Boundary-layer forced convective heat transfer at a moving flat surface parallel to a moving stream is presented for the case where the plate is subjected to a variable heat flux. In particular, we assume that the surface heat flux varies with spatial variable x according to a power-law rule. The similarity solutions for the problem are obtained by solving the reduced ordinary differential equations numerically, while exact solutions are provided for certain parametric values. It is noted that even in the case of prescribed surface heat flux, dual solutions exist when the surface and the fluid move in opposite directions.
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References
1.
Siekman
, J.
, 1962
, “The Laminar Boundary Layer Along a Flat Plate
,” Z. Flugwiss.
, 10
, pp. 278
–281
.2.
Klemp
, J. B.
, and Acrivos
, A.
, 1976
, “The Moving-Wall Boundary Layer With Reverse Flow
,” J. Fluid Mech.
, 76
, pp. 363
–381
.10.1017/S00221120760006703.
Abdulhafez
, T. A.
, 1985
, “Skin Friction and Heat Transfer on a Continuous Flat Surface Moving in a Parallel Free Stream
,” Int. J. Heat Mass Transfer
, 28
, pp. 1234
–1237
.10.1016/0017-9310(85)90132-24.
Chappidi
, P. R.
, and Gunnerson
, F. S.
, 1989
, “Analysis of Heat and Momentum Transport Along a Moving Surface
,” Int. J. Heat Mass Transfer
, 32
, pp. 1383
–1386
.10.1016/0017-9310(89)90039-25.
Hussaini
, M. Y.
, Lakin
, W. D.
, and Nachman
, A.
, 1987
, “On Similarity Solutions of a Boundary-Layer Problem With an Upstream Moving Wall
,” SIAM J. Appl. Math.
, 47
, pp. 699
–709
.10.1137/01470486.
Lin
, H. T.
, and Haung
, S. F.
, 1994
, “Flow and Heat Transfer of Plane Surface Moving in Parallel and Reversely to the Free Stream
,” Int. J. Heat Mass Transfer
, 37
, pp. 333
–336
.7.
Sparrow
, E. M.
, and Abraham
, J. P.
, 2005
, “Universal Solutions for the Streamwise Variation of the Temperature of a Moving Sheet in the Presence of a Moving Fluid
,” Int. J. Heat Mass Transfer
, 48
, pp. 3047
–3056
.10.1016/j.ijheatmasstransfer.2005.02.0288.
Cortell
, R.
, 2007
, “Flow and Heat Transfer in a Moving Fluid Over a Moving Flat Surface
,” Theor. Comput. Fluid Dyn.
, 21
, pp. 435
–446
.10.1007/s00162-007-0056-z9.
Afzal
, N.
, Badaruddin
, A.
, and Elgarvi
, A. A.
, 1993
, “Momentum and Heat Transport on a Continuous Flat Surface Moving in a Parallel Stream
,” Int. J. Heat Mass Transfer
, 36
(13
), pp. 3399
–3403
.10.1016/0017-9310(93)90022-X10.
Ishak
, A.
, Nazar
, R.
, and Pop
, I.
, 2009
, “The Effects of Transpiration on the Flow and Heat Transfer Over a Moving Permeable Surface in a Parallel Stream
,” Chem. Eng. J.
, 148
, pp. 63
–67
.10.1016/j.cej.2008.07.04011.
Ishak
, A.
, Nazar
, R.
, and Pop
, I.
, 2009
, “Flow and Heat Transfer Characteristics on a Moving Flat Plate in a Parallel Stream With Constant Surface Heat Flux
,” Heat Mass Transfer
, 45
, pp. 563
–567
.10.1007/s00231-008-0462-912.
Mukhopadhyay
, S.
, Vajravelu
, K.
, and Van Gorder
, R. A.
, 2012
, “Flow and Heat Transfer in a Moving Fluid Over a Moving Non-Isothermal Surface
,” Int. J. Heat Mass Transfer
, 55
, pp. 6632
–6637
.10.1016/j.ijheatmasstransfer.2012.06.07213.
Salleh
, M. Z.
, and Nazar
, R.
, 2008
, “Numerical Investigation of Free Convection Boundary Layer Flow on a Vertical Surface With Prescribed Wall Temperature and Heat Flux
,” J. Qual. Meas. Anal.
