Oblique Newtonian Fluid Flow with Heat Transfer Towards a Stretching Sheet

  • F. LabropuluEmail author
  • A. Ghaffar
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 307)


Oblique stagnation point flow and heat transfer towards a stretching sheet of a viscous fluid is investigated. The governing equations are transformed to a system of ordinary differential equations and then solved numerically for various values of the parameters. It is observed that the dual solution exists for velocity and temperature for certain values of velocity ratio parameter.


Oblique Stagnation point Heat transfer Stretching sheet 


  1. 1.
    Nazar R, Amin N, Pop I (2004) Unsteady boundary layer flow due to a stretching surface in a rotating fluid. Mech. Res. Communications 31: 121–128CrossRefzbMATHGoogle Scholar
  2. 2.
    Crane LJ (1970) Flow past a stretching plate. Z. Angew. Math. Phys. 21: 645–647CrossRefGoogle Scholar
  3. 3.
    Gupta PS, Gupta AS (1977) Heat and mass transfer on a stretching sheet with suction and blowing. Can. J. Chem. Eng. 55: 744–746CrossRefGoogle Scholar
  4. 4.
    Brady JF, Acrivos A (1981) Steady flow in a channel or tube with accelerating surfaces velocity. An exact solution to the Navier-Stokes equations with reverse flow. J. Fluid Mech. 112: 127–150CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Wang CY (1984) The three dimensional flow due to a stretching flat surface. Phys. Fluids 27: 1915–1917CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Wang CY (1988) Fluid flow due to a stretching cylinder. Phys. Fluids 31: 466–468CrossRefGoogle Scholar
  7. 7.
    Wang CY (1990) Liquid film on an unsteady stretching sheet. Quart. Appl. Math. 48: 601–610zbMATHMathSciNetGoogle Scholar
  8. 8.
    Usha R, Sridharan R (1995) The axisymmetrical motion of a liquid film on an unsteady stretching surface. J. Fluids Eng. 117: 81–85CrossRefGoogle Scholar
  9. 9.
    Mahapatra TR, Gupta AS (2002) Heat transfer in stagnation-point flow towards a stretching sheet. Heat Mass Transfer 38: 517–521CrossRefGoogle Scholar
  10. 10.
    Ishak A, Nazar R, Pop I (2006) Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet. Meccanica 41: 509–518CrossRefzbMATHGoogle Scholar
  11. 11.
    Layek GC, Mukhopadhyay S, Samad SA (2007) Heat and Mass Transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing. Int. Commun. Heat and Mass Transfer 34: 347–356CrossRefGoogle Scholar
  12. 12.
    Nadeem S, Hussain A, Khan M (2010) HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet. Commun. Nonlinear Sci. Numer. Simul. 15: 475–481CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Liao S (2005) A new branch of solutions of boundary-layer flows over an impermeable stretched surface. Int. J. Heat Mass Transfer 48: 2529–2539CrossRefzbMATHGoogle Scholar
  14. 14.
    Liao S (2007) A new branch of solutions of boundary-layer flows over a permeable stretching plate. Int. J. Non-Lin Mech 42: 819–830CrossRefzbMATHGoogle Scholar
  15. 15.
    Xu H, Liao SJ (2008) Dual solutions of boundary layer flow over an upstream moving plate. Comm. Nonlinear Sci. Numer. Simulation 13: 350–358zbMATHMathSciNetGoogle Scholar
  16. 16.
    Tan Y, You XC, Xu H, Liao SJ (2008) A new branch of the temperature distribution of boundary-layer flows over an impermeable stretching plate. Heat Mass Transfer 44: 501–504CrossRefGoogle Scholar
  17. 17.
    Lok YY, Amin N, Pop I (2006) Non-orthogonal stagnation-point flow towards a stretching sheet. Int. J. Non-Lin Mech 41: 622–627CrossRefGoogle Scholar
  18. 18.
    Stuart JT (1959) The viscous flow near a stagnation point when the external flow has uniform velocity. J. Aerospace Sci 26: 124–125CrossRefzbMATHGoogle Scholar
  19. 19.
    Tamada KJ (1979) Two-dimensional stagnation point flow impinging obliquely on a plane wall. J. Phys. Soc. Jpn. 46: 310–311CrossRefGoogle Scholar
  20. 20.
    Dorrepaal JM (1986) An exact solution of the Navier-Stokes equation which describes non-orthogonal stagnation-point flow in two dimension. J. Fluid Mech. 163: 141–147CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Dorrepaal JM (2000) Is two-dimensional oblique stagnation-point flow unique? Can. Appl. Math. Q 8: 61–66CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Labropulu F, Dorrepaal JM and Chandna OP (1996) Oblique flow impinging on a wall with suction or blowing. Acta Mech. 115: 15–25CrossRefzbMATHGoogle Scholar
  23. 23.
    Pozrikidis C (1997) Introduction to Theoretical and Computational Fluid Dynamics, Oxford University Press, OxfordzbMATHGoogle Scholar
  24. 24.
    Blyth MG, Pozrikidis C (2005) Stagnation-point flow against a liquid film on a plane wall, Acta Mech. 180: 203–219CrossRefzbMATHGoogle Scholar
  25. 25.
    Tooke RM, Blyth MG (2008) A note on oblique stagnation-point flow. Phys. Fluids 20: 033101-1-3CrossRefGoogle Scholar
  26. 26.
    Shampine LF (2003) Singular boundary value problems for ODEs. Appl. Math and Comp. 138: 99–112Google Scholar
  27. 27.
    Wang CY (2008) Stagnation flow towards a shrinking sheet. Int. J. Nonlinear Mech. 43: 377–382CrossRefGoogle Scholar
  28. 28.
    Li D, Labropulu F, Pop I (2009) Oblique Stagnation-point flow of a viscoe lastic fluid with heat transfer. Int. J. Non-Lin Mech 44: 1024–1030CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Luther College—MathematicsUniversity of ReginaReginaCanada

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