In this paper heat transfer in an electrically conducting fluid bonded by two parallel plates is studied in the presence of viscous dissipation. The plates and the fluid rotate with constant angular velocity about a same axis of rotation where the lower plate is a stretching sheet and the upper plate is a porous plate subject to constant injection. The governing partial differential equations are transformed to a system of ordinary differential equations with the help of similarity transformation. Homotopy analysis method is used to get complete analytic solution for velocity and temperature profiles. The effects of different parameters are discussed through graphs.
1.
Sakiadis
, B. C.
, 1961, “Boundary Layer Behavior on Continuous Solid Surface. I Boundary Layer Equations for Two-Dimensional and Axisymmetric Flow
,” AIChE J.
0001-1541, 7
, pp. 26
–28
.2.
Crane
, L. J.
,1970, “Flow Past a Stretching Plate
,” Z. Angew. Math. Phys.
0044-2275, 21
, pp. 645
–647
.3.
Andersson
, H. I.
, 1992, “MHD Flow of a Viscoelastic Fluid Past a Stretching Surface
,” Acta Mech.
0001-5970, 95
, pp. 227
–230
.4.
Troy
, W. C.
, Overman
, II, E. A.
, Eremont-Rout
, G. B.
, and Keener
, J. P.
, 1987, “Uniqueness of Flow of Second Order Fluid Past a Stretching Sheet
,” Q. Appl. Math.
0033-569X, 44
, pp. 753
–755
.5.
Ariel
, P. D.
,1994, “MHD Flow of a Viscoelastic Fluid Past a Stretching Sheet With Suction
,” Acta Mech.
0001-5970, 105
, pp. 49
–56
.6.
Jacobi
, A. M.
,1993, “A Scale Analysis Approach to the Correlation of Continuous Moving Sheet, (Backward Boundary Layer) Forced Convective Heat Transfer
,” ASME J. Heat Transfer
0022-1481, 115
, pp. 1058
–1061
.7.
Banks
, W. H. H.
, 1983, “Similarity Solutions of the Boundary-Layer Equations for a Stretching Wall
,” J. Mec. Theor. Appl.
0750-7240, 2
, pp. 375
–392
.8.
Banks
, W. H. H.
, and Zaturska
, M. B.
, 1986, “Eigensolutions in Boundary Layer Flow Adjacent to a Stretching Wall
,” IMA J. Appl. Math.
0272-4960, 36
, pp. 263
–273
.9.
Rajagopal
, K. R.
, 1987, “A Non Similar Boundary Layer on a Stretching Sheet in a Non-Newtonian Fluid With Uniform Stream
,” J. Mathematical and Physical Sciences
, 21
, pp. 189
–200
.10.
Chakrabarti
, A.
, and Gupta
, A. S.
, 1979, “Hydromagnetic Flow and Heat Transfer Over a Stretching Sheet
,” Q. Appl. Math.
0033-569X, 37
, pp. 756
–755
.11.
Chaudhary
, M. A.
, Merkin
, J. H.
, and Pop
, I.
, 1995, “Similarity Solutions in the Free Convection Boundary-Layer Flows Adjacent to Vertical Permeable Surface in Porous Media
,” Eur. J. Mech. B/Fluids
0997-7546, 14
, pp. 217
–237
.12.
Chamkha
, A. J.
, 1999, “Hydromagnetic Three-Dimensional Free Convection on a Vertical Stretching Surface With Heat Generation or Absorption
,” Int. J. Heat Fluid Flow
0142-727X, 20
, pp. 84
–92
.13.
Xu
, H.
, and Liao
, S. J.
, 2005, “Series Solution of Unsteady Magnetohydrodynamic Flows of Non-Newtonian Fluids Cause by an Impulsively Stretching Plate
,” J. Non-Newtonian Fluid Mech.
0377-0257, 129
, pp. 46
–55
.14.
Vajravelu
, K.
, 1986, “Hydromagnetic Flow and Heat Transfer Over a Continuous, Moving Porous Flat Surface
,” Acta Mech.
0001-5970, 64
, pp. 179
–185
.15.
Zakaria
, M.
, 2004, “Magnetohydrodynamic Viscoelastic Boundary Layer Flow Past a Stretching Plate and Heat Transfer
,” Appl. Math. Comput.
0096-3003, 155
, pp. 165
–177
.16.
Dutta
, B. K.
, Roy
, P.
, and Gupta
, A. S.
, 1985, “Temperature Field in Flow Over a Stretching Surface With Uniform Heat Flux
,” Int. Commun. Heat Mass Transfer
0735-1933, 12
, pp. 89
–94
.17.
Andersson
, H. I.
, Aarseth
, J. B.
, Braud
, N.
, and Dandapat
, B. S.
, 1996, “Flow of a Power-Law Fluid Film on an Unsteady Stretching Surface
,” J. Non-Newtonian Fluid Mech.
0377-0257, 62
(1
), pp. 1
–8
.18.
Bujurke
, N. M.
, Biradar
, S. N.
, and Hiremath
, P. S.
, 1987, “2nd-Order Fluid-Flow Past a Stretching Sheet With Heat-Transfer
,” ZAMP
0044-2275, 38
(4
), pp. 653
–657
.19.
Dandapat
, B. S.
, and Gupta
, A. S.
, 1989, “Flow and Heat Transfer in a Viscoelastic Fluid Over a Stretching Sheet
,” Int. J. Non-Linear Mech.
0020-7462, 24
pp. 215
–219
.20.
Mehmood
, A.
, and Ali
, A.
