The heat transfer characteristics of a viscous liquid film flow over an unsteady stretching sheet subject to variable heat flux are investigated numerically. The effect of thermal radiation applying to an optically thick medium is also considered. The governing boundary layer equations are transformed into a set of nonlinear ordinary differential equations using an efficient fifth-order step-adapted Runge–Kutta integration scheme together with Newton–Raphson method. The dimensionless temperature is plotted for various governing parameters; say, unsteadiness parameter, effective Prandtl number, distance index, as well as time index. It is found that the heat transfer aspects are strongly influenced by the relevant parameters.
Issue Section:
Research Papers
References
1.
2.
Gupta
, A. S.
, and Gupta
, P. S.
, 1977
, “Heat and Mass Transfer on a Stretching Sheet With Suction or Blowing
,” Can. J. Chem. Eng.
, 55
, pp. 744
–746
.10.1002/cjce.54505506193.
Carragher
, P.
, and Crane
, L. J.
, 1982
, “Heat Transfer on a Continuous Stretching Sheet
,” ZAMM
, 62
, pp. 564
–565
.10.1002/zamm.198206210094.
Jeng
, D. R.
, Chang
, T. C. A.
, and DeWitt
, K. J.
, 1986
, “Momentum and Heat Transfer on a Continuous Moving Surface
,” ASME J. Heat Trans.
, 108
, pp. 532
–539
.10.1115/1.32469675.
Wang
, C. Y.
, 1990
, “Liquid Film on an Unsteady Stretching Surface
,” Quart. Appl. Math.
, 48
, pp. 601
–610
.6.
Wang
, C.
, 2006
, “Analytic Solutions for a Liquid Film on an Unsteady Stretching Surface
,” Heat Mass Transfer
, 42
, pp. 759
–766
.10.1007/s00231-005-0027-07.
Andersson
, H. I.
, Aarseth
, J. B.
, Braud
, N.
, and Dandapat
, B. S.
, 1996
, “Flow of a Power-Law Fluid on an Unsteady Stretching Surface
,” J. Non-Newtonian Fluid Mech.
, 62
, pp. 1
–8
.10.1016/0377-0257(95)01392-X8.
Wang
, C.
, and Pop
, I.
, 2006
, “Analysis of the Flow of a Power-Law Fluid Film on an Unsteady Stretching Surface by Means of Homotopy Analysis Method
,” J. Non-Newtonian Fluid Mech.
, 138
, pp. 161
–172
.10.1016/j.jnnfm.2006.05.0119.
Abbas
, Z.
, Hayat
, T.
, Sajid
, M.
, and Asghar
, S.
, 2008
, “Unsteady Flow of a Second Grade Fluid Film Over an Unsteady Stretching Sheet
,” Math. Comput. Modelling
, 48
, pp. 518
–526
.10.1016/j.mcm.2007.09.01510.
Hayat
, T.
, Saif
, S.
, and Abbas
, Z.
, 2008
, “The Influence of Heat Transfer in an MHD Second Grade Fluid Film Over an Unsteady Stretching Sheet
,” Phys. Lett. A
, 372
, pp. 5037
–5045
.10.1016/j.physleta.2008.03.06611.
Elgazery
, N. S.
, and Hassan
, M. A.
, 2008
, “The Effects of Variable Fluid Properties and Magnetic Field on the Flow of Non-Newtonian Fluid Film on an Unsteady Stretching Sheet Through a Porous Medium
,” Commun. Numer. Methods Eng.
, 24
, pp. 2113
–2129
.10.1002/cnm.109912.
Andersson
, H. I.
, Aarseth
, J. B.
, and Dandapat
, B. S.
, 2000
, “Heat Transfer in a Liquid Film on an Unsteady Stretching Surface
,” Int. J. Heat Mass Transfer
, 43
, pp. 69
–74
.10.1016/S0017-9310(99)00123-413.
