Abstract
This communication studies the flow and heat transfer characteristics over a continuously moving surface in the presence of a free stream velocity. The Jeffrey fluid is treated as a rheological model. The series expressions of velocity and temperature fields are constructed by applying the homotopy analysis method (HAM). The influence of emerging parameters such as local Deborah number (β), the ratio of relaxation and retardation times (λ2), the Prandtl number (Pr), and the Eckert number (Ec) on the velocity and temperature profiles are presented in the form of graphical and tabulated results for different values of λ. It is found that the boundary layer thickness is an increasing function of local Deborah number (β). However, the temperature and thermal boundary layer thickness decreases with the increasing values of local Deborah number (β).
Issue Section:
Forced
Convection
References
1.
Fetecau
, C.
, Fetecau
, C.
, and Zierep
, J.
, 2002, “Decay of a Potential Vortex and Propagation of a Heat Wave in a Second Grade Fluid
,” Int. J. Non-Linear Mech.
, 37
, pp. 1051
–1056
.2.
Tan
, W. C.
, and Masuoka
, T.
, 2005, “Stokes Problem for a Second Grade Fluid in a Porous Half Space With Heated Boundary
,” Int. J. Non-Linear Mech.
, 40
, pp. 515
–522
.3.
Fetecau
, C.
, and Fetecau
, C.
, 2006, “Starting Solutions for the Motion of a Second Grade Fluid Due to Longitudinal and Torsional Oscillations of a Circular Cylinder
,” Int. J. Eng. Sci.
, 44
, pp. 788
–796
.4.
Fetecau
, C.
, and Fetecau
, C.
, 2003, “Decay of a Potential Vortex in a Maxwell Fluid
,” Int. J. Non-Linear Mech.
, 38
, pp. 985
–990
.5.
Hayat
, T.
, Qasim
, M.
, and Abbas
, Z.
, 2010, “Radiation and Mass Transfer Effects on the Magnetohydrodynamic Unsteady Flow Induced by a Stretching Sheet
,” Z. Naturforsch.
, 65
, pp. 231
–239
.6.
Hayat
, T.
, Abbas
, Z.
, and Sajid
, M.
, 2009, “MHD Stagnation Point-Flow of an Upper Convected Maxwell Fluid Over a Stretching Surface
,” Chaos, Solitons Fractals
, 39
, pp. 840
–848
.7.
Hayat
, T.
, Abbas
, Z.
, Pop
, I.
, and Asghar
, S.
, 2010, “Effects of Radiation and Magnetic Field on the Mixed Convection Stagnation-Point Flow Over a Vertical Stretching Sheet in a Porous Medium
,” Int. J. Heat Mass Transfer
, 53
, pp. 466
–474
.8.
Cortell
, R.
, 2005, “Flow and Heat Transfer of a Fluid Through a Porous Medium Over a Stretching Surface With Internal heat Generation/Absorption and Suction/Blowing
,” Fluid Dyn. Res.
, 37
, pp. 231
–245
.9.
Ishak
, A.
, Nazar
, R.
, Amin
, N.
, Filip
, D.
, and Pop
, I.
, 2007, “Mixed Convection of the Stagnation-Point Flow Towards a Stretching Vertical Permeable Sheet
,” Malays. J. Math. Sci.
, 2
, pp. 217
–226
.10.
Hayat
, T.
, and Qasim
, M.
, 2010, “Influence of Thermal Radiation and Joul Heating on MHD Flow of a Maxwell Fluid in the Presence of Thermophoresis
,” Int. J. Heat Mass Transfer
, 53
, pp. 4780
–4788
.11.
Sakiadis
, B. C.
, 1961, “Boundary Layer Behavior on Continuous Solid Surfaces. II: The Boundary Layer on a Continuous Flat Surface
,” AIChE J.
, 7
, pp. 221
–225
.12.
Banks
, W. H. H.
, 1983, “Similarity Solutions of the Boundary Layer Equations for Stretching Wall
,” J. Stat. Mech.: Theory Exp.
, 2
, pp. 375
–392
.13.
Afzal
, N.
, and Varshney
, I. S.
, 1980, “The Cooling of a Low Heat Resistance Stretching Sheet Moving Through a Fluid
,” Waerme- Stoffuebertrag.
, 14
, pp. 289
–293
.14.
Afzal
, N.
, 1993, “Heat Transfer From a Stretching Surface
,” Int. J. Heat Mass Transfer
, 36
, pp. 1128
–1131
.15.
Magyari
, E.
, and Keller
, B.
, 2000, “Exact Solutions for Self-Similar Boundary-Layer Flows Induced by Permeable Stretching Walls
,” Eur. J. Mech B/Fluids
, 19
, pp. 109
–122
.16.