, “An Explicit Analytic Solution of Steady Three-Dimensional Stagnation Point Flow of Second Grade Fluid Towards a Heated Plate
,” ASME J. Appl. Mech.
, to be published.21.
Mehmood
, A.
, and Ali
, A.
, 2006, “Analytic Solution of Generalized Three-Dimensional Flow and Heat Transfer Over a Stretching Plane Wall
,” Int. Commun. Heat Mass Transfer
0735-1933, 33
, pp. 1243
–1252
.22.
Chen
, C. K.
, and Chen
, M. I.
, 1988, “Heat and Mass Transfer of a Continuous Stretching Surface With Suction or Blowing
,” J. Math. Anal. Appl.
0022-247X, 135
, pp. 568
–580
.23.
Gupta
, P. S.
, and Gupta
, A. S.
, 1977, “Heat and Mass Transfer on a Stretching Sheet With Suction or Blowing
,” Can. J. Chem. Eng.
0008-4034, 55
, pp. 744
–746
.24.
Ali
, M. E.
, 1994, “Heat Transfer Characteristics of a Continuous Stretching Surface
,” Waerme- Stoffuebertrag.
0042-9929, 29
, pp. 227
–234
.25.
Mehmood
, A.
, Ali
, A.
, and Shah
, T.
, 2008, “Heat Transfer Analysis of Unsteady Boundary Layer Flow by Homotopy Analysis Method
,” Commun. Nonlinear Sci. Numer. Simul.
1007-5704, 13
(5
), pp. 902
–912
.26.
Borkakoti
, A. K.
, and Bharali
, A.
, 1983, “Hydromagnetic Flow and Heat Transfer Between Two Horizontal Plates, the Lower Plate Being a Stretching Sheet
,” Q. Appl. Math.
0033-569X, 41
, pp. 461
–467
.27.
Vajravelu
, K.
, and Kumar
, B. V. R.
, 2004, “Analytic and Numerical Solutions of Coupled Nonlinear System Arising in Three-Dimensional Rotating Flow
,” Int. J. Non-Linear Mech.
0020-7462, 39
, pp. 13
–24
28.
Liao
, S. J.
, 2003, Beyond Perturbation: Introduction to Homotopy Analysis Method
, CRC
, Boca Raton, FL
.29.
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
.30.
Liao
, S. J.
, and Pop
, I.
, 2004, “Explicit Analytic Solution for Similarity Boundary Layer Equations
,” Int. J. Heat Mass Transfer
0017-9310, 47
(1), pp. 75
–85
.31.
Wang
, C.
, Zhu
, J. M.
, Liao
, S. J.
, and Pop
, I.
, 2003, “On the Explicit Analytic Solutions of Cheng-Chang Equations
,” Int. J. Heat Mass Transfer
0017-9310, 46
(10
), pp. 1855
–1860
.32.
Liao
, S. J.
, 2006, “An Analytic Solution of Unsteady Boundary Layer Flows Caused by Impulsively Stretching Plate
,” Commun. Nonlinear Sci. Numer. Simul.
1007-5704, 11
, pp. 326
–339
.33.
Ali
, A.
, and Mehmood
, A.
, 2008, “Homotopy Analysis of Unsteady Boundary Layer Flow Adjacent to Permeable Stretching Surface in a Porous Medium
,” Commun. Nonlinear Sci. Numer. Simul.
1007-5704, 13
, pp. 340
–349
.34.
Allan
, F. M.
, and Syam
, M. I.
, 2005, “On Analytic Solution of the Non-Homogeneous Blasius Problem
,” J. Comput. Appl. Math.
0377-0427, 182
, pp. 355
–365
.35.
Liao
, S. J.
, 2005, “A New Branch of Solution of Boundary Layer Flows Over an Impermeable Stretched Plate
,” Int. J. Heat Mass Transfer
0017-9310, 48
, pp. 2529
–2539
.36.
Liao
, S. J.
, 1999, “A Uniformly Valid Analytical Solution of 2D Viscous Flow Past a Semi Infinite Flat Plate
,” J. Fluid Mech.
0022-1120, 385
, pp. 101
–128
.37.
Liao
, S. J.
, 1999, “An Explicit, Totally Analytic Approximate Solution for Blasius Viscous Flow Problems
,” Int. J. Non-Linear Mech.
0020-7462, 34
, pp. 759
–778
.38.
Mehmood
, A.
, and Ali
, A.
, 2007, “Unsteady Boundary Layer Flow Due to an Impulsively Started Moving Plate
,” Proc. Inst. Mech. Eng., Part G: J. Aero. Engr.
, 221
, pp. 385
–390
.39.
Liao
, S. J.
, and Campo
, A.
, 2002, “Analytic Solutions of the Temperature Distribution in Blasius Viscous Flow Problems
,” J. Fluid Mech.
0022-1120, 453
, pp. 411
–425
.40.
Yang
, C.
, andLiao
, S. J.
, 2006, “On the Explicit, Purely Analytic Solution of Von Karman Swirling Viscous Flow
,” Commun. Nonlinear Sci. Numer. Simul.
1007-5704, 11
(1
), pp. 83
–93
.41.
Liao
, S. J.
, 2003, “On the Analytic Solution of Magnetohydrodynamic Flows of Non-Newtonian Fluids Over a Stretching Sheet
,” J. Fluid Mech.
0022-1120, 488
, pp. 189
–212
.42.
Liao
, S. J.
, 2004, “On Homotopy Analysis Method for Nonlinear Problems
,” Appl. Math. Comput.
0096-3003, 147
, pp. 499
–513
.Copyright © 2008
by American Society of Mechanical Engineers
You do not currently have access to this content.
