Effects of Heat and Mass Transfer on Non-Linear MHD Boundary Layer Flow Over a Shrinking Sheet in the Presence of Suction

Muhaimin R. Kandasamy; Azme B. Khamis

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(10): 1191-1198

Muhaimin R. Kandasamy, Azme B. Khamis. Effects of Heat and Mass Transfer on Non-Linear MHD Boundary Layer Flow Over a Shrinking Sheet in the Presence of Suction[J]. Applied Mathematics and Mechanics, 2008, 29(10): 1191-1198.

Citation:

PDF( 361 KB)

Effects of Heat and Mass Transfer on Non-Linear MHD Boundary Layer Flow Over a Shrinking Sheet in the Presence of Suction

Centre for Science Studies, University Tun Hussein Onn Malaysia, 86400, Parit Raja, Batu Pahat Johor, Malaysia

Received Date: 2008-01-28
Rev Recd Date: 2008-09-10
Publish Date: 2008-10-15

Abstract

Abstract

The magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction is concerned with.The cases of two dimensional and axisymmetric shrinking were discussed.The governing boundary layer equations were written into a dimensionless form by similarity transformations.The transformed coupled nonlinear ordinary differential equations were solved numerically by using the advanced numeric technique.Favorable comparison with previously published work was performed.Numerical results for the dimensionless velocity,temperature and concentration profiles as well as for the skin friction,heat and mass transfer and deposition rate were obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.
- shrinking sheet,
- suction at the surface,
- R.K.Gill method,
- magnetic effect

FullText(HTML)

References(29)

References

[1]	Bhattacharyya S N，Gupta A S. On the stability of viscous flow over a stretching sheet[J].Quart Appl Math,1985,43(3):359-367.
[2]	Brady J F,Acrivos A.Steady flow in a channel or tube with accelerating surface velocity. An exact solution to the Navier-Stokes equations with reverse flow[J].J Fluid Mech,1981,112:127-150. doi: 10.1017/S0022112081000323
[3]	Crane L J. Flow past a stretching plate[J].ZAMP,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(1):744-746. doi: 10.1002/cjce.5450550619
[5]	Jensen K F, Einset E O,Fotiadis D I.Flow phenomena in chemical vapor deposition of thin films[J].Ann Rev Fluid Mech,1991,23(1):197-232. doi: 10.1146/annurev.fl.23.010191.001213
[6]	McLeod J B,Rajagopal K R.On the uniqueness of flow of a Navier-Stokes fluid due to a stretching boundary[J].Arch Rat Mech Anal,1987,98（4）:385-393. doi: 10.1007/BF00276915
[7]	Troy W, Overman II E A,Ermentrout G B,et al.Uniqueness of flow of a second-order fluid past a stretching sheet[J].Quart Appl Math,1987,44(4):753-755.
[8]	Usha R,Sridharan R.The axisymmetric motion of a liquid film on an unsteady stretching surface[J].J Fluids Eng,1995,117（1）:81-85. doi: 10.1115/1.2816830
[9]	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
[10]	Wang C Y.Fluid flow due to a stretching cylinder[J].Phys Fluids,1988,31(3):466-468. doi: 10.1063/1.866827
[11]	Wang C Y.Liquid film on an unsteady stretching sheet[J].Quart Appl Math,1990,48(4):601-610.
[12]	Hakiem M A EL,Mohammadeian A A,Kaheir S M M EL,et al.Joule heating effects on MHD free convection flow of a micropolar fluid[J].International Comms Heat Mass Transfer,1999,26(2):219-227. doi: 10.1016/S0735-1933(99)00008-1
[13]	Kuo Bor-Lih. Heat transfer analysis for the Falkner-Skan wedge flow by the differential transformation method[J].Internat J Heat Mass Transfer,2005,48(23/24): 5036-5046. doi: 10.1016/j.ijheatmasstransfer.2003.10.046
[14]	Cheng W T, Lin H T.Non-similarity solution and correlation of transient heat transfer in laminar boundary layer flow over a wedge[J].Internat J Engg Sci,2002,40(5):531-548. doi: 10.1016/S0020-7225(01)00081-7
[15]	Apelblat A. Mass transfer with a chemical reaction of the first order. Effects of axial diffusion[J].The Chemical Engineering Journal,1982,23(2):193-203. doi: 10.1016/0300-9467(82)80011-7
[16]	Cebeci T,Bradshaw P.Physical and Computational Aspects of Convective Heat Transfer[M].New York:Springer-Verlag, 1984,79-80.
[17]	Schlichting H,Gersten K.Boundary Layer Theory[M].New York: McGraw Hill Inc,1979,164.
[18]	Yih K A.Uniform suction/blowing effect on forced convection about a wedge: Uniform heat flux[J].Acta Mech,1998,128（3/4）：173-181. doi: 10.1007/BF01251888
[19]	Watanabe T.Thermal boundary layers over a wedge with uniform suction or injection in forced flow[J].Acta Mech,1990,83（3/4）：119-126. doi: 10.1007/BF01172973
[20]	Kafoussias N G,Nanousis N D. Magnetohydrodynamic laminar boundary-layer flow over a wedge with suction or injection[J].Can J Phys,1997,75(10): 733-745. doi: 10.1139/p97-024
[21]	Sajid M, Javed T,Hayat T. MHD rotating flow of a viscous fluid over a shrinking surface[J].Nonlinear Dynamics,2008,51(1/2): 259-265.
[22]	Hayat T, Abbas Z, Sajid M.On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet[J].Journal of Applied Mechanics,2007,74(6):1165-1170. doi: 10.1115/1.2723820
[23]	Sajid M,Hayat T.The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet[J].Chaos, Solutions and Fractals,on line 23 July,2007.
[24]	Miklavcic M,Wang C Y.Viscous flow due to a shrinking sheet[J].Quart Appl Math,2006,64(2)：283-290.
[25]	Gill S. A process for the step-by-step integration of differential equations in an automatic digital computing machine[J].Proceedings of the Cambridge Philosophical Society,1951,47(1)：96-108. doi: 10.1017/S0305004100026414
[26]	Minkowycz W J, Sparrow E M, Schneider G E,et al. Handbook of Numerical Heat Transfer[M].New York:John Wiley and Sons, 1988,192-195.
[27]	Kafoussias N G,Karabis A G.Magnetohydrodynamic laminar boundary layer flow over a wedge[A].In：Sotiropoulos D A,Beskos D E,Eds.Proceedings of the 2nd National Congress on Computational Mechanics[C].Chania, Greece, June 26-28, 1996, Vol Ⅱ.Greek Association of Computational Mechanics, Member of IACM, 1996, 801- 809.
[28]	Kafoussias N G,Williams E W. An improved approximation technique to obtain numerical solution of a class of two-point boundary value similarity problems in fluid mechanics[J].Internt J Num Methods Fluids,1993,17(2): 145-162. doi: 10.1002/fld.1650170204
[29]	Wilhelm Dirk,Hartel Crlos,Kleiser Leonhard.Computational analysis of the two-dimensional-three-dimensional transition in forward-facing step flow[J].J Fluid Mech,2003,489:1-27. doi: 10.1017/S0022112003004440