The optimal spacing between horizontal cylinders in a fixed volume cooled by natural convection
This is a theoretical, numerical and experimental study of how to select the spacing ( S) between horizontal cylinders in an array with laminar natural convection, such that the total heat transfer ( q) between the array and the ambient is maximized. The volume occupied by the array (height H, width...
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Published in | International journal of heat and mass transfer Vol. 38; no. 11; pp. 2047 - 2055 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Oxford
Elsevier Ltd
01.07.1995
Elsevier |
Subjects | |
Online Access | Get full text |
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Abstract | This is a theoretical, numerical and experimental study of how to select the spacing (
S) between horizontal cylinders in an array with laminar natural convection, such that the total heat transfer (
q) between the array and the ambient is maximized. The volume occupied by the array (height
H, width
W, cylinder length
L) and the cylinder diameter (
D) are arbitrary but fixed, while the spacing (or number of cylinders in the array) varies. The optimal spacing and maximum heat transfer results predicted theoretically are developed into accurate and well tested correlations by means of numerical simulations and experimental measurements. The recommended correlations are
S
opt/D = 2.72(H/D)
1
3
Ra
D
−
1
4
+0.263
and
q
̃
max
= 0.448[(
H
D
)
1
3
Ra
D
−
1
4
]
−
1
6
where
q
̃
max
is the dimensionless maximum overall thermal conductance,
q
̃
max
= q
max
D
2/[HLWk(T
w
- T
∞)]
. The optimal spacing is relatively insensitive to whether the cylinders are isothermal or with uniform heat flux. |
---|---|
AbstractList | This is a theoretical, numerical and experimental study of how to select the spacing (
S) between horizontal cylinders in an array with laminar natural convection, such that the total heat transfer (
q) between the array and the ambient is maximized. The volume occupied by the array (height
H, width
W, cylinder length
L) and the cylinder diameter (
D) are arbitrary but fixed, while the spacing (or number of cylinders in the array) varies. The optimal spacing and maximum heat transfer results predicted theoretically are developed into accurate and well tested correlations by means of numerical simulations and experimental measurements. The recommended correlations are
S
opt/D = 2.72(H/D)
1
3
Ra
D
−
1
4
+0.263
and
q
̃
max
= 0.448[(
H
D
)
1
3
Ra
D
−
1
4
]
−
1
6
where
q
̃
max
is the dimensionless maximum overall thermal conductance,
q
̃
max
= q
max
D
2/[HLWk(T
w
- T
∞)]
. The optimal spacing is relatively insensitive to whether the cylinders are isothermal or with uniform heat flux. |
Author | Stanescu, George Fowler, Alex J. Bejan, Adrian |
Author_xml | – sequence: 1 givenname: Adrian surname: Bejan fullname: Bejan, Adrian organization: Department of Mechanical Engineering, and Materials Science, Duke University, Durham, NC 27708-0300, U.S.A – sequence: 2 givenname: Alex J. surname: Fowler fullname: Fowler, Alex J. organization: Mechanical Engineering Department, University of Massachusetts Dartmouth, North Dartmouth, MA 02747-2300, U.S.A – sequence: 3 givenname: George surname: Stanescu fullname: Stanescu, George organization: Faculty of Mechanical Engineering, Polytechnic University of Bucharest, Bucharest 77206, Romania |
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Cites_doi | 10.1115/1.2911306 10.1115/1.2910457 10.1115/1.3246622 10.1115/1.2910512 10.1016/S0017-9310(83)80028-3 10.1016/0017-9310(92)90213-C 10.1016/0017-9310(72)90231-1 10.1115/1.3247377 10.1016/S0065-2717(08)70075-3 10.1115/1.3245526 10.1016/0017-9310(94)90165-1 |
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Keywords | Temperature distribution Cooling Electronic component Numerical simulation Flow pattern Natural convection Spacing Heat exchangers Cylinder set Optimization Heat transfer |
