Heat transfer often occurs effectively from horizontal elements of relatively complex shapes in natural convective cooling of electronic and electrical devices used in industrial applications. The effect of complex surface shapes on laminar natural convective heat transfer from horizontal isothermal polygons of hexagonal and octagonal flat surfaces facing upward and downward of different aspect ratios has been numerically investigated. The polygons’ surface is embedded in a large surrounding plane adiabatic surface, where the adiabatic surface is in the same plane as the surface of the heated element. For the Boussinesq approach used in this work, the density of the fluid varies with temperature, which causes the buoyancy force, while other fluid properties are assumed constants. The numerical solution of the full three-dimensional form of governing equations is obtained by using the finite volume method-based computational fluid dynamics (CFD) code, FLUENT14.5. The solution parameters include surface shape, dimensionless surface width, different characteristic lengths, the Rayleigh number, and the Prandtl number. These parameters are considered as follows: the Prandtl number is 0.7, the Rayleigh numbers are between 103 and 108, and for various surface shapes the width-to-height ratios are between 0 and 1. The effect of different characteristic lengths has been investigated in defining the Nusselt and Rayleigh numbers for such complex shapes. The effect of these parameters on the mean Nusselt number has been studied, and correlation equations for the mean heat transfer rate have been derived.

References

References
1.
Bejan
,
A.
,
1995
,
Convection Heat Transfer
,
John Willey & Sons, Inc.
,
New York
.
2.
Kakac
,
S.
, and
Yener
,
Y.
,
1995
,
Convective Heat Transfer
,
CRC Press
,
Boca Raton, FL
.
3.
Kays
,
W.
, and
Crawford
,
M.
,
2005
,
Convective Heat and Mass Transfer
,
McGraw-Hill
,
New York
.
4.
Martynenko
,
O.
, and
Khramtsov
,
P.
,
2005
,
Free-Convective Heat Transfer
,
Springer
,
Berlin
.
5.
Oosthuizen
,
P.
, and
Naylor
,
D.
,
1999
,
Introduction to Convective Heat Transfer Analysis
,
McGraw-Hill
,
New York
.
6.
Rohsenow
,
W.
,
Hartnett
,
J.
, and
Cho
,
Y.
,
1998
,
Handbook of Heat Transfer
,
McGraw-Hill
,
New York
.
7.
Rotem
,
Z.
, and
Claassem
,
L.
,
1996
, “
Natural Convection Above Unconfined Horizontal Surfaces
,”
J. Fluid Mech.
,
38
(
1
), pp.
173
192
.
8.
Lloyd
,
J.
, and
Moran
,
W.
,
1974
, “
Natural Convection Adjacent to Horizontal Surface of Various Platforms
,”
ASME J. Heat Transf.
,
96
, pp.
443
447
(74-WA/HT-66).
9.
Goldstein
,
R.
, and
Lau
,
K.
,
1983
, “
Laminar Natural Convection From a Horizontal Plate and the Influence Plate-Edge Extensions
,”
J. Fluid Mech.
,
129
, pp.
55
75
.
10.
Lewandowski
,
W.
,
1991
, “
Natural Convection Heat Transfer From Plates of Finite Dimensions
,”
Int. J. Heat Mass Transf.
,
34
(
3
), pp.
875
885
.
11.
Lewandowski
,
W.
,
Radziemska
,
E.
,
Buzuk
,
M.
, and
Bieszk
,
H.
,
2000
, “
Free Convection Heat Transfer and Fluid Flow Above Horizontal Rectangular Plates
,”
Appl. Energy
,
66
, pp.
177
197
.
12.
Fishenden
,
M.
, and
Saunders
,
O.
,
1950
,
An Introduction to Heat Transfer
,
Oxford University Press
,
London
.
13.
Al-Arabi
,
M.
, and
El-Riedy
,
M.
,
1986
, “
Natural Convection Heat Transfer From Isothermal of Horizontal Plates of Different Shapes
,”
Int. J. Heat Mass Transf.
,
19
(
12
), pp.
1399
1404
.
14.
