Convection heat transfer below a horizontal, hot, and isothermal strip of infinite length and width of 2L embedded in fluids with different Prandtl number (Pr) and Nusselt number (Nu) is analyzed with the aid of integral method. A new concept is utilized to determine the boundary layer thickness at the strip's edge, which is based on matching the flow rate of the boundary layer below the strip at its edge and the flow rate of the plume, which forms after the heated fluid detaches from the strip's edge. In addition to these novelties, a numerical model is developed to verify the analytical framework, and an excellent agreement is observed between the analytical and numerical models.
Issue Section:
Natural and Mixed Convection
References
1.
Mo
, D. C.
, Zou
, G. S.
, Wang
, Y. Q.
, and Lu
, S. S.
, 2014
, “Flat Loop Heat Pipe With Bi-Transport Loops for Graphics Card Cooling
,” Heat Transfer Eng.
, 35
(11–12
), pp. 1071
–1076
.10.1080/01457632.2013.8630952.
Ammann
, M. W.
, Walker
, A. M.
, Stackhouse
, S.
, Wookey
, J.
, Forte
, A. M.
, Brodholt
, J. P.
, and Dobson
, D. P.
, 2014
, “Variation of Thermal Conductivity and Heat Flux at the Earth's Core Mantle Boundary
,” Earth Planet. Sci. Lett.
, 390
, pp. 175
–185
.10.1016/j.epsl.2014.01.0093.
Yokoi
, S.
, Katsumata
, M.
, and Yoneyama
, K.
, 2014
, “Variability in Surface Meteorology and Air–Sea Fluxes Due to Cumulus Convective Systems Observed During CINDY/DYNAMO
,” J. Geophys. Res.: Atmos.
, 119
(5
), pp. 2064
–2078
.10.1002/2013JD0206214.
Clifton
, J. V.
, and Chapman
, A. J.
, 1969
, “Natural-Convection on a Finite-Size Horizontal Plate
,” Int. J. Heat Mass Transfer
, 12
(12
), pp. 1573
–1584
.10.1016/0017-9310(69)90092-15.
Fujii
, T.
, and Imura
, H.
, 1972
, “Natural-Convection Heat Transfer From a Plate With Arbitrary Inclination
,” Int. J. Heat Mass Transfer
, 15
(4
), pp. 755
–767
.10.1016/0017-9310(72)90118-46.
Saundersm
, O. A.
, Fishenden
, M.
, and Mansion
, H. D.
, 1935
, “Some Measurements of Convection by an Optical Method
,” Engineering
, 139
, pp. 483
–485
.7.
Birkebak
, R. C.
, and Abdulkadir
, A.
, 1970
, “Heat Transfer by Natural Convection From the Lower Side of Finite Horizontal, Heated Surface
,” Proceedings of the Fourth International Heat Transfer Conference
, V.
Grigull
, and E.
Hahne
, eds., Elsevier
, Amsterdam
, NC2.2, pp. 1
–10
.8.
Aihara
, T.
, Yamada
, Y.
, and Endo
, S.
, 1972
, “Free Convection Along the Downward Facing Surface of a Heated Horizontal Plate
,” Int. J. Heat Mass Transfer
, 15
(12
), pp. 2535
–2549
.10.1016/0017-9310(72)90145-79.
Restrepo
, F.
, and Glicksman
, L. R.
, 1974
, “The Effect of Edge Conditions on Natural Convection From a Horizontal Plate
,” Int. J. Heat Mass Transfer
, 17
(1
), pp. 135
–142
.10.1016/0017-9310(74)90046-510.
Sheriff
, N.
, and Davies
, N. W.
, 1979
, “Liquid Metal Natural Convection From Plane Surfaces: A Review Including Recent Sodium Measurements
,” Int. J. Heat Fluid Flow
, 1
(4
), pp. 149
–154
.10.1016/0142-727X(79)90002-X11.
Fussey
, D. E.
, and Warneford
, I. P.
