50
eq 12
eq 13
eq 14
10
eq 15
5
1
0.5
3
4
5
6
10
10
10
10
Grashof Number
Figure 2. Heat transfer correlations for vertical enclosures.
C
Y
Nu =
AGr B
(16)
W
where Y/W is the height/width ratio, and A, B, and C are the constants for air (see
table below).
Reference
A
B
C
eq
Newell and Schmidt (1969)
0.155
0.315
0.265
(17)
Eckert and Carlson (1961)
0.119
0.3
0.1
(18)
Jakob (1949)
0.18
0.25
0.111
(19)
MacGregor and Emery (1969)
0.25
0.25
0.25
(20)
Horizontal rectangular enclosures are described as cavities in which the lower
horizontal surface is heated while the upper surface is cooled; the sides are insu-
lated. The correlations obtained by several researchers can be presented in the form
of eq 10, when the Prandtl number for air is taken as 0.72. The characteristic length
L in the Ra number is the height of the enclosure. The constants for several corre-
lations are shown in the following table (Gebhart et al. 1988).
Reference
A
B
eq
Dropkin and Somerscales (1965)
0.0673
0.3333
(21)
Silveston (1958)
0.0877
0.31
(22)
Kraichnan (1962)
0.1524
0.3333
(23)
Probably the most investigated enclosure containing an interior heat source is
a concentric pipe system. Gebhart et al. (1988) reviewed the significant number of
experimental and numerical investigations of this geometry, noting that different
nondimensional systems have been used in most studies. For correlations based
on mean heat transfer rates, gap width (outer radius-inner radius) is often used as
the characteristic length (L). An example of this is the following equation by Grigull
and Hauf (1966):
5
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