, 4
(2
), pp. 57
–69
.14.
Sparrow
, E. M.
, and Gregg
, J. L.
, 1958
, “Similar Solutions for Free Convection From a Non-Isothermal Vertical Plate
,” ASME Trans. J. Heat Transfer
, 80
, pp. 379
–386
.15.
Avissar
, R.
, and Schmidt
, T.
, 1998
, “An Evaluation of the Scale at Which Ground-Surface Heat Flux Patchiness Affects the Convective Boundary Layer Using Large-Eddy Simulations
,” J. Atmos. Sci.
, 55
, pp. 2666
–2689
.10.1175/1520-0469(1998)055<2666:AEOTSA>2.0.CO;216.
Lin
, C. R.
, and Chen
, C. K.
, 1998
, “Exact Solution of Heat Transfer From a Stretching Surface With Variable Heat Flux
,” Heat Mass Transfer
, 33
, pp. 477
–480
.10.1007/s00231005021817.
Van Gorder
, R. A.
, and Vajravelu
, K.
, 2010
, “A Note on Flow Geometries and the Similarity Solutions of the Boundary Layer Equations for a Nonlinearly Stretching Sheet
,” Arch. Appl. Mech.
, 80
, pp. 1329
–1332
.10.1007/s00419-009-0370-618.
Mukhopadhyay
, S.
, 2011
, “Analysis of Heat Transfer in a Moving Fluid Over a Moving Non-Isothermal Flat Surface
,” Chin. Phys. Lett.
, 28
(12
), p. 124706
.10.1088/0256-307X/28/12/12470619.
Mukhopadhyay
, S.
, Bhattacharyya
, K.
, and Layek
, G. C.
, 2011
, “Steady Boundary Layer Flow and Heat Transfer Over a Porous Moving Plate in Presence of Thermal Radiation
,” Int. J. Heat Mass Transfer
, 54
, pp. 2751
–2757
.10.1016/j.ijheatmasstransfer.2011.03.01720.
Turkyilmazoglu
, M.
, 2011
, “Effects of Partial Slip on the Analytic Heat and Mass Transfer for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow
,” ASME J. Heat Transfer
, 133
, p. 122602
.10.1115/1.400455821.
Turkyilmazoglu
, M.
, 2012
, “Multiple Analytic Solutions of Heat and Mass Transfer of Magnetohydrodynamic Slip Flow for Two Types of Viscoelastic Fluids Over a Stretching Surface
,” ASME J. Heat Transfer
, 134
, p. 071701
.10.1115/1.400616522.
Abramowitz
, M.
, and Stegun
, I.
, eds., 1965
, Handbook of Mathematical Functions
, Dover
, New York
.23.
Weidman
, P. D.
, Kubitschek
, D. G.
, and Davis
, A. M. J.
, 2006
, “The Effect of Transpiration on Self-Similar Boundary Layer Flow Over Moving Surfaces
,” Int. J. Eng. Sci.
, 441
(1–12
), pp. 730
–737
.10.1016/j.ijengsci.2006.04.00524.
Mahapatra
, T. R.
, Nandy
, S. K.
, Vajravelu
, K.
, and Van Gorder
, R. A.
, 2011
, “Stability Analysis of Fluid Flow Over a Nonlinearly Stretching Sheet
,” Arch. Appl. Mech.
, 81
, pp. 1087
–1091
.10.1007/s00419-010-0423-x25.
Mahapatra
, T. R.
, Nandy
, S. K.
, Vajravelu
, K.
, and Van Gorder
, R. A.
, 2012
, “Stability Analysis of the Dual Solutions for Stagnation-Point Flow Over a Non-Linearly Stretching Surface
,” Meccanica
, 47
, pp. 1623
–1632
.10.1007/s11012-012-9541-626.
Mahapatra
, T. R.
, Nandy
, S. K.
, Vajravelu
, K.
, and Van Gorder
, R. A.
, 2012
, “Solutions for the Magnetohydrodynamic Stagnation-Point Flow of a Power-Law Fluid Over a Shrinking Sheet
,” ASME J. Appl. Mech.
, 79
, p. 024503
.10.1115/1.4005584Copyright © 2013 by ASME
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