Al-Arabi
,
M.
, and
Sakr
,
B.
,
1988
, “
Natural Convection Heat Transfer From Inclined Isothermal Plates
,”
Int. J. Heat Mass Transf.
,
31
(
3
), pp.
559
566
.
15.
Churchill
,
S. W.
,
1983
, “Free Convection Around Immersed Bodies,”
Heat Exchanger Design Handbook, Section 2, 5, 7
,
E. U.
Schlünder
, ed.,
Hemispheres
,
New York
.
16.
Fujii
,
T.
, and
Imura
,
H.
,
1972
, “
Natural Convection Heat Transfer From a Plate With Arbitrary Inclination
,”
Int. J. Heat Mass Transf.
,
15
, pp.
755
767
.
17.
Yousef
,
W.
,
Tarasuk
,
J.
, and
McKeen
,
W.
,
1982
, “
Free Convection Heat Transfer From Upward-Facing Isothermal Horizontal Surfaces
,”
J. Heat Transf.
,
104
, pp.
493
500
.
18.
Cheng
,
K.
, and
Kim
,
Y.
,
1988
, “
Flow Visualization Convection Flow Over Horizontal and Slightly Inclined Constant-Temperature Plate
,”
J. Heat Transf.
,
110
, pp.
608
615
.
19.
Clausing
,
A.
, and
Berton
,
J.
,
1989
, “
An Experimental Investigation of Natural Convection From an Isothermal Horizontal Plate
,”
J. Heat Transf.
,
111
, pp.
904
908
.
20.
Pretot
,
S.
,
Zeghmati
,
B.
, and
Le Palec
,
G.
,
2000
, “
Theoretical and Experimental Study of Natural Convection on a Horizontal Plate
,”
Appl. Therm. Eng.
,
20
, pp.
873
891
.
21.
Martorell
,
I.
,
Herrero
,
J.
, and
Grau
,
F.
,
2003
, “
Natural Convection From Narrow Horizontal Plates at Moderate Rayleigh Numbers
,”
Int. J. Heat Mass Transf.
,
46
(
13
), pp.
2389
2402
.
22.
Chamberlain
,
M.
,
Hollands
,
K.
, and
Raithby
,
G.
,
1985
, “
Experiments and Theory on Natural Convection Heat Transfer From Bodies of Complex Shape
,”
J. Heat Transf.
,
107
, pp.
624
629
.
23.
Yovanovich
,
M.
, and
Jafarpur
,
K.
,
1993
, “
Models of Laminar Natural Convection From Vertical and Horizontal Isothermal Cuboids for All Prandtl Numbers and All Rayleigh Numbers Below 1011
,” ,
264
, pp.
111
126
.
24.
Yovanovich
,
M.
, and
Jafarpur
,
K.
,
1993
, “
Bounds on Laminar Natural Convection From Isothermal Disks and Finite Plates of Arbitrary Shape for All Orientations and Prandtl Numbers
,” ,
264
, pp.
93
110
.
25.
Lee
,
S.
,
Yovanovich
,
M.
, and
Jafarpur
,
K.
,
1991
, “
Effects of Geometry and Orientation on Laminar Natural Convection From Isothermal Bodies
,”
J. Thermophys. Heat Transf.
,
5
(
2
), pp.
208
216
.
26.
Yovanovich
,
M.
,
1987
, “
On the Effect of Shape, Aspect Ratio and Orientation Upon Natural Convection From Isothermal Bodies of Complex Shape
,”
ASME National Heat Transfer Conference
,
Pittsburg, CA
,
Aug. 8–12
.
27.
Oosthuizen
,
P.
, and
Narayanan
,
S.
,
2016
, “
A Numerical Study of Natural Convective Heat Transfer From an Inclined Square Flat Element With a Uniform Surface Heat Flux Imbedded in a Flat Adiabatic Surrounding Surface
,”
Proceedings of ASME International Mechanical Engineering Congress and Exposition IMECE
,
Phoenix, AZ
,
Nov. 11–17
.
28.
Oosthuizen
,
P.
, and
Kalendar
,
A.
