Skip to main content
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
1.R. B. Bird, C. F. Curtiss, R. C. Armstrong, and O. Hassager, “Dynamics of polymeric liquids,” Fluid Mechanics (Wiley, 1987), Vol. 1.
2.J. Harris, Rheology and Non-Newtonian Flow (Longman, London, 1977).
3.J. E. Dunn and K. R. Rajagopal, “Fluids of differential type: Critical review and thermodynamic analysis,” Int. J. Eng. Sci. 33, 689729 (1995).
4.K. R. Rajagopal, “A note on unsteady unidirectional flows of a non-Newtonian fluid,” Int. J. Non-Linear Mech. 17, 369373 (1982).
5.R. Bandelli and K. R. Rajagopal, “Start-up flows of second grade fluids in domains with one finite dimension,” Int. J. Non-Linear Mech. 30, 817839 (1995).
6.T. Hayat, Y. Wang, A. M. Siddiqui and K. Hutter, “Couette flow of a third-grade fluid with variable magnetic field,” Math. Mod. Meth. Appl. Sci. 12, 16911706 (2004).
7.T. Hayat and A. H. Kara, “Couette flow of a third-grade fluid with variable magnetic field,” Math. Comput. Mod. 43, 132137 (2006).
8.M. Sajid and T. Hayat, “Non-similar series solution for boundary layer flow of a third-order fluid over a stretching sheet,” Appl. Math. Comput. 189, 1576-1585 (2007).
9.K. Hiemenz, “Die Grenzschicht an einem in den gleich formigen ussig keitsstrom eingetacuhten geraden krebzylinder,” Dingl Polytech J. 32, 321-324 (1911).
10.F. Homann, “Der Einfluss grosser Zähigkeit bei der Strömung um den Zylinder und um die Kugel,” Z. Angew. Math. Mech. (ZAMM) 16, 153164 (1936).
11.T. R. Mahapatra and A.S. Gupta, “Heat transfer in stagnation-point flow towards a stretching surface,” Heat Mass Transf. 38, 517-521 (2002).
12.T. R. Mahapatra and A.S. Gupta, “Stagnation-point flow of a viscoelastic fluid towards a stretching surface,” Int. J. Non-Linear Mech. 39, 811-820 (2004).
13.R. Nazar, N. Amin, D. Filip, and I. Pop, “Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet,” Int. J. Eng. Sci. 42, 1241-1253 (2004).
14.R. Nazar, N. Amin, D. Filip, and I. Pop, “Stagnation point flow of a micropolar fluid towards a stretching sheet,” Int. J Non-Linear Mech. 39, 1227-1235 (2004).
15.T. Hayat, Z. Abbas, and M. Sajid, “MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface,” Chaos, Solitons & Fractals 39, 840-848 (2009).
16.M. Sajid, Z. Abbas, T. Javed, and N. Ali, “Boundary layer flow of an Oldroyd-B fluid in the region of stagnation point over a stretching sheet,” Can. J. Phys. 88, 635-640 (2010).
17.G. K. Ramesh, B. J. Gireesha, and C. S. Bagewadi, “MHD flow of a dusty fluid near the stagnation point over a permeable stretching sheet with non-uniform source/sink,” Int. J. Heat Mass Transfer 55(17-18), 4900-4907 (2012).
18.W. Ibrahim, B. Shanker, and M. M. Nandeppanavar, “MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet,” Int. J. Heat Mass Transfer 56(1-2), 1-9 (2013).
19.M. Turkyilmazoglu and I. Pop, “Exact analytical solutions for the flow and heat transfer near the stagnation point on a stretching/shiriking sheet in a Jeffery fluid,” Int. J. Heat Mass Transfer 57(1), 82-88 (2013).
20.A. Malvandi, F. Hedayati, and D. D. Ganji, “Slip effects on unsteady stagnation point flow of a nanofluid over a stretching sheet,” Power Technology 253, 377-384 (2014).
21.A. Yeckel, L. Strong, and S. Middleman, “Viscous film flow in the stagnation region of the jetimpinging on planar surface,” AIChE J. 40, 16111617 (1994).
22.M. G. Blyth and C. Pozrikidis, “Stagnation-point flow against a liquid film on a plane wall,” Acta Mech. 180, 203219 (2005).
23.H. I. Andersson and M. Rousselet, “Slip flow over a lubricated rotating disk,” Int. J. Heat Fluid Flow 27, 329335 (2006).
