Some Aspects of Non-Orthogonal Stagnation-Point Flow towards a Stretching Surface

ABSTRACT

The problem of steady two-dimensional oblique stagnation-point flow of an incompressible viscous fluid towards a stretching surface is reexamined. Here the surface is stretched with a velocity proportional to the distance from a fixed point. Previous studies on this problem are reviewed and the errors in the boundary conditions at infinity are rectified. It is found that for a very small value of shear in the free stream, the flow has a boundary layer structure when , where and are the free stream stagnation-point velocity and the stretching velocity of the sheet, respectively, being the distance along the surface from the stagnation-point. On the other hand, the flow has an inverted boundary layer structure when . It is also observed that for given values of and free stream shear, the horizontal velocity at a point decreases with increase in the pressure gradient parameter.

The problem of steady two-dimensional oblique stagnation-point flow of an incompressible viscous fluid towards a stretching surface is reexamined. Here the surface is stretched with a velocity proportional to the distance from a fixed point. Previous studies on this problem are reviewed and the errors in the boundary conditions at infinity are rectified. It is found that for a very small value of shear in the free stream, the flow has a boundary layer structure when , where and are the free stream stagnation-point velocity and the stretching velocity of the sheet, respectively, being the distance along the surface from the stagnation-point. On the other hand, the flow has an inverted boundary layer structure when . It is also observed that for given values of and free stream shear, the horizontal velocity at a point decreases with increase in the pressure gradient parameter.

Cite this paper

nullM. Reza and A. Gupta, "Some Aspects of Non-Orthogonal Stagnation-Point Flow towards a Stretching Surface,"*Engineering*, Vol. 2 No. 9, 2010, pp. 705-709. doi: 10.4236/eng.2010.29091.

nullM. Reza and A. Gupta, "Some Aspects of Non-Orthogonal Stagnation-Point Flow towards a Stretching Surface,"

References

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[2] T. C. Chiam, “Stagnation-Point Flow towards a Stretching Plate,” Journal of Physical Society of Japan, Vol. 63, No. 6, pp. 2443-2444.

[3] T. R. Mahapatra and A. S. Gupta, “Heat Transfer in Stagnation-Point Flow towards a Stretching Sheet,” Heat and Mass Transfer, Vol. 38, No. 6, 2002, pp. 517-521.

[4] M. Reza and A. S. Gupta, “Steady Two-Dimensional Oblique Stagnation Point Flow towards a Stretching Surface,” Fluid Dynamics Research, Vol. 37, No. 5, 2005, pp. 334-340.

[5] Y. Y. Lok, N. Amin and I. Pop, “Non-Orthogonal Stagnation Point towards a Stretching Sheet,” International Journal of Non-Linear Mechanics, Vol. 41, No. 4, 2006, pp. 622-627.

[6] P. G. Drazin and N. Riley, “The Navier-Stokes Equations: A Classification of Flows and Exact Solutions,” Cambridge University Press, Cambridge, 2006.

[7] J. T. Stuart, “The Viscous Flow near a Stagnation Point when External Flow has Uniform Vorticity,” Journal of the Aero/Space Sciences, Vol. 26, 1959, pp. 124-125.

[8] K. Tamada, “Two-Dimensional Stagnation-Point Flow Impinging Obliquely on a Plane Wall,” Journal of Physical Society of Japan, Vol. 46, No. 1, 1979, pp. 310-311.

[9] J. M. Dorrepaal, “An Exact Solution of the Navier-Stokes Equation which Describes Non-Orthogonal Stagnation- Point Flow in Two Dimensions,” Journal of Fluid Mechanics, Vol. 163, 1986, pp. 141-147.

[10] D. Weidman and V. Putkaradzeb, “Axisymmetric Stagnation Flow Obliquely Impinging on a Circular Cylinder,” European Journal of Mechanics - B/Fluids, Vol. 22, No. 2, 2003, pp. 123-131.

[11] B. S. Tilley, P. D. Weidman, “Oblique Two-Fluid Stagnation-Point Flow,” European Journal of Mechanics - B/Fluids, Vol. 17, No. 2, 1998, pp. 205-217.