, 1978
, “Free Convection From a Downward Facing Inclined Flat Plate
,” Int. J. Heat Mass Transfer
, 21
(2
), pp. 119
–126
.10.1016/0017-9310(78)90214-412.
Faw
, R. E.
, and Dullforce
, T. A.
, 1981
, “Holographic Interferometry Measurement of Convective Heat Transport Beneath a Heated Horizontal Plate in Air
,” Int. J. Heat Mass Transfer
, 24
(5
), pp. 859
–869
.10.1016/S0017-9310(81)80009-913.
Faw
, R. E.
, and Dullforce
, T. A.
, 1982
, “Holographic Interferometry Measurement of Convective Heat Transport Beneath a Heated Horizontal Circular Plate in Air
,” Int. J. Heat Mass Transfer
, 25
(8
), pp. 1157
–1166
.10.1016/0017-9310(82)90210-114.
Hatfield
, D. W.
, and Edwards
, D. K.
, 1981
, “Edge and Aspect Ratio Effects on Natural Convection From the Horizontal Heated Plate Facing Downwards
,” Int. J. Heat Mass Transfer
, 24
(6
), pp. 1019
–1024
.10.1016/0017-9310(81)90132-015.
Kobus
, C. J.
, and Wedekind
, G. L.
, 2001
, “An Experimental Investigation Into Natural Convection Heat Transfer From Horizontal Isothermal Circular Disks
,” Int. J. Heat Mass Transfer
, 44
(17
), pp. 3381
–3384
.10.1016/S0017-9310(00)00330-616.
Kobus
, C. J.
, and Wedekind
, G. L.
, 2002
, “An Empirical Correlation for Natural Convection Heat Transfer From Thin Isothermal Circular Disks at Arbitrary Angles of Inclination
,” Int. J. Heat Mass Transfer
, 45
(5
), pp. 1159
–1163
.10.1016/S0017-9310(01)00213-717.
Kobus
, C. J.
, 2007
, “Investigation of Natural Convection Heat Transfer From Uniformly Heated (Isoflux), Thin, Stationary Circular Disks at Arbitrary Angles of Inclination
,” Exp. Therm. Fluid Sci.
, 31
(3
), pp. 191
–195
.10.1016/j.expthermflusci.2006.03.02718.
Singh
, S. N.
, and Birkebak
, R. C.
, 1969
, “Laminar Free Convection From a Horizontal Infinite Strip Facing Downwards
,” Z. Angew. Math. Phys.
, 20
(4
), pp. 454
–461
.10.1007/BF0159503819.
Fujii
, T.
, and Fujii
, M.
, 1976
, “The Dependence of Local Nusselt Number on Prandtl Number in the Case of Free Convection Along a Vertical Surface With Uniform Heat Flux
,” Int. J. Heat Mass Transfer
, 19
(1
), pp. 121
–122
.20.
Hollands
, K. G. T.
, Raithby
, G. D.
, and Konicek
, L.
, 1975
, “Correlation Equations for Free Convection Heat Transfer in Horizontal Layers of Air and Water
,” Int. J. Heat Mass Transfer
, 18
(7–8
), pp. 879
–884
.10.1016/0017-9310(75)90179-921.
Singh
, S. N.
, Birkebak
, R. C.
, and Drake
, R. M.
, 1969
, “Laminar Free Convection Heat Transfer From Downward-Facing Horizontal Surfaces of Finite Dimensions
,” Prog. Heat Mass Transfer
, 2
, pp. 87
–98
.22.
Fuji
, T.
, Honda
, H.
, and Morioka
, I.
, 1973
, “A Theoretical Study of Natural Convection Heat Transfer From Downward-Facing Horizontal Surfaces With Uniform Heat Flux
,” Int. J. Heat Mass Transfer
, 16
(3
), pp. 611
–627
.10.1016/0017-9310(73)90227-523.
Schulenberg
, T.
, 1984
, “Natural Convection Heat Transfer to Liquid Metals Below Downward Facing Horizontal Surfaces
,” Int. J. Heat Mass Transfer
, 27
(3
), pp. 433
–441
.10.1016/0017-9310(84)90290-424.