,
2015
, “
Laminar and Turbulent Natural Convective Heat Transfer From a Horizontal Circular Element With Unheated Inner Circular Section
,”
Proceedings of 23rd Annual Conference of the Society of Canada
,
Waterloo, ON
,
Jun. 7–10
.
29.
Oosthuizen
,
P.
, and
Kalendar
,
A.
,
2016
Numerical Study of the Simultaneous Natural Convective Heat Transfer From the Upper and Lower Surfaces of a Thin Isothermal Horizontal Circular Plate
,”
Proceedings of ASME International Mechanical Engineering Congress and Exposition IMECE
,
Phoenix, AZ
,
Nov. 11–17
.
30.
Oosthuizen
,
P.
,
2015
, “
A Numerical Study of Natural Convective Heat Transfer From a Horizontal Isothermal Square Element With an Unheated Square Adiabatic Inner Section
,”
Proceedings of the 11th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
,
Skukuza, SA
,
Jul. 20–23
.
31.
Oosthuizen
,
P.
,
2014
, “
A Numerical Study of Natural Convective Heat Transfer From a Horizontal Isothermal Square Element Imbedded in Adiabatic Surface With a Parallel Adiabatic Covering Surface
,”
Proceedings of the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT2014)
,
Jun.
, Paper 1569876763.
32.
Oosthuizen
,
P.
,
2014
, “
Natural Convective Heat Transfer From a Horizontal Rectangular Isothermal Element Imbedded in a Plane Adiabatic Surface With a Parallel Adiabatic Covering Surface
,”
Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition
, Paper IMECE2014-36780.
33.
Oosthuizen
,
P.
,
2014
, “
Natural Convective Heat Transfer From a Horizontal Isothermal Circular Element Imbedded in a Flat Adiabatic Surface With a Parallel Adiabatic Covering Surface
,”
Proceeding of the AIAA/ASME Joint Thermophysics and Heat Transfer Conference
,
Jun.
, Paper AIAA-2014-3357.
34.
Oosthuizen
,
P.
,
2015
, “
Laminar, Transitional and Turbulent Natural Convective Heat Transfer From a Horizontal Rectangular Isothermal Element Imbedded in a Flat Adiabatic Surrounding Surface
,”
Proceedings of the 6th ICHMT International Symposium on Advance Computational Heat Transfer
, Paper CHT-15-145.
35.
Oosthuizen
,
P.
,
2015
, “
A Numerical Study of Natural Convective Heat Transfer From a Pair of Adjacent Horizontal Isothermal Square Elements Imbedded in an Adiabatic Surface Effect of Element Spacing on Heat Transfer Rate
,”
Proceedings of the 11th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics HEFAT
.
36.
Oosthuizen
,
P.
,
2015
, “
A Numerical Study of Natural Convective Heat Transfer From Horizontal Isothermal Heated Elements of Complex Shape
,”
Proceedings 1st Thermal and Fluids Engineering Summer Conference ASTFE
, Paper TFESC-12863.
37.
Oosthuizen
,
P.
, and
Kalendar
,
A.
,
2016
, “
Numerical Study of Natural Convective Heat Transfer From Horizontal Heated Elements of Relatively Complex Shape Having a Uniform Surface Heat Flux
,”
Proceedings of 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
,
Malaga, Spain
,
Jul. 11–13
.
38.
Kalendar
,
A.
,
Karar
,
S.
,
Kalendar
,
A.
, and
Oosthuizen
,
P.
,
2017
, “
Correlations for Natural Convective Heat Transfer From Isothermal Surface of Octagonal and Hexagonal Shapes of Different Aspect Ratios
,”
J. Heat Transf. Asian Res.
,
46
(
4
), pp.
262
283
.
39.
Oosthuizen
,
P.
, and
Kalendar
,
A.
,
2018
,
Natural Convective Heat Transfer From Horizontal and Near Horizontal Surfaces
,
Springer Briefs in Applied Science and Technology, Thermal Engineering and Applied Science, Springer
,
New York
.
You do not currently have access to this content.