24.B. Santra, B. S. Dandapat, and H. I. Andersson, “Axisymmetric stagnation point flow over a lubricated surface,” Acta Mech. 194, 1-7 (2007).
25.M. Sajid, K. Mahmood, and Z. Abbas, “Axisymmetric stagnation-point flow with a general slip boundary condition over a lubricated surface,” Chin. Phys. Lett. 29, 1-4 (2012).
26.M. Sajid, T. Javed, Z. Abbas, and N. Ali, “Stagnation point flow of a viscoelastic fluid over a lubricated surface,” Int. J. Non-Linear Sci. Numer. Simul. 14, 285-290 (2013).
27.M. Sajid, M. Ahmad, and I. Ahmad, “Axisymmetric stagnation point flow of a second grade fluid over a lubricated surface,” Eur. Int. J. Sci. Tech. in press.
28.M. Sajid, M. Ahmad, I. Ahmad, M. Taj, and A. Abbasi, “Axisymmetric stagnation point flow of a third grade fluid over a lubricated surface,” Adv. Mech. Engin. in press.
29.S. J. Liao, “The proposed homotopy analysis technique for the solution of non-linearproblems,” Ph.D Thesis, Shanghai Jiao Tong University 1992.
30.S. J. Liao, Beyond perturbation–Introduction to the homotopy analysis method (Chapman & Hall/CRC, Boca Raton, 2003).
31.S. J. Liao, Homotopy analysis method in nonlinear differential equations (Springer & Higher Education Press, Heidelberg, 2012).
32.M. Turkyilmazoglu, “Solution of the Thomas-Fermi equation with a convergent approach,” Commun. Nonlinear Sci. Numer. Simulat. 17, 4097-4103 (2012).
33.S. Abbasbandy, M. S. Hashemi, and I. Hashim, “On convergence of homotopy analysis method and its application to fractional integro-differential equations,” Quaestions Mathematicae 36, 93-105 (2013).
34.M. M. Rashidi, B. Rostani, N. Freidoonimehr, and S. Abbasbandy, “Free convective heat and mass transfer for MHD fluid flow over a permeable vertical stretching sheet in the presence of the radiation and buoyancy effects,” Ain shams Eng. J. 5, 901-912 (2014).
35.T. Hayat, S. Asad, M. Mustafa, and A. Alsaedi, “MHD stagnation point flow of Jeffery fluid over a convectively heated stretching sheet,” Comput. Fluids 108, 179-185 (2015).
36.T. Hayat, T. Muhammad, S. A. Shehzad, and A. Alsaedi, “Similarity solution to three dimensional boundary flow of second grade nanofluid past a stretching surface with thermal radiation and heat source/sink,” AIP Adv. 5, 017107 (2015).
37.T. Y. Na, Computational methods in engineering boundary value problems (Academic Press, New York, 1979).
38.M. Pakdemirli, “The boundary layer equations of third grade fluids,” Int. J. Non-Linear Mech. 27, 785-793 (1992).

Data & Media loading...


Article metrics loading...



This article addresses the two-dimensional boundary layer flow of third order fluid in the region of a stagnation point over a surface lubricated with a power law fluid. The lubricant is assumed to have a thin layer of variable thickness over the surface. The third order fluid experiences a partial slip due to this lubrication layer. Mathematical model of the flow problem is represented through a system of nonlinear partial differential equations with nonlinear boundary conditions. The non-similar numerical and analytic solutions of the transformed ordinary differential equation are obtained using hybrid homotopy analysis method based on the combination of homotopy analysis and shooting methods. It is observed that extra drag force is required in order to achieve no-slip regime from full slip and thus slip has suppressed the effects of free stream velocity. The results varying from no-slip to full slip case are discussed under the influence of pertinent parameters.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd