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Analytical solution of stagnation-point flow of a viscoelastic fluid towards a stretching surface. (English) Zbl 1221.76027
Summary: The problem of stagnation-point flow of a viscoelastic fluid towards a stretching surface [T.R. Mahapatra, A.S. Gupta, Int. J. Non-Linear Mech. 39, No. 5, 811–820 (2004; Zbl 1221.76035)] is solved analytically by using the homotopy analysis method (HAM). The results for velocity and temperature profiles are obtained. It is noted that the behavior of the HAM solution for velocity and temperature profiles is in good agreement with the numerical solution given in [loc. cit.].

MSC:
76A10 Viscoelastic fluids
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[1] Mahapatra, T.R.; Gupta, A.S., Stagnation-point flow of a viscoelastic fluid towards a stretching surface, Int J non-linear mech, 39, 811, (2004) · Zbl 1221.76035
[2] Liao SJ. The proposed homotopy analysis technique for the solution of nonlinear problem. Ph.D. Thesis. Shanghai Jiao Tong University, 1992.
[3] Liao, S.J., An explicit, totally analytic approximate solution for blasius’ viscous flow problems, Int J non-linear mech, 34, 759, (1999) · Zbl 1342.74180
[4] Liao, S.J., A simple way to enlarge the convergence region of perturbation approximations, Int J non-linear dyn, 19, 2, 93, (1999)
[5] Liao, S.J., A uniformly valid analytic solution of 2-D viscous flow past a semi-infinite flat plate, J fluid mech, 385, 101, (1999) · Zbl 0931.76017
[6] Liao, S.J.; Campo, A., Analytic solutions of the temperature distribution in Blasius viscous flow problems, J fluid mech, 453, 411, (2002) · Zbl 1007.76014
[7] Liao, S.J., An analytic approximation of the drag coefficient for the viscous flow past a sphere, Int J non-linear mech, 7, 1, (2002) · Zbl 1116.76335
[8] Liao, S.J., An explicit analytic solution to the Thomas-Fermi equation, Appl math comput, 144, 433, (2003)
[9] Liao, S.J., An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude, Int J non-linear mech, 38, 8, 1173, (2003) · Zbl 1348.74225
[10] Wang, C.; Zhu, J.M.; Liao, S.J.; Pop, I., On the explicit analytic solution of cheng – chang equation, Int J heat mass transfer, 46, 10, 1855, (2003) · Zbl 1029.76050
[11] Ayub, M.; Rashid, A.; Hayat, T., Exact solution of a third grade fluid past a porous plate using homotopy analysis method, Int J eng sci, 41, 18, 2091, (2003) · Zbl 1211.76076
[12] Hayat, T.; Khan, M.; Ayub, M., On the explicit analytic solution of an Oldroyd 6-constant fluid, Int J eng sci, 42, 123, (2004) · Zbl 1211.76009
[13] Hayat, T.; Khan, M.; Asghar, S., Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid, Acta mech, 168, 213, (2004) · Zbl 1063.76108
[14] Crane, L.J., Flow past a stretching plate, Zamp, 21, 645, (1970)
[15] Carragher, P.; Crane, L.J., Heat transfer on a continuous stretching sheet, Zamm, 62, 564, (1982)
[16] Dutta, B.K.; Roy, P.; Gupta, A.S., Temperature field in the flow over a stretching surface with uniform heat flux, Int comm heat mass transfer, 12, 89, (1985)
[17] Chiam, T.C., Stagnation-point flow towards a stretching plate, J phys soc jpn, 63, 2443, (1994)
[18] Mahapatra, T.R.; Gupta, A.S., Heat transfer in stagnation-point flow towards a stretching sheet, Heat mass transfer, 38, 517, (2002)
[19] Rajagopal, K.R.; Na, T.Y.; Gupta, A.S., Flow of a viscoelastic fluid over a stretching sheet, Rheol acta, 23, 213, (1984)
[20] Bhattacharya, S.; Pal, A.; Gupta, A.S., Heat transfer in the flow of a viscoelastic fluid over a stretching surface, Heat mass transfer, 34, 41, (1998)
[21] Vajravelu, K.; Roper, T., Flow and heat transfer in a second grade fluid over a stretching sheet, Int J non-linear mech, 34, 1031, (1999) · Zbl 1006.76005
[22] Nazar, R.; Amin, N.; Filip, D.; Pop, I., Unsteady boundary layer flow in the region of the stagnation-point on a stretching sheet, Int J eng sci, 42, 1241, (2004) · Zbl 1211.76042
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