Time-dependent stagnation-point flow over rotating disk impinging oncoming flow

doi:10.1007/s10483-013-1655-8

Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (1): 85-96.doi: https://doi.org/10.1007/s10483-013-1655-8

Time-dependent stagnation-point flow over rotating disk impinging oncoming flow

S. MUNAWAR^1,2, A. MEHMOOD³, A. ALI ¹

1. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan
2. Department of Mathematics, School of Science and Technology, University of Management and Technology, Lahore 54000, Pakistan;
3. Department of Mathematics, International Islamic University, Islamabad 44000, Pakistan

收稿日期:2012-01-05 修回日期:2012-08-06 出版日期:2013-01-03 发布日期:2013-01-03
通讯作者: S. MUNAWAR E-mail:sufian.munawar@hotmail.com

Time-dependent stagnation-point flow over rotating disk impinging oncoming flow

S. MUNAWAR^1,2, A. MEHMOOD³, A. ALI ¹

1. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan
2. Department of Mathematics, School of Science and Technology, University of Management and Technology, Lahore 54000, Pakistan;
3. Department of Mathematics, International Islamic University, Islamabad 44000, Pakistan

Received:2012-01-05 Revised:2012-08-06 Online:2013-01-03 Published:2013-01-03
Contact: S. MUNAWAR E-mail:sufian.munawar@hotmail.com

摘要/Abstract

摘要： The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. The three-dimensional axisymmetric boundary-layer flow is described by the Navier-Stokes equations. The governing equations are solved numerically, and two distinct similarity solution branches are obtained. Both solution branches exhibit different flow patterns. The upper branch solution exists for all values of the impinging parameter and the rotating parameter
. However, the lower branch solution breaks down at some moderate values of . The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of . The results of the velocity profile, the skin friction, and the stream lines are demonstrated through graphs and tables for both solution branches. The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.

Abstract: The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. The three-dimensional axisymmetric boundary-layer flow is described by the Navier-Stokes equations. The governing equations are solved numerically, and two distinct similarity solution branches are obtained. Both solution branches exhibit different flow patterns. The upper branch solution exists for all values of the impinging parameter and the rotating parameter
. However, the lower branch solution breaks down at some moderate values of . The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of . The results of the velocity profile, the skin friction, and the stream lines are demonstrated through graphs and tables for both solution branches. The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.

S. MUNAWAR A. MEHMOOD A. ALI . Time-dependent stagnation-point flow over rotating disk impinging oncoming flow[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(1): 85-96.

S. MUNAWAR; A. MEHMOOD; A. ALI . Time-dependent stagnation-point flow over rotating disk impinging oncoming flow[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(1): 85-96.

参考文献

[1] Von Karman, T. ¨Uberlaminare und turbulente Reibung. Journal of Applied Mathematics and Mechanics, 1, 233–252 (1921)

[2] Cochran, W. G. The flow due to a rotating disc. Proceedings of Cambridge Philosophical Society, 30, 365–375 (1934)
[3] Stuart, J. T. On the effects of uniform suction on the steady flow due to a rotating disk. The Quarterly Journal of Mechanics and Applied Mathematics, 7, 446–457 (1954)

[4] Sparrow, E. M. and Gregg, J. L. Mass transfer, flow, and heat transfer about a rotating disk. ASME Journal of Heat Transfer, 82, 294–302 (1960)

[5] Kuiken, H. K. The effect of normal blowing on the flow near a rotating disk of infinite extent.Journal of Fluid Mechanics, 47, 789–798 (1971)

[6] Ackroyd, J. A. D. On the steady flow produced by a rotating disc with either surface suction or injection. Journal of Engineering Mathematics, 12(3), 207–220 (1978)

[7] Kakutani, T. Hydromagnetic flow due to a rotating disk. Journal of Physics Society of Japan, 17, 1496–1506 (1962)

[8] Sparrow, E. M. and Chess, R. D. Magnetohydrodynamic flow and heat transfer about a rotating disk. ASME Journal of Applied Mechanics, 29, 181–187 (1962)

[9] Thacker, W. I., Kumar, S. K., and Watson, L. T. Magnetohydrodynamic flow and heat transfer about a rotating disk with suction and injection at the disk surface. Computers & Fluids, 16, 183–193 (1988)

