IJE TRANSACTIONS A: Basics Vol. 20, No. 1 (February 2007) 67-82   

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A. B. Rahimi* and V. Mossavinik

Department of Mechanical Engineering, Faculty of Engineering
Ferdowsi University of Mashhad, Mashhad, Iran, P. O. Box 91775-1111

*Corresponding Author

( Received: July 15, 2006 – Accepted in Revised Form: January 18, 2007 )

Abstract    Laminar stagnation flow, axi-symmetrically yet obliquely impinging on a rotating circular cylinder, as well as its heat transfer is formulated as an exact solution of the Navier-Stokes equations. Rotational velocity of the cylinder is time-dependent while the surface transpiration is uniform and steady. The impinging stream is composed of a rotational axial flow superposed onto irrotational radial stagnation flow normal to the cylinder with strength Γ. The relative importance of these two flows is measured by a parameter γ. The governing parameters are the stagnation-flow Reynolds number Re = Γa2/2υ and the dimensionless transpiration S = U0/Γa, where a is cylinder radius, ν is kinematic viscosity of the fluid and U0 is the transpiration rate. An exact solution is obtained by reducing the Navier-Stokes equations to a system of differential equations governed by Reynolds number and the dimensionless wall transpiration rate. Dimensionless shear stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. Heat transfer is independent of cylinder rotation and its coefficient increases with the increasing suction rate, Reynolds number and Prandtl number.


Keywords    Oblique Stagnation Flow, Axisymmetric, Time-Dependent Rotation, Time-Dependent Heat Transfer, Transpiration, Exact Solution



1. Wang, C., “Axisymmetric stagnation flow on a cylinder”, Quarterly of Applied Mathematics, Vol. 32, (1974), 207-213.

2. Stuart, J. T., “The viscous flow near a stagnation point when the external flow has uniform vorticity”, J. Aero/Space Sci., Vol. 26, (1959), 124-125.

3. Tamada, K., “Two-dimensional stagnation-point flow impinging obliquely on a plane wall”, J. Phys. Soc. Japan, Vol. 46, (1979), 310-311.

4. Dorrepaal, J. M., “An exact solution of the Navier -Stokes equation which describes non-orthogonal stagnation - point flow in two dimensions”, J. Fluid Mech., Vol. 163, (1986), 141-147.

5. Liu, T., “Nonorthogonal stagnation flow on the surface of a quiescent fluid-an exact solution of the Navier-Stokes equation”, Quart. Appl. Math., Vol. 50, (1992), 39-47.

6. Tilley, B. S. and Weidman, P. D., “Oblique two-fluid stagnation-point flow”, Eur. J. Mech. B/Fluids, Vol. 17, (1998), 205-217.

7. Gorla, R. S. R., “Transient response behavior of an axisymmetric stagnation flow on a circular cylinder due to a time dependent free stream velocity”, Lett. Appl. Eng. Sci., Vol. 16, (1978), 493-502.

8. Gorla, R. S. R., “Unsteady viscous flow in the vicinity of an axisymmetric stagnation-point on a cylinder”, Int. J. Engineering Science, Vol, 17, (1979), 87-93.

9. Gorla, R. S. R., “Heat transfer in an axisymmetric stagnation flow on a cylinder”, Applied Scientific Research J., Vol. 32, (November 1976), 541-553.

10. Cunning, G. M., Davis, A. M. J. and Weidman, P. D., “Radial stagnation flow on a rotating cylinder with uniform transpiration”, Journal of Engineering Mathematics, Vol. 33, (1998), 113-128.

11. Rahimi, A. B., “Heat transfer in an axisymmetric stagnation flow on a cylinder at high Prandtl numbers using perturbation techniques”, Int. J. of Engr. Science, Vol. 10, No. 3, (1999).

12. Saleh, R. and Rahimi, A. B., “Axisymmetric stagnation-point flow and heat transfer of a viscous fluid on a moving cylinder with time - dependent axial velocity and uniform transpiration”, Journal of Fluids Engineering, Vol. 126, (November 2004).

13. Peregrine, D. H., “The fascination of fluid mechanics, J. Fluid Mech., Vol. 106, (1981), 59-80.

14. Hiemenz, K., “Die Grenzchicht an einem in den gleichformingen flussigkeitsstrom eingetauchten geraden kreiszylinder”, Dinglers Polytech. J., Vol. 326, (1911), 321-410.

15. Weidman, P. D. and Putkaradze, V., “Axisymmetric stagnation flow obliquely impinging on a circular cylinder”, European J. of Mechanics B/Fluids, Vol. 22, (2003), 123-131.

16. Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T., “Numerical recipes, the art of scientific computing”, Cambridge University Press, Cambridge, (1997).


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