-0.02 * L D*

i

i

for 30, 000 ≤ *Gr*L ≤ 716, 000

(24)

and 0.55 ≤ *L D *≤ 2.65

i

where *D*i is the diameter of the internal cylinder. Gap width, however, does not

for the two surfaces are not obtained individually, but are lumped together. The

is defined as the ratio of actual heat flow to that due to conduction alone across

the region. For concentric cylinders, the equivalent conductivities based on the

inside and outside surface areas are

( )i

*D *

= i i ln o

=

(25)

*D*i

2*k*

( )o

*D *

= o o ln o

=

(26)

*D*i

2*k*

where

2

.

(27)

ln (Do Di )

The total energy lost by one cylinder equals that gained by the other (i.e., eq 25

equals eq 26). The subscript *i *refers to the inner cylinder and *o *to the outer one,

and *Nu*cond is the Nusselt number for pure conduction between concentric cylin-

ders (Gebhart et al. 1988).

Kuehn and Goldstein (1978) combined a large amount of data and obtained the

following correlations for *Pr *= 0.7 (air):

2

(28)

(

) + (0.12*Ra *)

15 1/15

15

1/ 4

1/ 3

ln 1 + 2

0.5*Ra*D

i

-2

(29)

(

) (

)

1/ 3 15 1/15

1/ 4 15

+

ln 1 - 2

0.12*Ra*D

o

o

(

)

φb =

=

(30)

-1

1

1

+

(31)

*Nu*i Nuo

2

(32)

ln (*D*o Di )

[

]

+ (Nuconv )

15 1/15

15

(33)

6

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