Unsteady Oscillatory Stagnation Point Flow of a Jeffrey Fluid
Publication: Journal of Aerospace Engineering
Volume 27, Issue 3
Abstract
In the present paper, the unsteady oscillatory stagnation point flow of a Jeffrey fluid is discussed. The oscillatory stagnation point flows have been discussed in a fixed frame of reference and a moving frame of reference. The convergence of the obtained analytical solutions has been discussed by plotting . Lastly, the physical significance of various parameters is discussed through graphs.
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Acknowledgments
S. Nadeem thanks Quaid-i-Azam University for providing a University Research Fund.
References
Abbas, Z., Wang, Y., Hayat, T., and Oberlack, M. (2008). “Hydromagnetic flow in a viscoelastic fluid due to the oscillatory stretching surface.” Int. J. Non Linear Mech., 43(8), 783–793.
Abbasbandy, S., and Hayat, T. (2009). “Solution of the MHD Falkner-Skan flow by homotopy analysis method.” Commun. Nonlinear Sci. Numer. Simul., 14(9–10), 3591–3598.
Asghar, S., Hanif, K., Nadeem, S., and Hayat, T. (2004). “Magnetohydrodynamic rotating flow of a second grade fluid with a given volume flow rate variation.” Meccanica, 39(5), 483–488.
Ayub, M., Zaman, H., Sajid, M., and Hayat, T. (2008). “Analytical solution of stagnation-point flow of a viscoelastic fluid towards a stretching surface.” Comm. Nonlinear Sci. Numer. Simul., 13(9),1822–1835.
Bergström, L. B. (2003). “Transient growth of small disturbances in a Jeffrey fluid flowing through a pipe.” Fluid Dyn. Res., 32(1–2), 29–44.
Fetecau, C., Hayat, T., and Fetecau, C. (2008). “Starting solutions for oscillating motions of Oldroyd-B fluids in cylindrical domains.” J. Non-Newtonian Fluid Mech., 153(2–3), 191–201.
Hayat, T., Hutter, K., Nadeem, S., and Asghar, S. (2004a). “Unsteady hydromagnetic rotating flow of a conducting second grade fluid.” Z. Angew. Math. Phys. ZAMP, 55(4), 626–641.
Hayat, T., Javed, T., and Abbas, Z. (2009). “MHD flow of a micropolar fluid near a stagnation-point towards a non-linear stretching surface.” Nonlinear Anal. Real World Appl., 10(3), 1514–1526.
Hayat, T., Nadeem, S., Asghar, S., and Siddiqui, A. M. (2001). “MHD rotating flow of a third-grade fluid on an oscillating porous plate.” Acta Mech., 152(1–4), 177–190.
Hayat, T., Nadeem, S., Asghar, S., and Siddiqui, A. M. (2004b). “An oscillating hydromagnetic non-Newtonian flow in a rotating system.” Appl. Math. Lett., 17(5), 609–614.
Hayat, T., Nadeem, S., Pudasaini, S. P., and Asghar, S. (2003). “Fluctuating flow of a third order fluid past an infinite plate with variable suction.” Arch. Mech., 55(3), 305–324.
Hayat, T., and Sajid, M. (2007). “Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid.” Int. J. Eng. Sci., 45(2–8), 393–401.
Hiemenz, K. (1911). “Die grenzschicht an einem in den gleichformingen flussigkeitsstrom eingetauchten geraden kreiszylinder.” Dinglers Polytech. J., 326, 321–410 (in German).
Homann, F., and Angew, Z. (1936). “Der einfluss grosser zahighkeit bei der stromung um den zylinder und um die kugel.” Zeitschrift für Angewandte Mathematik und Mechanik, 16, 153–164 (in German).
Ishak, A., Nazar, R., Arfin, N. M., and Pop, I. (2008). “Dual solutions in mixed convection flow near a stagnation point on a vertical porous plate.” Int. J. Therm. Sci., 47(4), 417–422.
Kawaguti, M., and Hamano, K. (1976). “Two-dimensional model of pulsatile flow through constricted artery.” Proc., 10th Int. Congress on Angiology, 26, Tokyo, 4–10.
