Startseite Naturwissenschaften Nonorthogonal Stagnation-point Flow of a Second-grade Fluid Past a Lubricated Surface
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Nonorthogonal Stagnation-point Flow of a Second-grade Fluid Past a Lubricated Surface

  • Khalid Mahmood EMAIL logo , Muhammad Sajid und Nasir Ali
Veröffentlicht/Copyright: 28. Januar 2016

Abstract

The stagnation-point flow of a second-grade fluid past a power law lubricated surface is considered in this paper. It is assumed that the fluid impinges on the wall obliquely. A suitable choice of similarity transformations reduces the governing partial differential equations into ordinary differential equations. The thin lubrication layer suggests that the interface conditions between the fluid and the lubricant can be imposed on the boundary. An implicit finite difference scheme known as the Keller-Box method is employed to obtain the numerical solutions. The effects of slip parameter and Weissenberg number on the fluid velocity and streamlines is discussed in the graphs. The limiting cases of partial-slip and no-slip can be deduced from the present solutions.


Corresponding author: Khalid Mahmood, Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan, Tel.: +92 51 9019756, E-mail:

References

[1] K. Hiemenz, Dinglers Polytech. J. 326, 321 (1911).Suche in Google Scholar

[2] J. T. Stuart, J. Aerospace Sci. 26, 124 (1959).10.2514/8.7963Suche in Google Scholar

[3] K. J. Tamada, J. Phys. Soc. Jpn. 46, 310 (1979).10.1143/JPSJ.46.310Suche in Google Scholar

[4] J. M. Dorrepaal, J. Fluid Mech. 163, 141 (1986).10.1017/S0022112086002240Suche in Google Scholar

[5] C. Y. Wang, Z. Angew. Math. Phys. 54, 184 (2003).10.1007/PL00012632Suche in Google Scholar

[6] P. Drazin and N. Riley, in: London Mathematical Society Lecture Note Series, Vol. 334, Cambridge University Press, Cambridge, (2006).Suche in Google Scholar

[7] R. M. Tooke and M. G. Blyth, Phys. Fluids 20, 033101 (2008).10.1063/1.2876070Suche in Google Scholar

[8] A. Borrelli, G. Giantesio, and M. C. Patria, ZAMP 63, 271 (2012).10.1007/s00033-011-0174-8Suche in Google Scholar

[9] Y. Y. Lok, J. H. Merkin, and I. Pop, Meccanica, 50, 2949 (2015).10.1007/s11012-015-0188-ySuche in Google Scholar

[10] M. G. Blyth and C. Pozrikidis, Acta Mech. 180, 203 (2005).10.1007/s00707-005-0240-4Suche in Google Scholar

[11] H. I. Andersson and M. Rousselet, Int. J. Heat Fluid Flow 27, 329 (2006).10.1016/j.ijheatfluidflow.2005.09.002Suche in Google Scholar

[12] B. Santra, B. S. Dandapat, and H. I. Andersson, Acta Mech. 194, 1 (2007).10.1007/s00707-007-0484-2Suche in Google Scholar

[13] M. Sajid, K. Mahmood, and Z. Abbas, Chin. Phys. Lett. 29, 024702 (2012).10.1088/0256-307X/29/2/024702Suche in Google Scholar

[14] K. R. Rajagopal, in: Navier-Stokes Equations and Related Nonlinear Problems (Ed. A. Sequeira), Plenum Press, New York 1995, p. 273.10.1007/978-1-4899-1415-6_22Suche in Google Scholar

[15] K. R. Rajagopal and A. S. Gupta, Meccanica 19, 158 (1984).10.1007/BF01560464Suche in Google Scholar

[16] K. R. Rajagopal and P. N. Kaloni, Some Remarks on Boundary Conditions for Flows of Fluids of the Differential Type, Control Mechanics and Its Applications, Hemisphere Press, New York 1989.Suche in Google Scholar

[17] B. W. Beard and K. Walters, Proc. Camb. Phil. Soc. 60, 667 (1964).10.1017/S0305004100038147Suche in Google Scholar

[18] V. K. Garg and K. R. Rajagopal, Mech. Res. Commun. 17, 415 (1990).10.1016/0093-6413(90)90059-LSuche in Google Scholar

[19] P. D. Ariel, Int. J. Eng. Sci. 40, 145 (2002).10.1016/S0020-7225(01)00031-3Suche in Google Scholar

[20] F. Labropulu, J. M. Dorrepaal, and O. P. Chandna, Mech. Res. Commun. 20, 143 (1993).10.1016/0093-6413(93)90021-FSuche in Google Scholar

[21] D. Li, F. Labropulu, and I. Pop, Int. J. Non-Linear Mech. 44, 1024 (2009).10.1016/j.ijnonlinmec.2009.07.007Suche in Google Scholar

[22] F. Labropulu, X. Xu, and M. Chinichian, Int. J. Math. Math. Sci. 60, 3797 (2003).10.1155/S0161171203212357Suche in Google Scholar

[23] F. Labropulu and D. Li, Int. J. Non-Linear Mech. 43, 941 (2008).10.1016/j.ijnonlinmec.2008.07.004Suche in Google Scholar

[24] T. R. Mahapatra, S. Dholey, and A. S. Gupta, Int. J. Non-Linear Mech. 42, 484 (2007).10.1016/j.ijnonlinmec.2007.01.008Suche in Google Scholar

[25] Y. Y. Lok, N. Amin, and I. Pop, Int. J. Non-Linear Mech. 41, 622 (2006).10.1016/j.ijnonlinmec.2006.03.002Suche in Google Scholar

[26] M. Sajid, T. Javed, Z. Abbas, and N. Ali, Int. J. Nonlinear Sci. Numer. Simul. 14, 285 (2013).10.1515/ijnsns-2012-0046Suche in Google Scholar

[27] M. Ahmed, M. Sajid, and I. Ahmad, Eur. Int. J. Sci. Technol., in press (2015).Suche in Google Scholar

[28] M. Ahmed, M. Sajid, I. Ahmad, M. Taj, and A. Abbasi, Adv. Mech. Eng. 7, 1 (2015).10.59400/mea.v1i1.258Suche in Google Scholar

[29] M. Ahmed, M. Sajid, T. Hayat, and I. Ahmad, AIP Adv. 5, 067138 (2015).10.1063/1.4922878Suche in Google Scholar

[30] H. B. Keller and T. Cebeci, AIAA J. 10, 1193 (1972).10.2514/3.50349Suche in Google Scholar

[31] V. Bradshaw, T. Cebeci, and I. H. Whitelaw, Engineering Calculation Methods for Turbulent Flows, Academic Press, London 1981.Suche in Google Scholar

[32] H. B. Keller, in: Numerical Solution of Partial Differential Equations (Ed. J. Bramble), Vol. II, Academic Press, New York 1970.Suche in Google Scholar

[33] K. Ahmad and R. Nazar, J. Qual. Meas. Anal. 6, 105 (2010).Suche in Google Scholar

[34] W. Ibrahim and B. Shanker, Comput. Fluids 70, 21 (2012).10.1016/j.compfluid.2012.08.019Suche in Google Scholar

[35] N. M. Sarif, M. Z. Salleh, and R. Nazar, Proc. Eng. 53, 542 (2013).10.1016/j.proeng.2013.02.070Suche in Google Scholar

Received: 2015-11-12
Accepted: 2015-12-20
Published Online: 2016-1-28
Published in Print: 2016-3-1

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