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References | Sadeghipour, Asheghi (BIB2) 1994; 37 Marsters (BIB3) 1972; 15 Sparrow, Vemuri (BIB5) 1985; 107 Morgan (BIB12) 1975; 11 Bejan (BIB17) 1995 Anand, Kim, Fletcher (BIB10) 1992; 114 Bejan, Sciubba (BIB11) 1992; 35 Tokura, Saito, Kishinami, Muramoto (BIB6) 1983; 105 Bejan, Lage (BIB13) 1990; 112 (BIB14) 1991 (BIB16) 1970; Vol 3, 6 and 11 Bejan (BIB7) 1984 Kim, Anand, Fletcher (BIB9) 1991; 113 Farouk, Guceri (BIB4) 1983; 26 Bar-Cohen, Rohsenow (BIB8) 1984; 106 Kline, McClintock (BIB15) 1953; 3 Guceri, Farouk (BIB1) 1985 Guceri (10.1016/0017-9310(94)00312-J_BIB1) 1985 Anand (10.1016/0017-9310(94)00312-J_BIB10) 1992; 114 (10.1016/0017-9310(94)00312-J_BIB16) 1970; Vol 3, 6 and 11 Kim (10.1016/0017-9310(94)00312-J_BIB9) 1991; 113 (10.1016/0017-9310(94)00312-J_BIB14) 1991 Bejan (10.1016/0017-9310(94)00312-J_BIB7) 1984 Sadeghipour (10.1016/0017-9310(94)00312-J_BIB2) 1994; 37 Marsters (10.1016/0017-9310(94)00312-J_BIB3) 1972; 15 Bar-Cohen (10.1016/0017-9310(94)00312-J_BIB8) 1984; 106 Bejan (10.1016/0017-9310(94)00312-J_BIB17) 1995 Tokura (10.1016/0017-9310(94)00312-J_BIB6) 1983; 105 Bejan (10.1016/0017-9310(94)00312-J_BIB13) 1990; 112 Morgan (10.1016/0017-9310(94)00312-J_BIB12) 1975; 11 Sparrow (10.1016/0017-9310(94)00312-J_BIB5) 1985; 107 Kline (10.1016/0017-9310(94)00312-J_BIB15) 1953; 3 Bejan (10.1016/0017-9310(94)00312-J_BIB11) 1992; 35 Farouk (10.1016/0017-9310(94)00312-J_BIB4) 1983; 26 |
References_xml | – volume: 106 start-page: 116 year: 1984 end-page: 123 ident: BIB8 article-title: Thermally optimum spacing of vertical, natural convection cooled, parallel plates publication-title: J. Heat Transfer contributor: fullname: Rohsenow – year: 1991 ident: BIB14 publication-title: FIDAP, Theoretical Manual, V.6.03 – volume: 26 start-page: 231 year: 1983 end-page: 243 ident: BIB4 article-title: Natural convection from horizontal cylinders in interacting flow fields publication-title: Int. J. Heat Mass Transfer contributor: fullname: Guceri – volume: 105 start-page: 102 year: 1983 end-page: 107 ident: BIB6 article-title: An experimental study of free convection heat transfer from a horizontal cylinder in a vertical array set in free space between parallel walls publication-title: J. Heat Transfer contributor: fullname: Muramoto – volume: 3 year: 1953 ident: BIB15 article-title: Describing uncertainties in single-sample experiments publication-title: Mech. Engng contributor: fullname: McClintock – volume: 37 start-page: 103 year: 1994 end-page: 109 ident: BIB2 article-title: Free convection heat transfer from arrays of vertically separated horizontal cylinders at low Rayleigh numbers publication-title: Int. J. Heat Mass Transfer contributor: fullname: Asheghi – volume: Vol 3, 6 and 11 year: 1970 ident: BIB16 publication-title: Thermophysical Properties of Matter – volume: 107 start-page: 190 year: 1985 end-page: 197 ident: BIB5 article-title: Natural convection/radiation heat transfer from highly populated pin fin arrays publication-title: J. Heat Transfer contributor: fullname: Vemuri – volume: 35 start-page: 3259 year: 1992 end-page: 3264 ident: BIB11 article-title: The optimal spacing of parallel plates cooled by forced convection publication-title: Int. J. Heat Mass Transfer contributor: fullname: Sciubba – volume: 15 start-page: 921 year: 1972 end-page: 933 ident: BIB3 article-title: Arrays of heated horizontal cylinders in natural convection publication-title: Int. J. Heat Mass Transfer contributor: fullname: Marsters – year: 1984 ident: BIB7 article-title: Convection Heat Transfer contributor: fullname: Bejan – volume: 113 start-page: 108 year: 1991 end-page: 115 ident: BIB9 article-title: Free convection between series of vertical parallel plates with embedded line heat sources publication-title: J. Heat Transfer contributor: fullname: Fletcher – year: 1995 ident: BIB17 article-title: Convection Heat Transfer publication-title: Problems 3.25 and 4.29 contributor: fullname: Bejan – volume: 112 start-page: 787 year: 1990 end-page: 790 ident: BIB13 article-title: The Prandtl number effect on the transition in natural convection along a vertical surface publication-title: J. Heat Transfer contributor: fullname: Lage – start-page: 615 year: 1985 end-page: 654 ident: BIB1 article-title: Numerical solutions in laminar and turbulent natural convection publication-title: Natural Convection Fundamentals and Applications contributor: fullname: Farouk – volume: 114 start-page: 515 year: 1992 end-page: 518 ident: BIB10 article-title: The effect of plate spacing on free convection between heated parallel plates publication-title: J. Heat Transfer contributor: fullname: Fletcher – volume: 11 start-page: 199 