The development of two-dimensional or axisymmetric stagnation flow of an incompressible viscous fluid over a moving plate with partial slip has been investigated. The effects of partial slip on the flow and heat transfer characteristics are considered. The equations of conservation of mass, momentum, and energy, which govern the flow and heat transfer, are solved analytically using homotopy analysis method. The convergence of the series solution is analyzed explicitly. Comparison of the present homotopy results is made with the existing numerical and asymptotic solution (Wang, 2006, “Stagnation Slip Flow and Heat Transfer on a Moving Plate,” Chem. Eng. Sci., 23, pp. 7668–7672) and an excellent agreement is achieved.
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1.
Hiemenz
, K.
, 1911, “Die Grenzschicht Neinem in den Gleichförmigen Flüssigkeitsstrom Eingetauchten Geraden Kreiszylinder
,” Dinglers Polytechniches Journal
, 326
, pp. 321
–410
.2.
Homann
, F.
, 1936, “Der Einfluss Grosser Zähigkeit bei der Strömung um den Zylinder und um die Kugel
,” Z. Angew. Math. Mech.
0044-2267, 16
, pp. 153
–164
.3.
Howarth
, L.
, 1951, “The Boundary Layer in Three-Dimensional Flow, Part II: The Flow Near a Stagnation Point
,” Philos. Mag.
0031-8086, 42
, pp. 1433
–1440
.4.
Davey
, A.
, 1961, “Boundary Layer Flow at a Saddle Point of Attachment
,” J. Fluid Mech.
0022-1120, 10
, pp. 593
–610
.5.
J. T.
Stuart
, 1959, “The Viscous Flow Near a Stagnation Point When the External Flow has Uniform Vorticity
,” J. Aerosp. Sci.
0095-9820, 26
, pp. 124
–125
.6.
Tamada
, K.
, 1979, “Two-Dimensional Stagnation Point Flow Impinging Obliquely on a Plane Wall
,” J. Phys. Soc. Jpn.
0031-9015, 46
, pp. 310
–311
.7.
Dorrepaal
, J. M.
, 1986, “An Exact Solution of the Navier-Stokes Equation Which Describes Non-Orthogonal Stagnation-Point Flow in Two Dimensions
,” J. Fluid Mech.
0022-1120, 163
, pp. 141
–147
.8.
Rott
, N.
, 1956, “Unsteady Viscous Flow in the Vicinity of a Stagnation Point
,” Q. Appl. Math.
0033-569X, 13
, pp. 444
–451
.9.
Wang
, C. Y.
, 1973, “Axisymmetric Stagnation Flow Towards a Moving Plate
,” AIChE J.
0001-1541, 19
, pp. 1080
–1081
.10.
Libby
, P. A.
, 1974, “Wall Shear at a Three-Dimensional Stagnation Point With a Moving Wall
,” AIAA J.
0001-1452, 12
, pp. 408
–409
.11.
Weidman
, P. D.
, and Mahalingam
, S.
, 1997, “Axisymmetric Stagnation Point Flow Impinging on a Transversely Oscillating Plate With Suction
,” J. Eng. Math.
0022-0833, 31
, pp. 305
–318
.12.
Baris
, S.
, and Dokuz
, M. S.
, 2006, “Three-Dimensional Stagnation Point Flow of a Second Grade Fluid Towards a Moving Plate
,” Int. J. Eng. Sci.
0020-7225, 44
, pp. 49
–58
.13.
Shairpov
, F.
, and Selezev
, V.
, 1998, “Data on Internal Rarefied Gas Flows
,” J. Phys. Chem. Ref. Data
0047-2689, 27
, pp. 657
–706
.14.
Navier
, C. L. M. H.
, 1827, “Sur les lois du Mouvement des Fluides
,” Mem. Acad. Sci. Inst. Fr.
0368-9263, 6
, pp. 389
–440
.15.
Wang
, C. Y.
, 2003, “Stagnation Flow With Slip: Exact Solution of the Navier-Stokes Equations
,” Z. Angew. Math. Phys.
0044-2275, 54
, pp. 184
–189
.16.
Wang
, C. Y.
, 2003, “Flow Over a Surface With Parallel Grooves
,” Phys. Fluids
1070-6631, 15
, pp. 1114
–1121
.17.
Wang
, C. Y.
, 2006, “Stagnation Slip Flow and Heat Transfer on a Moving Plate
,” Chem. Eng. Sci.
0009-2509, 61
, pp. 7668
–7672
.18.
Liao
, S. J.
, 2003, Beyond Perturbation: Introduction to Homotopy Analysis Method
, Chapman and Hall
, London
/CRC
, Boca Raton, FL
.19.
Liao
, S. J.
, 2004, “On the Homotopy Analysis Method for Nonlinear Problems
,” Appl. Math. Comput.
