretching sheet[J]. Rheological Acta, 1984, 24:213–215.

    Article  Google Scholar 

  13. Troy W C, Overman E A, Ermentrout H G B, Keener J P. Uniqueness of flow of a second-order fluid past a stretching sheet[J]. Quarterly Journal of Applied Mathematics, 1987, 44:753–755.

    MATH  MathSciNet  Google Scholar 

  14. Sadeghy K, Sharifi M. Local similarity solution for the flow of a “second-grade” viscoelastic fluid above a moving plate[J]. International Journal Non-linear Mechanics, 2004, 39:1265–1273.

    Article  MATH  Google Scholar 

  15. Sadeghy K, Najafi A H, Saffaripour M. Sakiadis flow of an upper convected Maxwell fluid[J]. International Journal Non-linear Mechanics, 2005, 40:1220–1228.

    Article  MATH  Google Scholar 

  16. Hassanien I A. Flow and heat transfer from a continuous surface in a parallel free stream of viscoelastic second-order fluid[J]. Applied Scientific Research, 1992, 49:335–344.

    Article  MATH  Google Scholar 

  17. Hady F M, Gorla R S R. Heat transfer from a continuous surface in a parallel free stream of viscoelastic fluid[J]. Acta Mechanica, 1998, 128:201–208.

    Article  MATH  Google Scholar 

  18. Bhatnagar R K, Gupta G, Rajagopal K R. Flow of an Oldroyd-B fluid due to a stretching sheet in the presence of a free stream velocity[J]. International Journal Non-linear Mechanics, 1995, 30:391–405.

    Article  MATH  Google Scholar 

  19. Allan F M. Similarity solutions of a boundary layer problem over moving surfaces[J]. Applied Mathematics Letter, 1997, 10:81–85.

    Article  MATH  MathSciNet  Google Scholar 

  20. Kumari M, Nath G. MHD boundary-layer flow of a non-Newtonian fluid over a continuously moving surface with a parallel free stream[J]. Acta Mechanica, 2001, 146:139–150.

    Article  MATH  Google Scholar 

  21. Abo-Eldahab E M, Salem A M. MHD free-convection flow of a non-Newtonian power-law fluid at a stretching surface with a uniform free-stream[J]. Applied Mathematics and Computation, 2005, 169:806–818.

    Article  MATH  MathSciNet  Google Scholar 

  22. Rajeshwari G K, Rathna S L. Flow of a particular class of non-Newtonian visco-elastic fluid near a stagnation point[J]. Journal of Applied Mathematics and Physics, ZAMP, 1962, 13:43–57.

    Article  Google Scholar 

  23. Beard D W, Walters K. Elastico-viscous boundary layer flows. I. Two-dimensional flow near a stagnation point[J]. Proceedings Cambridge Philosophical Society, 1964, 60:667–674.

    Article  MATH  MathSciNet  Google Scholar 

  24. Mishra S P, Mohapatra U. Elasticoviscous flow between a rotating and a stationary disk with uniform suction at the stationary disk[J]. Journal of Applied Physics, 1977, 48:1515–1521.

    Article  Google Scholar 

  25. Shrestha G M. Laminar elastico-viscous flow through channels with porous walls with different permeability[J]. Applied Science Research, 1969, 20:289–305.

    Article  Google Scholar 

  26. Garg V K, Rajagopal K R. Stagnation point flow of a non-Newtonian fluid[J]. Mechanics Research Communication, 1990, 17:415–421.

    Article  MATH  MathSciNet  Google Scholar 

  27. Garg V K, Rajagopal K R. Flow of a non-Newtonian fluid past a wedge[J]. Acta Mechanica, 1991, 88:113–123.

    Article  MathSciNet  Google Scholar 

  28. Davies M H. A note a elastico-viscous boundary layer flows[J]. Journal of Applied Mathematics and Physics, ZAMP, 1960, 17:189–191.

    Article  Google Scholar 

  29. Chiang K T. Dealing with complicated starting value in shooting process with Broyden’s mehtod: examples of the onset of convection for the viscoelastic fluid[J]. International Communication in Heat and Mass Transfer, 2004, 31:815–826.

    Article  Google Scholar 

  30. Teipel I. Die Räumliche staupunktströmung für ein viscoelastisches fluid[J]. Rheological Acta, 1986 25:75–79.

    Article  MATH  Google Scholar 

  31. Ariel P D. A hybrid method for computing the flow of viscoelastic fluids[J]. International Journal for Numerical Methods in Fluids, 1992, 14:757–774.

    Article  MATH  Google Scholar 

  32. Labropulu F, Xu X, Chinichian M. Unsteady stagnation point flow of a non-Newtonian second grade fluid[J]. International Journal of Mathematics and Mathematical Sciences, 2003, 60:3797–3807.

    Article  MathSciNet  Google Scholar 

  33. Labropulu F, Husain I, Chinichian M. Stagnation point flow of the Walters’ B fluid with slip[J]. International Journal of Mathematics and Mathematical Sciences, 2004, 61:3249–3258.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bikash Sahoo.

Additional information

Communicated by ZHOU Zhe-wei

Project supported by the Ministry of Human Resources and Development of the Government of India

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sahoo, B., Sharma, H.G. MHD flow and heat transfer from continuous surface in uniform free stream of non-Newtonian fluid. Appl. Math. Mech.-Engl. Ed. 28, 1467–1477 (2007). https://doi.org/10.1007/s10483-007-1106-z

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-007-1106-z

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Navigation