year: 1975 end-page: 264 ident: BIB12 article-title: The overall convective heat transfer from smooth circular cylinders publication-title: Adv. Heat Transfer contributor: fullname: Morgan – volume: 114 start-page: 515 year: 1992 ident: 10.1016/0017-9310(94)00312-J_BIB10 article-title: The effect of plate spacing on free convection between heated parallel plates publication-title: J. Heat Transfer doi: 10.1115/1.2911306 contributor: fullname: Anand – volume: 112 start-page: 787 year: 1990 ident: 10.1016/0017-9310(94)00312-J_BIB13 article-title: The Prandtl number effect on the transition in natural convection along a vertical surface publication-title: J. Heat Transfer doi: 10.1115/1.2910457 contributor: fullname: Bejan – year: 1991 ident: 10.1016/0017-9310(94)00312-J_BIB14 – volume: 106 start-page: 116 year: 1984 ident: 10.1016/0017-9310(94)00312-J_BIB8 article-title: Thermally optimum spacing of vertical, natural convection cooled, parallel plates publication-title: J. Heat Transfer doi: 10.1115/1.3246622 contributor: fullname: Bar-Cohen – year: 1995 ident: 10.1016/0017-9310(94)00312-J_BIB17 article-title: Convection Heat Transfer contributor: fullname: Bejan – volume: 113 start-page: 108 year: 1991 ident: 10.1016/0017-9310(94)00312-J_BIB9 article-title: Free convection between series of vertical parallel plates with embedded line heat sources publication-title: J. Heat Transfer doi: 10.1115/1.2910512 contributor: fullname: Kim – volume: 26 start-page: 231 year: 1983 ident: 10.1016/0017-9310(94)00312-J_BIB4 article-title: Natural convection from horizontal cylinders in interacting flow fields publication-title: Int. J. Heat Mass Transfer doi: 10.1016/S0017-9310(83)80028-3 contributor: fullname: Farouk – volume: 35 start-page: 3259 year: 1992 ident: 10.1016/0017-9310(94)00312-J_BIB11 article-title: The optimal spacing of parallel plates cooled by forced convection publication-title: Int. J. Heat Mass Transfer doi: 10.1016/0017-9310(92)90213-C contributor: fullname: Bejan – start-page: 615 year: 1985 ident: 10.1016/0017-9310(94)00312-J_BIB1 article-title: Numerical solutions in laminar and turbulent natural convection contributor: fullname: Guceri – volume: 15 start-page: 921 year: 1972 ident: 10.1016/0017-9310(94)00312-J_BIB3 article-title: Arrays of heated horizontal cylinders in natural convection publication-title: Int. J. Heat Mass Transfer doi: 10.1016/0017-9310(72)90231-1 contributor: fullname: Marsters – volume: 3 year: 1953 ident: 10.1016/0017-9310(94)00312-J_BIB15 article-title: Describing uncertainties in single-sample experiments publication-title: Mech. Engng contributor: fullname: Kline – volume: Vol 3, 6 and 11 year: 1970 ident: 10.1016/0017-9310(94)00312-J_BIB16 – volume: 107 start-page: 190 year: 1985 ident: 10.1016/0017-9310(94)00312-J_BIB5 article-title: Natural convection/radiation heat transfer from highly populated pin fin arrays publication-title: J. Heat Transfer doi: 10.1115/1.3247377 contributor: fullname: Sparrow – volume: 11 start-page: 199 year: 1975 ident: 10.1016/0017-9310(94)00312-J_BIB12 article-title: The overall convective heat transfer from smooth circular cylinders publication-title: Adv. Heat Transfer doi: 10.1016/S0065-2717(08)70075-3 contributor: fullname: Morgan – volume: 105 start-page: 102 year: 1983 ident: 10.1016/0017-9310(94)00312-J_BIB6 article-title: An experimental study of free convection heat transfer from a horizontal cylinder in a vertical array set in free space between parallel walls publication-title: J. Heat Transfer doi: 10.1115/1.3245526 contributor: fullname: Tokura – year: 1984 ident: 10.1016/0017-9310(94)00312-J_BIB7 contributor: fullname: Bejan – volume: 37 start-page: 103 year: 1994 ident: 10.1016/0017-9310(94)00312-J_BIB2 article-title: Free convection heat transfer from arrays of vertically separated horizontal cylinders at low Rayleigh numbers publication-title: Int. J. Heat Mass Transfer doi: 10.1016/0017-9310(94)90165-1 contributor: fullname: Sadeghipour |
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SubjectTerms | Convection and heat transfer Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Physics Turbulent flows, convection, and heat transfer |
Title | The optimal spacing between horizontal cylinders in a fixed volume cooled by natural convection |
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