[10] Pande, G. S. On the effects of uniform high suction on the steady hydromagnetic flow due to a rotating disk. Applied Scientific Research, 11, 205–212 (1971)

[11] Watson, L. T. and Wang, C. Y. Deceleration of a rotating disk in a viscous fluid. Physics of Fluids, 22, 2267–2269 (1979)

[12] Kumar, S. K., Thacker, W. I., and Watson, L. T. Magnetohydrodynamic flow past a porous rotating disk in a circular magnetic field. International Journal for Numerical Methods in Fluids, 8, 659–669 (1988)

[13] Watanabe, T. and Oyama, T. Magnetohydrodynamic boundary layer flow over a rotating disk. Zeitschrift f¨ur Angewandte Mathematik und Mechanik, 71(12), 522–524 (1991)

[14] Munawar, S., Mehmood, A., and Ali, A. Three-dimensional squeezing flow in a rotating channel of lower stretching porous wall. Computers & Mathematics with Applications, 64, 1575–1586 (2012)

[15] Frusteri, F. and Osalusi, E. On MHD and slip flow over a rotating porous disk with variable properties. International Communication in Heat and Mass Transfer, 34, 492–501 (2007)

[16] Miklavcic, M. and Wang, C. Y. The flow due to a rotating disk. Journal of Applied Mathematics and Physics, 54, 1–12 (2004)

[17] Hannah, D. M. Forced Flow Against a Rotating Disc, British Aeronautical Research Council Reports and Memoranda, No. 2772, University of Michigan (1947)

[18] Tifford, A. N. and Chu, S. T. On the flow around a rotating disc in a uniform stream. Journal of the Aeronautical Science, 19, 284–285 (1952)

[19] Wang, C. Y. Off-centered stagnation flow towards a rotating disc. International Journal of Engineering Science, 46, 391–396 (2008)

[20] Nourbakhsh, S. H., Zanoosi, A. A. P., and Shateri, A. R. Analytical solution for off-centered stagnation flow towards a rotating disc problem by homotopy analysis method with two auxiliary parameters. Communication in Nonlinear Science and Numerical Simulation, 16, 2772–2787
(2011)

[21] Mehmood, A. and Ali, A. An explicit analytic solution of steady three-dimensional stagnation point flow of second grade fluid toward a heated plate. ASME Journal of Applied Mechanics, 75, 061003 (2008)

[22] Yang, K. T. Unsteady laminar boundary layers in an incompressible stagnation flow. ASME Journal of Applied Mechanics, 25, 421–427 (1958)

[23] Williams, J. C. Non-steady stagnation-point flow. AIAA Journal, 6(12), 2417–2419 (1968)

[24] Cheng, E. H. W., Ozisik, M. N., and Williams, J. C. Non-steady three-dimensional stagnation point flow. ASME Journal of Applied Mechanics, 38(1), 282–287 (1971)

[25] Kumari, M. and Nath, G. Unsteady MHD film flow over a rotating infinite disk. International Journal of Engineering Science, 42, 1099–1117 (2004)

[26] Munawar, S., Mehmood, A., and Ali, A. Effects of slip on flow between two stretchable disks using optimal homotopy analysis method. Canadian Journal of Applied Sciences, 1(2), 50–(2011)
[27] Nazar, R., Amin, N., Filip, D., and Pop, I. Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet. International Journal of Engineering Science, 42, 1241–1253 (2004)

[28] Fang, T. and Lee, C. F. Three-dimensional wall-bounded laminar boundary layer with span-wise cross free stream and moving boundary. Acta Mechanica, 204, 235–248 (2009)

[29] Fang, T. Flow over a stretchable disk. Physics of Fluids, 19, 128105 (2007)

[30] Cheng, J. and Dai, S. Q. A uniformly valid series solution to the unsteady stagnation-point flow towards an impulsively stretching surface. Science in China Series G: Physics, Mechanics & Astronomy, 53(3), 521–526 (2010)

[31] Zhong, Y. and Fang, T. Unsteady stagnation-point flow over a plate moving along the direction of flow impingement. International Journal of Heat and Mass Transfer, 54, 3103–3108 (2011)

Time-dependent stagnation-point flow over rotating disk impinging oncoming flow

Time-dependent stagnation-point flow over rotating disk impinging oncoming flow

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