Hayat
, T.
, Abbas
, Z.
, and Pop
, I.
, 2010, “Momentum and Heat Transfer Over a Continuously Moving Surface With a Parallel Free Stream in a Viscoelastic Fluid
,” Numer. Methods Partial Differ. Equ.
, 26
, pp. 305
–319
. 17.
Zaman
, H.
, Hayat
, T.
, and Ayub
, M.
, 2009, “Series Solution for Heat Transfer From a Continuous Surface in a Parallel Free Stream of Viscoelastic Fluid
,” Numer. Methods Partial Differ. Equ.
18.
Ishak
, A.
, Nazar
, R.
, and Pop
, I.
, 2008, “Hydromagnetic Flow and Heat Transfer Adjacent to a Stretching Vertical Sheet
,” Heat Mass Transfer
, 44
, pp. 921
–927
.19.
Barletta
, A.
, Rossi di Schio
, E.
, and Selmi
, L.
, 2011, “Thermal Nonequilibrium and Viscous Dissipation in the Thermal Entrance Region of a Darcy Flow With Streamwise Periodic Boundary Conditions
,” J. Heat Transfer
, 133
, p. 072602
.20.
Sun
, Z.
, and Jaluria
, Y.
, 2011, “Conjugate Thermal Transport in Gas Flow in Long Rectangular Microchannel Zhanyu Sun and Yogesh Jaluria
,” J. Heat Transfer
, 133
, p. 021008
.21.
Jaluria
, Y.
, and Yang
, J.
, 2011, “A Review of Microscale Transport in the Thermal Processing of New and Emerging Advanced Materials
,” J. Heat Transfer
, 133
, p. 060906
.22.
Coelho
, P. M.
, and Faria
, J. C.
, 2011, “On the Generalized Brinkman Number Definition and Its Importance for Bingham Fluids
,” J. Heat Transfer
, 133
, p. 054505
.23.
Turkyilmazoglu
, M.
, 2011, “Heat and Mass Transfer on the MHD Fluid Flow Due to a Porous Rotating Disk With Hall Current and Variable Properties
,” J. Heat Transfer
, 133
, p. 021701
.24.
Hayat
, T.
, Ahmad
, N.
, and Ali
, N.
, 2008, “Effects of an Endoscope and Magnetic Field on the Peristalsis Involving Jeffrey Fluid
,” Commun. Nonlinear Sci. Numer. Simul.
, 13
, pp. 1581
–1591
.25.
Kothandapani
, M.
, and Srinivas
, S.
, 2008, “Peristaltic Transport of a Jeffrey Fluid Under the Effect of Magnetic Field in an Asymmetric Channel
,” Int. J. Nonlinear Mech.
, 43
, pp. 915
–924
.26.
Hayat
, T.
, and Ali
, N.
, 2008, “Peristaltic Motion of a Jeffrey Fluid Under the Effect of a Magnetic Field in a Tube
,” Commun. Nonlinear Sci. Numer. Simul.
, 13
, pp. 1343
–1352
.27.
Nadeem
, S.
, and Akbar
, N. S.
, 2009, “Peristaltic Flow of a Jeffrey Fluid With Variable Viscosity in an Asymmetric Channel
,” Z. Naturforsch.
, 64
, pp. 713
–722
.28.
Liao
, S. J.
, 2009, “Notes on the Homotopy Analysis Method: Some Definitions and Theorems
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
, pp. 983
–997
.29.
Cheng
, J.
, Liao
, S. J.
, Mohapatra
, R. N.
, and Vajravelu
, K.
, 2009, “Series Solutions of Stagnation Slip Flow and Heat Transfer by the Homotopy Analysis Method
,” Sci. China Ser. G
, 52
, pp. 893
–899
.30.
Liao
, S. J.
, 2010, “On the Relationship Between the Homotopy Analysis Method and Euler Transform
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
, pp. 1421
–1431
.31.
Khan
, H.
, Mohapatra
, R. N.
, Vajravelu
, K.
, and Liao
, S. J.
, 2009, “The Explicit Series Solution of SIR and SIS Epidemic Models
,” Appl. Math. Comput.
, 215
, pp. 653
–669
.32.
Abbasbandy
, S.
, and Shivanian
, E.
, 2010, “Prediction of Multiplicity of Solutions of Nonlinear Boundary Value Problems: Novel Application of Homotopy Analysis Method
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
, pp. 3830
–3846
.33.
Abbasbandy
, S.
, 2010, “Homotopy Analysis Method for the Kawahara Equation
,” Nonlinear Anal.: Real World Appl.
, 11
, pp. 307
–312
.34.
Abbasbandy
, S.
