This work is accomplished to investigate the Hall and ion-slip effects on mixed convection three-dimensional flow of a Maxwell fluid over a stretching vertical surface. The problem is first formulated and then nondimensionalized by using suitable variables. The solutions are computed by homotopy analysis method (HAM). The results are compared with the already limiting results. The convergence of derived series solutions is studied. The velocity components and temperature have been examined for several important parameters. Numerical computations for Nusselt number are presented and analyzed.
Issue Section:
Natural and Mixed Convection
References
1.
Crane
, L. J.
, 1970
, “Flow Past a Stretching Plate,”
J. Appl. Math. Phys. (ZAMP)
, 21
, pp. 645
–647
.10.1007/BF015876952.
Hayat
, T.
, Hussain
, Q.
, and Javed
, T.
, 2009
, “The Modified Decomposition Method and Padé Approximants for the MHD Flow Over a Non-Linear Stretching Sheet
,” Nonlinear Anal.: Real World Appl.
, 10
, pp. 966
–973
.10.1016/j.nonrwa.2007.11.0203.
Bataller
, R. C.
, 2007
, “Viscoelastic Fluid Flow and Heat Transfer Over a Stretching Sheet Under the Effects of a Non-Uniform Heat Source, Viscous Dissipation and Thermal Radiation
,” Int. J. Heat Mass Transfer
, 50
, pp. 3152
–3162
.10.1016/j.ijheatmasstransfer.2007.01.0034.
Prasad
, K. V.
, and Vajravelu
, K.
, 2009
, “Heat Transfer in the MHD Flow of a Power Law Fluid Over a Non-Isothermal Stretching Sheet
,” Int. J. Heat Mass Transfer
, 52
, pp. 4956
–4965
.10.1016/j.ijheatmasstransfer.2009.05.0225.
Liu
, I. C.
, 2004
, “Flow and Heat Transfer of an Electrically Conducting Fluid of Second Grade Over a Stretching Sheet Subject to a Transverse Magnetic Field
,” Int. J. Heat Mass Transfer
, 47
, pp. 4427
–4437
.10.1016/j.ijheatmasstransfer.2004.03.0296.
Prasad
, K. V.
, Pal
, D.
, Umesh
, V.
, and Rao
, N. S. P.
, 2010
, “The Effect of Variable Viscosity on MHD Viscoelastic Fluid Flow and Heat Transfer Over a Stretching Sheet
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
, pp. 331
–344
.10.1016/j.cnsns.2009.04.0037.
Abo-Eldahab
, E. M.
, and Elbarbary
, E. M. E.
, 2001
, “Hall Current Effect on Magnetohydrodynamic Free-Convection Flow Past a Semi-Infinite Vertical Plate With Mass Transfer
,” Int. J. Eng. Sci.
, 39
, pp. 1641
–1652
.10.1016/S0020-7225(01)00020-98.
Abo-Eldahab
, E. M.
, and Salem
, A. M.
, 2004
, “Hall Effects on MHD Free Convection Flow of a Non-Newtonian Power-Law Fluid at a Stretching Surface
,” Int. Commun. Heat Mass Transfer
, 31
, pp. 343
–354
.10.1016/j.icheatmasstransfer.2004.02.0059.
Liao
, S. J.
, 2003
, Beyond Perturbation: Introduction to Homotopy Analysis Method
, Chapman and Hall
, London
.10.
Liao
, S. J.
, 2004
, “On the Homotopy Analysis Method for Nonlinear Problems
,” Appl. Math. Comput
, 147
, pp. 499
–513
.10.1016/S0096-3003(02)00790-711.
Liao
, S. J.
, 2005
, “A New Branch of Solutions of Unsteady Boundary Layer Flows Over an Impermeable Stretched Plate
,” Int. J. Heat Mass Transfer
, 48
, pp. 2529
–2539
.10.1016/j.ijheatmasstransfer.2005.01.00512.
Cheng
, J.
, and Liao
, S. J.
, 2008
, “Series Solutions of Nano-Boundary Layer Flows by Means of the Homotopy Analysis Method
,” J. Math. Anal. Appl.
, 343
, pp. 233
–245
.10.1016/j.jmaa.2008.01.05013.
Abbasbandy
, S.
, and Parkes
, E. J.
, 2008
, “Solitary Smooth Hump Solutions of the Camassa-Holm Equation by Means of Homotopy Analysis Method
,” Chaos, Solitons Fractals
, 36
, pp. 581
–591
.10.1016/j.chaos.2007.10.03414.
Abbasbandy
, S.