Chen
, C. H.
, 2003
, “Heat Transfer in a Power-Law Fluid Film Over a Unsteady Stretching Sheet
,” Heat Mass Transfer
, 39
, pp. 791
–796
.10.1007/s00231-002-0363-214.
Dandapat
, B. S.
, Santra
, B.
, and Andersson
, H. I.
, 2003
, “Thermocapillarity in a Liquid Film on an Unsteady Stretching Surface
,” Int. J. Heat Mass Transfer
, 46
, pp. 3009
–3015
.10.1016/S0017-9310(03)00078-415.
Dandapat
, B. S.
, Santra
, B.
, and Andersson
, H. I.
, 2007
, “The Effect of Variable Properties and Thermocapillarity on the Flow of a Thin Film on an Unsteady Stretching Sheet
,” Int. J. Heat Mass Transfer
, 50
, pp. 991
–996
.10.1016/j.ijheatmasstransfer.2006.08.00716.
Noor
, N. F. M.
, and Hashim
, I.
, 2010
, “Thermocapillarity and Magnetic Field Effects in a Thin Liquid Film on an Unsteady Stretching Surface
,” Int. J. Heat Mass Transfer
, 53
, pp. 2044
–2051
.10.1016/j.ijheatmasstransfer.2009.12.05217.
Chen
, C. H.
, 2007
, “Marangoni Effects on Forced Convection of Power-Law Liquids in a Thin Film Over a Stretching Surface
,” Phys. Lett. A
, 370
, pp. 51
–57
.10.1016/j.physleta.2007.05.02418.
Mahmoud
, M. A. A.
, and Megahed
, A. M.
, 2009
, “MHD Flow and Heat Transfer in a Non-Newtonian Liquid Film Over an Unsteady Stretching Sheet With Variable Fluid Properties
,” Can. J. Phys.
, 87
, pp. 1065
–1071
.10.1139/P09-06619.
Chen
, C. H.
, 2006
, “Effect of Viscous Dissipation on Heat Transfer in a Non-Newtonian Liquid Film Over an Unsteady Stretching Sheet
,” J. Non-Newtonian Fluid Mech.
, 135
, pp. 128
–135
.10.1016/j.jnnfm.2006.01.00920.
Abel
, M. S.
, Mahesha
, N.
, and Tawade
, J.
, 2009
, “Heat Transfer in a Liquid Film Over an Unsteady Stretching Surface With Viscous Dissipation in the Presence of External Magnetic Field
,” Appl. Math. Modelling
, 33
, pp. 3430
–3441
.10.1016/j.apm.2008.11.02121.
Abel
, M. S.
, Tawade
, J.
, and Nandeppanavar
, M. M.
, 2009
, “Effect of Non-Uniform Heat Source on MHD Heat Transfer in a Liquid Film Over an Unsteady Stretching Sheet
,” Int. J. Nonlinear Mech.
, 44
, pp. 990
–998
.10.1016/j.ijnonlinmec.2009.07.00422.
Kiwan
, S.
, and Al-Nimr
, M. A.
, 2009
, “Flow and Heat Transfer Over a Stretched Mirco-Surface
,” ASME J. Heat Transfer
, 131
(6
), pp. 1
–8
.10.1115/1.309081123.
Dandapat
, B. S.
, and Maity
, S.
, 2006
, “Flow of a Thin Film on an Unsteady Stretching Sheet
,” Phys. Fluids
, 18
, p. 102101
.10.1063/1.236025624.
Santra
, B.
, and Dandapat
, B. S.
, 2009
, “Unsteady Thin Film on an Unsteady Stretching Sheet
,” Int. J. Heat Mass Transfer
, 52
, pp. 1956
–1970
.10.1016/j.ijheatmasstransfer.2008.09.03625.
Dandapat
, B. S.
, and Chakraborty
, S.