, and Shirzadi
, A.
, 2011, “A New Application of the Homotopy Analysis Method: Solving the Sturm–Liouville Problems
,” Commun. Nonlinear Sci. Numer. Simul.
, 16
, pp. 112
–126
.35.
Hashim
, I.
, Abdulaziz
, O.
, and Momani
, S.
, 2009, “Homotopy Analysis Method for Fractional IVPs
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
, pp. 674
–684
.36.
Chowdhury
, M. S. H.
, Hashim
, I.
, and Abdulaziz
, O.
, 2009, “Comparison of Homotopy Analysis Method and Homotopy-Perturbation Method for Purely Nonlinear Fin-Type Problems
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
, pp. 371
–378
.37.
Bataineh
, A. S.
, Noorani
M. S. M.
, and Hashim
, I.
, 2009, “Homotopy Analysis Method for Singular IVPs of Emden–Fowler Type
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
, pp. 1121
–1131
.38.
Hayat
, T.
, Awais
M.
, and Sajid
, M.
, 2010, “Similar Solutions of Stretching Flow With Mass Transfer
,” Int. J. Numer. Methods Fluids
, 64
, pp. 908
–921
.39.
Hayat
, T.
, Qasim
, M.
, and Abbas
, Z.
, 2010, “Homotopy Solution for Unsteady Three-Dimensional MHD Flow and Mass Transfer in a Porous Space
,” Commun. Nonlinear. Sci. Numer. Simul.
, 15
, pp. 2375
–2387
.40.
Hayat
, T.
, Naz
, R.
, and Abbasbandy
, S.
, 2010, “On Flow of a Fourth Grade Fluid With Heat Transfer
,” Int. J. Numer. Methods Fluids
.41.
Hayat
, T.
, Mustafa
, M.
, and Mesloub
, S.
, 2010, “Mixed Convection Boundary Layer Flow Over a Stretching Surface Filled With a Maxwell Fluid in Presence of Soret and Dufour Effects
,” Z. Naturforsch.
, 65
, pp. 401
–410
.42.
Cortell
, R.
, 2010, “Radiation Effects for the Blasius and Sakiadis Flows With a Convective Surface Boundary Conditions
,” Appl. Math. Comput.
, 206
, pp. 832
–840
.43.
Sadeghy
, K.
, Najafi
, A.
, and Saffaripour
, M.
, 2005, “Sakiadis Flow of an Upper-Convected Maxwell Fluid
,” Int. J. Nonlinear Mech.
, 40
, pp. 1220
–1228
.44.
Alam
, M. S.
, and Rahman
, M. M.
, 2006, “Dufour and Soret Effects on Mixed Convection Flow Past a Vertical Porous Flat Plate with Variable Suction
,” Nonlinear Anal.: Model. Control
, 11
, pp. 3
–12
.45.
Sahoo
, B.
, and Do
, Y.
, 2010, “Effects of Slip on Sheet-Driven Flow and Heat Transfer of a Third Grade Fluid Past a Stretching Sheet
,” Int. Commun. Heat Mass Transfer
, 37
, pp. 1064
–1071
.46.
Sahoo
, B.
, 2009, “Hiemenz Flow and Heat Transfer of a Third Grade Fluid
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
, pp. 811
–826
.47.
Sahoo
, B.
, 2009, “Flow and Heat Transfer of a Non-Newtonian Fluid Past a Stretching Sheet With Partial Slip
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
, pp. 811
–826
.48.
Sajid
, M.
, Hayat
, T.
, and Asghar
, S.
, 2007, “Non-Similar Analytic Solution for MHD Flow and Heat Transfer in a Third-Order Fluid Over a Stretching Sheet
,” Int. J. Heat Mass Transfer
, 50
, pp. 1723
–1736
.49.
Hayat
, T.
, Mustafa
, M.
, and Asghar
, S.
, 2010, “Unsteady Flow With Heat and Mass Transfer of a Third Grade Fluid Over a Stretching Surface in the Presence of Chemical Reaction
,” Nonlinear Anal.: Real World Appl.
, 11
, pp. 3186
–3197
.50.
Mukhopadhyay
, S.
, 2009, “Effect of Thermal Radiation on Unsteady Mixed Convection Flow and Heat Transfer Over a Porous Stretching Surface in Porous Medium
,” Int. J. Heat Mass Transfer
, 52
, pp. 3261
–3265
.51.
Cortell
, R.
, 2011, “Suction, Viscous Dissipation and Thermal radiation Effects on the Flow and Heat Transfer of a Power-Law Fluid Past an Infinite Porous Plate
,” Chem. Eng. Res. Des.
, 89
, pp. 85
–93
.52.
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
.Copyright © 2012
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