Analytical relations between the heat flux, temperature rise, thermal boundary layer thickness, and characteristic velocity have been derived for the two-dimensional vertical channel, without use of the Boussinesq approximation. Results have been put into the context of well-established scaling behavior in the literature. In addition, useful implications of the analytical results have been described, including a criterion to determine the suitability of a heat-sink configuration to a particular application.
Issue Section:
Electronic Cooling
References
1.
Elenbaas
, W.
, 1942
, “Heat Dissipation of Parallel Plates by Free Convection
,” Physica
, 9
(1
), pp. 1
–28
.2.
Yovanovich
, M. M.
, Teertstra
, P.
, and Muzychka
, Y. S.
, 2001
, “Natural Convection Inside Vertical Isothermal Ducts of Constant Arbitrary Cross-Section
,” AIAA
Paper No. AIAA-2001-0368.3.
Karki
, K. C.
, and Patankar
, S. V.
, 1987
, “Cooling of a Vertical Shrouded Fin Array by Natural Convection: A Numerical study
,” ASME J. Heat Transfer
, 109
(3
), pp. 671
–676
.4.
Ramakrishna
, K.
, Rubin
, S. G.
, and Khosla
, P. K.
, 1982
, “Laminar Natural Convection Along Vertical Square Ducts
,” Numer. Heat Transfer
, 5
(1), pp. 59
–79
.5.
Ofi
, O.
, and Hetherington
, H. J.
, 1977
, “Application of the Finite Element Method to Natural Convection Heat Transfer From the Open Vertical Channel
,” Int. J. Heat Mass Transfer
, 20
(11
), pp. 1195
–1204
.6.
Desrayaud
, G.
, and Fichera
, A.
, 2002
, “Laminar Natural Convection in a Vertical Isothermal Channel With Symmetric Surface-Mounted Rectangular Ribs
,” Int. J. Heat Fluid Flow
, 23
(4
), pp. 519
–529
.7.
Davis
, L. P.
, and Perona
, J. J.
, 1971
, “Development of Free Convection Flow of a Gas in a Heated Vertical Open Tube
,” Int. J. Heat Mass Transfer.
, 14
, pp. 889
–903
.8.
Li
, B.
, and Byon
, C.
, 2015
, “Experimental and Numerical Study on the Heat Sink With Radial Fins and a Concentric Ring Subject to Natural Convection
,” Appl. Therm. Eng.
, 90
, pp. 345
–351
.9.
El-Ghnam
, R. I.
, 2015
, “Numerical Investigation of Natural Convection Heat Transfer Between Two Vertical Plates With Symmetric Heating
,” Int. J. Therm. Technol.
, 5
(1
), pp. 31
–44
.10.
Ahmadi
, M.
, Bahrami
, M.
, and Fakoor-Pakdaman
, M.
, 2014
, “Natural Convection From Vertical Parallel Plates: An Integral Method Solution
,” J. Thermophys. Heat Transfer
, 29
(1
), pp. 1
–10
.11.
Ostrach
, S.
, 1952
, “An Analysis of Laminar-Free-Convection Flow and Heat Transfer About a Flat Plate Parallel to the Direction of the Generating Body Force
,” Lewis Flight Propulsion Laboratory
, Cleveland, OH
, Report No. NACA TN 2635
.12.
Ostrach
, S.
, 1982
, “Low-Gravity Fluid Flows
,” Ann. Rev. Fluid Mech.
, 14
(1
), pp. 313
–345
.13.
Bejan
, A.
, 2004
, Convection Heat Transfer
, 3rd ed., Wiley
, Hoboken, NJ
.14.
Bejan
, A.
, 1987
, “The Basic Scales of Natural Convection Heat and Mass Transfer in Fluids and Fluid-Stratified Porous Media
,” Int. Commun. Heat Mass Transfer
, 14
(2
), pp. 107
–123
.15.
Thirumaleshwar
, M.
, 2006
, Fundamentals of Heat & Mass Transfer
, Dorling Kindersley
, New Delhi, India
.16.
Kays
, W.
, Crawford
, M.
, and Weigand
, B.