, 2010
, “Effect of Variable Fluid Properties on Unsteady Thin-Film Flow Over a Non-Linear Stretching Sheet
,” Int. J. Heat Mass Transfer
, 53
, pp. 5757
–5763
.10.1016/j.ijheatmasstransfer.2010.08.00726.
Dandapat
, B. S.
, and Singh
, S. K.
, 2011
, “Thin Film Flow Over a Heated Nonlinear Stretching Sheet in Presence of Uniform Transverse Magnetic Field
,” Int. Commun. Heat Mass Transfer
, 38
, pp. 324
–328
.10.1016/j.icheatmasstransfer.2010.11.00927.
Liu
, I.-C.
, and Andersson
, H. I.
, 2008
, “Heat Transfer in a Liquid Film on an Unsteady Stretching Sheet
,” Int. J. Therm. Sci.
, 47
, pp. 766
–772
.28.
Dutta
, B. K.
, Roy
, P.
, and Gupta
, A. S.
, 1985
, “Temperature Field in Flow Over a Stretching Sheet With Uniform Heat Flux
,” Int. Commun. Heat Mass Transfer
, 12
, pp. 89
–94
.10.1016/0735-1933(85)90010-729.
Elbashbeshy
, E. M. A.
, 1998
, “Heat Transfer Over a Stretching Surface With Variable Surface Heat Flux
,” J. Phys. D: Appl. Phys.
, 31
, pp. 1951
–1954
.10.1088/0022-3727/31/16/00230.
Surma Devi
, C. D.
, Takhar
, H. S.
, and Nath
, G.
, 1986
, “Unsteady Three-Dimensional Boundary-Layer Flow Due to a Stretching Surface
,” Int. J. Heat Mass Transfer
, 29
, pp. 1996
–1999
.10.1016/0017-9310(86)90020-731.
Lakshmisha
, K. N.
, Venkateswaran
, S.
, and Nath
, G.
, 1998
, “Three-Dimensional Unsteady Flow With Heat and Mass Transfer Over a Continuous Stretching Surface
,” ASME J. Heat Mass Transfer
, 110
, pp. 590
–595
.10.1115/1.325053332.
Abd El-Aziz
, M.
, 2009
, “Radiation Effect on the Flow and Heat Transfer Over an Unsteady Stretching Sheet
,” Int. Commun. Heat Mass Transfer
, 36
, pp. 521
–524
.10.1016/j.icheatmasstransfer.2009.01.01633.
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
.10.1016/j.ijheatmasstransfer.2008.12.02934.
Pal
, D.
, 2011
, “Combined Effects of Non-Uniform Heat Source/Sink and Thermal Radiation on Heat Transfer Over an Unsteady Stretching Permeable Surface
,” Commun. Nonlin. Sci. Numer. Simul.
, 16
, pp. 1890
–1904
.10.1016/j.cnsns.2010.08.02335.
Rosseland
, S.
, 1931
, Astrophysik und Atom-Theoretische Grundlagen
, Springer-Verlag
, Berlin
, pp. 41
–44
.36.
Christen
, T.
, Kassubek
, F.
, and Gati
, R.
, 2011
, “Radiative Heat Transfer and Effective Transport Coefficients
,” Heat Transfer—Mathematically Modelling, Numerical Methods and Information Technology
, A.
Belmiloudi
, ed., InTech
, New York
, pp. 102
–120
.37.
Magyari
, E.
, and Pantokratoras
, A.
, 2011
, “Note on the Effect of Thermal Radiation in the Linearized Rosseland Approximation on the Heat Transfer Characteristics of Various Boundary Layer Flows
,” Int. Commun. Heat Mass Trans.
, 38
, pp. 554
–556
.10.1016/j.icheatmasstransfer.2011.03.00638.
Abramowitz
, M.
, and Stegun
, I. A.
, 1965
, Handbook of Mathematical Functions
, Chap. 13, Dover Publishers
, New York
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