[12] T. R. Mahapatra, S. Dholey and A. S. Gupta, “Heat Transfer in Oblique Stagnation-Point Flow of an Incom-pressible Viscous Fluid towards a Stretching Surface,” Heat and Mass Transfer, Vol. 43, No. 8, 2007, pp. 767-773.

[13] T. R. Mahapatra, S. Dholey and A. S. Gupta, “Oblique Stagna-tion-Point flow of an Incompressible Visco-Elastic Fluid to-wards a Stretching Surface,” International Journal of Non-Linear Mechanics, Vol. 42, No. 3, 2007, pp. 484-499.

[14] C. A. J. Fletcher, “Computational Techniques for Fluid Dynamics,” Vol. 2, Springer-Verlag, Berlin, 1988.

[1] L. J. Crane, “Flow Past a Stretching Plate,” Zeitschrift für an-gewandte Mathematik und Physik, Vol. 21, 1970, pp. 645-657.

[2] T. C. Chiam, “Stagnation-Point Flow towards a Stretching Plate,” Journal of Physical Society of Japan, Vol. 63, No. 6, pp. 2443-2444.

[3] T. R. Mahapatra and A. S. Gupta, “Heat Transfer in Stagnation-Point Flow towards a Stretching Sheet,” Heat and Mass Transfer, Vol. 38, No. 6, 2002, pp. 517-521.

[4] M. Reza and A. S. Gupta, “Steady Two-Dimensional Oblique Stagnation Point Flow towards a Stretching Surface,” Fluid Dynamics Research, Vol. 37, No. 5, 2005, pp. 334-340.

[5] Y. Y. Lok, N. Amin and I. Pop, “Non-Orthogonal Stagnation Point towards a Stretching Sheet,” International Journal of Non-Linear Mechanics, Vol. 41, No. 4, 2006, pp. 622-627.

[6] P. G. Drazin and N. Riley, “The Navier-Stokes Equations: A Classification of Flows and Exact Solutions,” Cambridge University Press, Cambridge, 2006.

[7] J. T. Stuart, “The Viscous Flow near a Stagnation Point when External Flow has Uniform Vorticity,” Journal of the Aero/Space Sciences, Vol. 26, 1959, pp. 124-125.

[8] K. Tamada, “Two-Dimensional Stagnation-Point Flow Impinging Obliquely on a Plane Wall,” Journal of Physical Society of Japan, Vol. 46, No. 1, 1979, pp. 310-311.

[9] J. M. Dorrepaal, “An Exact Solution of the Navier-Stokes Equation which Describes Non-Orthogonal Stagnation- Point Flow in Two Dimensions,” Journal of Fluid Mechanics, Vol. 163, 1986, pp. 141-147.

[10] D. Weidman and V. Putkaradzeb, “Axisymmetric Stagnation Flow Obliquely Impinging on a Circular Cylinder,” European Journal of Mechanics - B/Fluids, Vol. 22, No. 2, 2003, pp. 123-131.

[11] B. S. Tilley, P. D. Weidman, “Oblique Two-Fluid Stagnation-Point Flow,” European Journal of Mechanics - B/Fluids, Vol. 17, No. 2, 1998, pp. 205-217.

[12] T. R. Mahapatra, S. Dholey and A. S. Gupta, “Heat Transfer in Oblique Stagnation-Point Flow of an Incom-pressible Viscous Fluid towards a Stretching Surface,” Heat and Mass Transfer, Vol. 43, No. 8, 2007, pp. 767-773.

[13] T. R. Mahapatra, S. Dholey and A. S. Gupta, “Oblique Stagna-tion-Point flow of an Incompressible Visco-Elastic Fluid to-wards a Stretching Surface,” International Journal of Non-Linear Mechanics, Vol. 42, No. 3, 2007, pp. 484-499.

[14] C. A. J. Fletcher, “Computational Techniques for Fluid Dynamics,” Vol. 2, Springer-Verlag, Berlin, 1988.