0096-3003, 147
, pp. 499
–513
.20.
Liao
, S. J.
, and Cheung
, K. F.
, 2003, “Homotopy Analysis of Nonlinear Progressive Waves in Deep Water
,” J. Eng. Math.
0022-0833, 45
, pp. 105
–116
.21.
Wu
, W.
, and Liao
, S. J.
, 2005, “Solving Solitary Waves With Discontinuity by Means of Homotopy Analysis Method
,” Chaos, Solitons Fractals
0960-0779, 26
, pp. 177
–185
.22.
Liao
, S. J.
, 1999, “A Uniformly Valid Analytic Solution of 2D Viscous Flow Past a Semi-Infinite Flat Plate
,” J. Fluid Mech.
0022-1120, 385
, pp. 101
–128
.23.
Tan
, Y.
, Xu
, H.
, and Liao
, S. J.
, 2007, “Explicit Series Solution of Travelling Waves With a Front of Fisher Equation
,” Chaos, Solitons Fractals
0960-0779, 31
, pp. 462
–472
.24.
Liao
, S. J.
, 2006, “An Analytic Solution of Unsteady Boundary-Layer Flows Caused by an Impulsively Stretching Plate
,” Commun. Nonlinear Sci. Numer. Simul.
1007-5704, 11
, pp. 326
–339
.25.
Liao
, S. J.
, 2005, “Comparison Between the Homotopy Analysis Method and Homotopy Perturbation Method
,” Appl. Math. Comput.
0096-3003, 169
, pp. 1186
–1194
.26.
Abbasbandy
, S.
, 2008, “The Application of Homotopy Analysis Method to Nonlinear Equations Arising in Heat Transfer
,” Phys. Lett. A
0375-9601, 360
, pp. 109
–113
.27.
Hayat
, T.
, and Khan
, M.
, 2005, “Homotopy Solution for a Generalized Second Grade Fluid Past a Porous Plate
,” Nonlinear Dyn.
0924-090X, 42
, pp. 395
–405
.28.
Hayat
, T.
, and Abbas
, Z.
, 2008, “Heat Transfer Analysis on the MHD Flow of a Second Grade Fluid in a Channel With Porous Medium
,” Chaos, Solitons Fractals
0960-0779, 38
, pp. 556
–567
.29.
Hayat
, T.
, Abbas
, Z.
, and Javed
, T.
, 2008, “Mixed Convection Flow of a Micropolar Fluid Over a Non-Linearly Stretching Sheet
,” Phys. Lett. A
0375-9601, 372
, pp. 637
–647
.30.
Hayat
, T.
, and Sajid
, M.
, 2007, “On Analytic Solution for Thin Film Flow of a Fourth Grade Fluid Down a Vertical Cylinder
,” Phys. Lett. A
0375-9601, 361
, pp. 316
–322
.31.
Hayat
, T.
, Abbas
, Z.
, and Sajid
, M.
, 2007, “On the Analytic Solution of MHD Flow of a Second Grade Fluid Over a Shrinking Sheet
,” ASME J. Appl. Mech.
0021-8936, 74
, pp. 1165
–1171
.32.
Hayat
, T.
, Khan
, M.
, and Ayub
, M.
, 2004, “Couette and Poiseuille Flows of an Oldroyd 6-Constant Fluid With Magnetic Field
,” J. Math. Anal. Appl.
0022-247X, 298
, pp. 225
–244
.33.
Hayat
, T.
, Abbas
, Z.
, and Sajid
, M.
, 2006, “Series Solution for the Upper-Convected Maxwell Fluid Over a Porous Stretching Plate
,” Phys. Lett. A
0375-9601, 358
, pp. 396
–403
.34.
Sajid
, M.
, Hayat
, T.
, and Asghar
, S.
, 2006, “On the Analytic Solution of the Steady Flow of a Fourth Grade Fluid
,” Phys. Lett. A
0375-9601, 355
, pp. 18
–26
.35.
Abbas
, Z.
, Sajid
, M.
, and Hayat
, T.
, 2006, “MHD Boundary-Layer Flow of an Upper-Convected Maxwell Fluid in a Porous Channel
,” Theor. Comput. Fluid Dyn.
0935-4964, 20
, pp. 229
–238
.36.
Hayat
, T.
, Abbas
, Z.
, Sajid
, M.
, and Asghar
, S.
, 2007, “The Influence of Thermal Radiation on MHD Flow of a Second Grade Fluid
,” Int. J. Heat Mass Transfer
0017-9310, 50
, pp. 931
–941
.37.
Sajid
, M.
, Hayat
, T.
, and Asghar
, S.
, 2007, “Comparison of the HAM and HPM Solutions of Thin Film Flow of Non-Newtonian Fluids on a Moving Belt
,” Nonlinear Dyn.
0924-090X, 50
, pp. 27
–35
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