Schulenberg
, T.
, 1985
, “Natural Convection Heat Transfer Below Downward Facing Horizontal Surfaces
,” Int. J. Heat Mass Transfer
, 28
(2
), pp. 467
–477
.10.1016/0017-9310(85)90080-825.
Miyamoto
, M.
, Katoh
, Y.
, Kurima
, J.
, Kurihara
, S.
, and Yamashita
, K.
, 1985
, “Free Convection Heat Transfer From Vertical and Horizontal Short Plates
,” Int. J. Heat Mass Transfer
, 28
(9
), pp. 1733
–1745
.10.1016/0017-9310(85)90147-426.
Higuera
, F. J.
, 1993
, “Natural Convection Below Heated Horizontal Rectangular Plates
,” Int. J. Heat Mass Transfer
, 36
(14
), pp. 3565
–3671
.10.1016/0017-9310(93)90174-527.
Radziemska
, E.
, and Lewandowski
, W. M.
, 2001
, “Heat Transfer by Natural Convection From an Isothermal Downward-Facing Round Plate in Unlimited Space
,” Appl. Energy
, 68
(4
), pp. 347
–366
.10.1016/S0306-2619(00)00061-128.
Dayan
, A.
, Kushnir
, R.
, and Ullmann
, A.
, 2002
, “Laminar Free Convection Underneath a Hot Horizontal Infinite Flat Strip
,” Int. J. Heat Mass Transfer
, 45
(19
), pp. 4021
–4031
.10.1016/S0017-9310(02)00116-329.
Samanta
, S.
, and Guha
, A.
, 2012
, “A Similarity Theory for Natural Convection From a Horizontal Plate for Prescribed Heat Flux or Wall Temperature
,” Int. J. Heat Mass Transfer
, 55
(13–14
), pp. 3857
–3868
.10.1016/j.ijheatmasstransfer.2012.02.03130.
Khani
, F.
, Aziz
, A.
, and Hamedi-Nezhad
, S.
, 2012
, “Simultaneous Heat and Mass Transfer in Natural Convection About an Isothermal Vertical Plate
,” J. King Saud Univ., Sci.
, 24
(2
), pp. 123
–129
.10.1016/j.jksus.2010.09.00231.
Abouei Mehrizi
, A.
, Vazifeshenas
, Y.
, and Domairry
, G.
, 2012
, “New Analysis of Natural Convection Boundary Layer Flow on a Horizontal Plate With Variable Wall Temperature
,” J. Theor. Appl. Mech.
, 50
(4
), pp. 1001
–1010
.32.
Arpaci
, V. S.
, and Larsen
, P. S.
, 1984
, Convection Heat Transfer
, Prentice-Hall
, Englewood Cliffs, NJ
, pp. 164
–202
.33.
Koyama
, H.
, and Nakayama
, A.
, 1982
, “An Integral Method in Free Convection Flows Under Non-Uniform Gravity
,” Lett. Heat Mass Transfer
, 9
(3
), pp. 151
–158
.10.1016/0094-4548(82)90053-434.
Bejan
, A.
, 1995
, Convection Heat Transfer
, 2nd ed., Wiley
, New York
, pp. 387
–392
.10.1002/978111867162735.
Turner
, J. S.
, 1973
, Buoyancy Effects in Fluids
, Cambridge University Press
, Cambridge, New York, pp. 167
–176
.10.1017/CBO978051160882736.
Kaminski
, E.
, Tait
, S.
, and Carazzo
, G.
, 2005
, “Turbulent Entrainment in Jets With Arbitrary Buoyancy
,” J. Fluid Mech.
, 526
, pp. 361
–376
.10.1017/S002211200400320937.
Patankar
, S. V.
, 1980
, Numerical Heat Transfer and Fluid Flow
, Hemisphere
, New York
.Copyright © 2015 by ASME
You do not currently have access to this content.