Abstract
A problem of unsteady flow of a second grade fluid over flat plates with the impulsive and oscillating motion, starting from rest, and with the wall transpiration is considered. The exact solutions are derived by the Laplace transform, the perturbation techniques, and an extension of the variable separation technique together with similarity arguments. These solutions are written as the sum between the permanent solutions and the transient solutions. The variations of fluid behaviors with various physical parameters are shown graphically and analyzed. The results are validated by comparing the limiting cases of the present paper with the results of the related published articles.
Similar content being viewed by others
References
Stokes, G. G. On the effect of the internal friction of fluids on the motion of pendulums. Transaction of the Cambridge Philosophical Society, 9, 8–106 (1851)
Panton, R. The transient for Stokes’ oscillating plate: a solution in terms of tabulated functions. J. Fluid Mech., 31, 819–825 (1968)
Erdoğan, M. E. A note on an unsteady flow of a viscous fluid due to an oscillating plane wall. Int. J. Non-Linear Mech., 35, 1–6 (2000)
Fetecau, C., Vieru, D., and Fetecau, C. A note on the second problem of Stokes for Newtonian fluids. Int. J. Non-Linear Mech., 43, 451–457 (2008)
Cruz, D. O. D. A. and Lins, E. F. The unsteady flow generated by an oscillating wall with transpiration. Int. J. Non-Linear Mech., 45, 453–457 (2010)
Rajagopal, K. R. A note on unsteady unidirectional flows of a non-Newtonian fluid. Int. J. Non-Linear Mech., 17, 369–373 (1982)
Asghar, S., Nadeem, S., Hanif, K., and Hayat, T. Analytical solution of Stokes second problem for second grade fluid. Math. Problems Eng., 1–8 (2006) DOI 10.1155/MPE/2006/72468
Nazar, M., Fetecau, C., Vieru, D., and Fetecau, C. New exact solutions corresponding to the second problem of Stokes for second grade fluids. Non-Linear Anal. Real World Appl., 11, 584–591 (2010)
Ali, F., Norzieha, M., Sharidan, S., Khan, I., and Hayat, T. New exact solutions of Stokes’ second problem for an MHD second grade fluid in a porous space. Int. J. Non-Linear Mech., 47, 521–525 (2012)
Yao, Y. and Liu, Y. Some unsteady flows of a second grade fluid over a plane wall. Nonlinear Analysis: Real World Appl., 11, 4442–4450 (2010)
Barbeau, E. J. Polynomials, Springer-Verlag, New York (1989)
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the Research Management Centre of Universiti Teknologi Malaysia (Nos. 04H27 and 4F255)
Rights and permissions
About this article
Cite this article
Abdulhameed, M., Khan, I., Vieru, D. et al. Exact solutions for unsteady flow of second grade fluid generated by oscillating wall with transpiration. Appl. Math. Mech.-Engl. Ed. 35, 821–830 (2014). https://doi.org/10.1007/s10483-014-1837-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-014-1837-9