, 2008
, “Approximate Solution of the Nonlinear Model of Diffusion and Reaction Catalysts by Means of the Homotopy Analysis Method
,” Chem. Eng. J.
, 136
, pp. 144
–150
.10.1016/j.cej.2007.03.02215.
Abbasbandy
, S.
, and Zakaria
, F. S.
, 2008
, “Soliton Solutions for the Fifth-Order KdV Equation With the Homotopy Analysis Method
,” Nonlinear Dyn.
, 51
, pp. 83
–87
.10.1007/s11071-006-9193-y16.
Hashim
, I.
, Abdulaziz
, O.
, and Momani
, S.
, 2009
, “Homotopy Analysis Method for Fractional IVPs
,” Commun. Commun. Nonlinear Sci. Numer. Simul.
, 14
, pp. 674
–684
.10.1016/j.cnsns.2007.09.01417.
Bataineh
, A. S.
, Noorani
, M. S. M.
, and Hashim
, I.
, 2009
, “On a New Reliable Modification of Homotopy Analysis Method
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
, pp. 409
–423
.10.1016/j.cnsns.2007.10.00718.
Allan
, F. M.
, 2007
, “Derivation of the Adomian Decomposition Method Using the Homotopy Analysis Method
,” Appl. Math. Comput.
, 190
, pp. 6
–14
.10.1016/j.amc.2006.12.07419.
Hayat
, T.
, Mustafa
, M.
, and Pop
, I.
, 2010
, “Heat and Mass Transfer for Soret and Dufour's Effect on Mixed Convection Boundary Layer Flow Over a Stretching Vertical Surface in a Porous Medium Filled With a Viscoelastic Fluid
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
, pp. 1183
–1196
.10.1016/j.cnsns.2009.05.06220.
Hayat
, T.
, Qasim
, M.
, and Abbas
, Z.
, 2010
, “Radiation and Mass Transfer Effects on the Magnetohydrodynamic Unsteady Flow Induced by a Stretching Sheet
,” Z. Naturforch
, 65
, pp. 231
–239
.21.
Hayat
, T.
, Qasim
, M.
, and Abbas
, Z.
, 2010
, “Homotopy Solution for the Unsteady Three-Dimensional MHD Flow and Mass Transfer in a Porous Space
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
, pp. 2375
–2387
.10.1016/j.cnsns.2009.09.01322.
Hayat
, T.
, Mustafa
, M.
, and Pop
, I.
, 2010
, “Heat and Mass Transfer for Soret and Dufour's Effect on Mixed Convection Boundary Layer Flow Over a Stretching Vertical Surface in a Porous Medium Filled With a Viscoelastic Fluid
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
, pp. 1183
–1196
.10.1016/j.cnsns.2009.05.06223.
Hayat
, T.
, and Nawaz
, M.
, 2011
, “Hall and Ion-Slip Effects on Three-Dimensional Flow of a Second Grade Fluid
,” Int. J. Numer. Methods Fluids
, 66
(2
), pp. 183
–193
.10.1002/fld.225124.
Hayat
, T.
, and Awais
, M.
, 2011
, “Three-Dimensional Flow of an Upper-Convected Maxwell (UCM) Fluid
,” Int. J. Numer. Methods Fluids
, 66
(7
), pp. 875
–884
.10.1002/fld.228925.
Gupta
, P. S.
, and Gupta
, T. S.
, 1977
, “Heat and Mass Transfer on Stretching Sheet With Suction or Blowing
,” Can. J. Chem. Eng.
, 55
, pp. 744
–746
.10.1002/cjce.545055061926.
Grubka
, L. J.
, and Bobba
, K. M.
, 1985
, “Heat Transfer Characteristics on a Continuous Stretching Surface With Variable Temperature
,” ASME J. Heat Transfer
, 107
(1)
, pp. 248
–250
.10.1115/1.324738727.
Ali
, M. E.
, 1995
, “On Thermal Boundary Layer on a Power-Law Stretched Surface With Suction or Injection
,” Int. J. Heat Fluid Flow
, 16
, pp. 280
–290
.10.1016/0142-727X(95)00001-728.
Salem
, A. M.
, and El-Aziz
, M. A.
, 2008
, “Effects of Hall Current and Chemical Reaction on Hydromagnetic Flow of a Stretching Vertical Surface With Internal Heat Generation/Absorption
,” Appl. Math. Modeling
, 32
, pp. 1236
–1254
.10.1016/j.apm.2007.03.008Copyright © 2013 by ASME
You do not currently have access to this content.