Unsteady Three-Dimensional Boundary Layer Flow Due to a Permeable Shrinking Sheet

Norfifah Bachok; Anuar Ishak; Ioan Pop

doi:10.3879/j.issn.1000-0887.2010.11.007

Volume 31 Issue 11

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Norfifah Bachok, Anuar Ishak, Ioan Pop. Unsteady Three-Dimensional Boundary Layer Flow Due to a Permeable Shrinking Sheet[J]. Applied Mathematics and Mechanics, 2010, 31(11): 1344-1350. doi: 10.3879/j.issn.1000-0887.2010.11.007

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Unsteady Three-Dimensional Boundary Layer Flow Due to a Permeable Shrinking Sheet

doi: 10.3879/j.issn.1000-0887.2010.11.007

1.
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia;

Received Date: 1900-01-01
Rev Recd Date: 2010-09-08
Publish Date: 2010-11-15

Abstract

Abstract

The unsteady viscous flow over a continuously permeable shrinking surface was studied. Similarity equations were obtained through the application of similarity transformation techniques. Numerical techniques were used to solve the similarity equations for different values of the unsteadiness parameter, the mass suction parameter,the shrinking parameter and Prandtl number on the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. Different from an unsteady stretching sheet,it is found that dual solutions exist for a certain range of mass suction and unsteadiness parameters.
- unsteady,
- three-dimensional flow,
- boundary layer,
- shrinking sheet,
- dual solutions

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References

[1]	Lin C R, Chen C K. Exact solution of heat transfer from a stretching surface with variable heat flux[J].Heat Mass Transfer, 1998,33(5/6)：477-480. doi: 10.1007/s002310050218
[2]	Abraham J P, Sparrow E M. Friction drag resulting from the simultaneous imposed motions of a freestream and its bounding surface[J].Int J Heat Fluid Flow, 2005, 26(2):289-295. doi: 10.1016/j.ijheatfluidflow.2004.08.007
[3]	Crane L J. Flow past a stretching plate[J].Z Angew Math Phys, 1970,21(4):645-647. doi: 10.1007/BF01587695
[4]	Gupta P S, Gupta A S. Heat and mass transfer on a stretching sheet with suction and blowing[J].Can J Chem Eng, 1977, 55(6):744-746. doi: 10.1002/cjce.5450550619
[5]	Chakrabarti A C, Gupta A S. Hydromagnetic flow and heat transfer over a stretching sheet[J].Q Appl Math, 1979,37: 73-78 .
[6]	Kuiken H K. On boundary layers in fluid mechanics that decay algebraically along stretches of wall that are not vanishingly small[J].IMA J Appl Math, 1981,27(4):387-405. doi: 10.1093/imamat/27.4.387
[7]	Carragher P, Crane L J. Heat transfer on a continuous stretching sheet[J].Z Angew Math Mech, 1982, 62(10):564-565. doi: 10.1002/zamm.19820621009
[8]	Banks W H H. Similarity solutions of the boundary layer equations for a stretching wall[J]. J Mech Theor Appl, 1983, 2(3):375-392.
[9]	Magyari E, Keller B. Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls[J].Eur J Mech B-Fluids, 2000, 19(1):109-122. doi: 10.1016/S0997-7546(00)00104-7
[10]	朱婧，郑连存，张志刚. 幂律速度运动表面上磁流体在驻点附近的滑移流动[J]. 应用数学和力学, 2010, 31(4):411-419.
[11]	Wang C Y. The three-dimensional flow due to a stretching flat surface[J].Phys Fluids, 1984, 27（8）:1915-1917. doi: 10.1063/1.864868
[12]	Surma Devi C D, Takhar H S, Nath G. Unsteady three-dimensional boundary-layer due to a stretching surface[J]. Int J Heat Mass Transfer, 1986, 29（12）:1996-1999. doi: 10.1016/0017-9310(86)90020-7
[13]	Miklavcˇicˇ M, Wang C Y. Viscous flow due to a shrinking sheet[J].Quart Appl Math, 2006, 64（4）:283-290.
[14]	Wang C Y. Stagnation flow towards a shrinking sheet[J].Int J Non-Linear Mech, 2008, 43（5）:377-382. doi: 10.1016/j.ijnonlinmec.2007.12.021
[15]	Fang T. Boundary layer flow over a shrinking sheet with power-law velocity[J].Int J Heat Mass Transfer, 2008, 51（25/26）:5838-5843. doi: 10.1016/j.ijheatmasstransfer.2008.04.067
[16]	Fang T, Liang W, Lee C F. A new solution branch for the Blasius equation a shrinking sheet problem[J].Comput Math Appl, 2008, 56（12）:3088-3095. doi: 10.1016/j.camwa.2008.07.027
[17]	Fang T, Zhang J, Yao S S. Viscous flow over an unsteady shrinking sheet with mass transfer[J].Chin Phys Lett, 2009, 26（1）:014703. doi: 10.1088/0256-307X/26/1/014703
[18]	Hayat T, Abbas Z, Sajid M. On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet[J]. J Appl Mech-Trans ASME, 2007, 74（6）:1165-1171. doi: 10.1115/1.2723820
[19]	Sajid M, Hayat T, Javed T. MHD rotating flow of a viscous fluid over a shrinking surface[J].Nonlinear Dyn, 2008, 51（1/2）:259-265.
[20]	Fang T, Zhang J. Thermal boundary layers over a shrinking sheet: an analytical solution[J].Acta Mechanica, 2010, 209（3/4）:325-343. doi: 10.1007/s00707-009-0183-2
[21]	Cebeci T, Bradshaw P. Physical and Computational Aspects of Convective Heat Transfer[M]. New York: Springer, 1988.
[22]	Bachok N, Ishak A, Pop I. Mixed convection boundary layer flow near the stagnation point on a vertical surface embedded in a porous medium with anisotropy effect[J].Transp Porous Med, 2010,82（2）:363-373. doi: 10.1007/s11242-009-9431-0
[23]	Bachok N, Ishak A, Pop I. Boundary-layer flow of nanofluids over a moving surface in a flowing fluid[J].Int J Thermal Sci, 2010, 49（9）:1663-1668. doi: 10.1016/j.ijthermalsci.2010.01.026
[24]	Ishak A, Nazar R, Pop I. Boundary-layer flow of a micropolar fluid on a continuous moving or fixed surface[J].Can J Phys, 2006, 84（5）:399-410. doi: 10.1139/p06-059
[25]	Ishak A, Nazar R, Pop I. MHD boundary-layer flow due to a moving extensible surface[J].J Eng Math, 2008, 62（1）:23-33. doi: 10.1007/s10665-007-9169-z