Khan, M., Naheed, E., Fetecau, C., and Hayat, T. (2008). “Exact solutions of starting flows for second grade fluid in a porous medium” Int. J. Non Linear Mech., 43(9), 868–879.
Labropulu, F., and Chinichian, M. (2004). “Unsteady oscillatory stagnation-point flow of a viscoelastic fluid.” Int. J. Eng. Sci., 42(7), 625–633.
Labropulu, F., Xu, X., and Chinichian, M. (2003). “Unsteady stagnation-point flow of a non-Newtonian second grade fluid.” Int. J. Math. Math. Sci., 2003(60), 3797–3807.
Liao, S. (2009). “Notes on the homotopy analysis method: Some definitions and theorems.” Comm. Nonlinear Sci. Numer. Simul., 14(4), 983–997.
Liao, S. J. (2003). Beyond perturbation: Introduction to homotopy analysis method, Chapman & Hall/CRC, Boca Raton, FL.
Lighthill, M. J. (1954). “The response of laminar skin friction and heat transfer to fluctuations in the stream velocity.” Proc. R. Soc. London, Ser. A, 224(1156), 1–23.
Lok, Y. Y., Amin, N., and Pop, I. (2006). “Unsteady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface.” Int. J. Therm. Sci., 45(12), 1149–1157.
Lok, Y. Y., Amin, N., and Pop, I. (2007). “Mixed convection flow near a non-orthogonal stagnation point towards a stretching vertical plate.” Int. J. Heat Mass Transfer, 50(23–24), 4855–4863.
Mahapatra, T. R., and Gupta, A. S. (2001). “Magnetohydrodynamics stagnation point flow towards a stretching sheet.” Acta Mech., 152(1–4), 191–196.
Matunobu, Y. (1977a). “Structure of pulsatile Hiemenz flow and temporal variation of wall shear stress near the stagnation point. I.” J. Phys. Soc. Jpn., 42(6), 2041–2048.
Matunobu, Y. (1977b). “Structure of pulsatile Hiemenz flow and temporal variation of wall shear stress near the stagnation point. II.” J. Phys. Soc. Jpn., 43(1), 326–329.
Nadeem, S. (2007). “General periodic flows of fractional Oldroyd-B fluid for an edge.” Phys. Lett. A, 368(3–4), 181–187.
Nadeem, S., Abbasbandy, S., and Hussain, M. (2009). “Series solutions of boundary layer flow of a micropolar fluid near the stagnation point towards a shrinking sheet.” Zeitschrift für Naturforschung A, 64a, 575–582.
Nadeem, S., and Ali, M. (2009). “Analytical solutions for pipe flow of a fourth grade fluid with Reynold and Vogel’s models of viscosities.” Comm. Nonlinear Sci. Numer. Simul., 14(5), 2073–2090.
Nadeem, S., Asghar, S., Hayat, T., and Hussain, M. (2008). “The Rayleigh Stokes problem for rectangular pipe in Maxwell and second grade fluids.” Meccanica, 43(5), 495–504.
Nadeem, S., Hussain, A., and Khan, M. (2010). “HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet.” Comm. Nonlinear Sci. Numer. Simul., 15(3), 475–481.
Nazar, R., Amin, N., Filip, D., and Pop, I. (2004). “Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet.” Int. J. Eng. Sci., 42(11–12), 1241–1253.
Takemitsu, N., and Matunobu, Y. (1979). “Unsteady stagnation-point flow impinging obliquely on an oscillating flat plate.” J. Phys. Soc. Jpn., 47(4), 1347–1353.
Vieru, D., Fetecau, C., and Fetecau, C. (2008). “Flow of a generalized Oldroyd-B fluid due to a constantly accelerated plate.” Appl. Math. Comput., 201(1–2), 834–842.
Wang, C. Y. (2008a). “Off-centered stagnation flow towards a rotating disc.” Int. J. Eng. Sci., 46(4), 391–396.
Wang, C. Y. (2008b). “Stagnation flow towards a shrinking sheet.” Int. J. Non Linear Mech., 43(5), 377–382.
Information & Authors
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Published In
Journal of Aerospace Engineering
Volume 27 • Issue 3 • May 2014
Pages: 636 - 643
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 18, 2010
Accepted: Jan 10, 2012
Published online: Apr 15, 2014
Published in print: May 1, 2014
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