, 2005
, Convective Heat and Mass Transfer
, McGraw-Hill
, New York
.17.
Churchill
, S. W.
, and Chu
, H. S.
, 1975
, “Correlating Equations for Laminar and Turbulent Free Convection From a Vertical Plate
,” Int. J. Heat Mass Transfer
, 18
(11
), pp. 1323
–1329
.18.
Boussinesq
, J.
, 1903
, Theorie Analytique de la Chaleur Mise en Harmonie avec la Thermodynamique et avec la Theorie Mecaniquie de la Lumiere
, Gather-Villars
, Paris, France
.19.
Frohlich
, J.
, Laure
, P.
, and Peyret
, R.
, 1992
, “Large Departures From Boussinesq Approximation in the Rayleigh—Benard Problem
,” Phys. Fluids A
, 4
(7
), pp. 1355
–1372
.20.
Becker
, R.
, and Braack
, M.
, 2002
, “Solution of a Stationary Benchmark Problem for Natural Convection With Large Temperature Difference
,” Int. J. Therm. Sci.
, 41
(5
), pp. 428
–439
.21.
Chenoweth
, D. R.
, and Paolucci
, S.
, 1986
, “Natural Convection in an Enclosed Vertical Air Layer With Large Horizontal Temperature Difference
,” J. Fluid Mech.
, 169
, pp. 173
–210
.22.
Darbandi
, M.
, and Hosseinizadeh
, S. F.
, 2007
, “Numerical Study of Natural Convection in Vertical Enclosures Using a Novel Non-Boussinesq Algorithm
,” Num. Heat Trans., Part A
, 52
(9
), pp. 849
–873
.23.
Graebel
, W. P.
, 1981
, “The Influence of Prandtl Number on Free Convection in a Rectangular Cavity
,” Int. J. Heat Mass Transfer
, 24
(1
), pp. 125
–131
.24.
Hung
, K.
, and Cheng
, C.-H.
, 2002
, “Pressure Effects on Natural Convection for Non-Boussinesq Fluid in a Rectangular Enclosure
,” Numer. Heat Transfer Part A
, 41
(5
), pp. 515
–528
.25.
Pesso
, T.
, and Piva
, S.
, 2009
, “Laminar Natural Convection in a Square Cavity: Low Prandtl Numbers and Large Density Differences
,” Int. J. Heat Mass Transfer
, 52
, pp. 1036
–1043
.26.
Narendran
, N.
, and Gu
, Y.
, 2005
, “Life of LED-Based White Light Sources
,” IEEE/OSA J. Disp. Technol.
, 1
(1
), pp. 167
–171
.27.
Gurrum
, S. P. S.
, Suman
, S.
, Shivesh
, K.
, Joshi
, Y. K.
, and Federov
, A. G.
, 2004
, “Thermal Issues in Next-Generation Integrated Circuits
,” IEEE Trans. Device Mater. Reliab.
, 4
(4
), pp. 709
–714
.28.
Kakac
, S.
, and Yener
, Y.
, 1995
, Convective Heat Transfer
, CRC Press
, Boca Raton, FL
.29.
Launder
, B. E.
, Reece
, G. J.
, and Rodi
, W.
, 1975
, “Progress in the Development of a Reynolds-Stress Turbulence Closure
,” J. Fluid Mech.
, 68
(3
), pp. 537
–566
.30.
Durbin
, P. A.
, 1991
, “Near-Wall Turbulence Closure Modeling Without Damping Functions
,” Theor. Comput. Fluid Dyn.
, 3
(1), pp. 1
–13
.31.
Durbin
, P. A.
, 1993
, “A Reynolds-Stress Model for Near-Wall Turbulence
,” J. Fluid Mech.
, 249
, pp. 465
–498
.32.
Durst
, F.
, Ray
, S.
, Uensal
, B.
, and Bayoumi
, O. A.
, 2005
, “The Development Lengths of Laminar Pipe and Channel Flows
,” ASME J. Fluids Eng.
, 127
(6
), pp. 1154
–1160
.33.
Incropera
, F. P.
, and Dewitt
, D. P.
, 1985
, Introduction to Heat Transfer
, Wiley
, Hoboken, NJ
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