Page 164 - Design and Operation of Heat Exchangers and their Networks

152 Design and operation of heat exchangers and their networks

The correlation for natural convective heat transfer from an isothermal
downward-facing horizontal round plate was presented by Radziemska and
Lewandowski (2001):
1=5 4 9
Nu l ¼ 0:52Ra 10 Ra l 10 (4.6)
l
For laminar and turbulent natural convection from a horizontal cylinder
with uniform surface temperature, a correlation was developed by Churchill
and Chu (1975) for all Ra range as follows:
92
1=6
8 2 3
> >
< =
Ra d,l
6 7
Nu d,l ¼ 0:60 + 0:387 h i 16=9 5 (4.7)
4
> 9=16 >
: ;
ð
1+ 0:559=Pr l Þ
The correlation for natural convection between two vertical parallel
plates was proposed by Elenbaas (1942a):
b h i 3=4
ð
Nu b,l ¼ Ra b,l 1 e 35H= bRa b,lÞ (4.8)
24H
in which H is the plate height and b is the spacing between the two plates that
is also taken as the characteristic length. The volumetric thermal expansion
coefficient β refers to the surrounding temperature t ∞ , and other properties
refer to the wall temperature. The measured data cover the range of
5
0.2 Ra b b/h 10 .
For a vertical tube, the correlation was given by Elenbaas (1942b) as

3=4
r h f Re l 0:5H= r h Ra r h ,lÞ½ ð Š
Nu r h ,l ¼ Ra r h ,l 1 e (4.9)
f Re l H
where r h is the hydraulic radius and f is the Fanning friction factor for laminar
flow: for round tube, fRe l ¼16; for equilateral triangular tube, f Re l ¼13⅓;
for square tube, f Re l ¼14.225; and for parallel plates, f Re l ¼24. The exper-
4
imental data cover the range of 0.4 (r h /h)Ra r h , l 10 .
For the vertical rectangular tube with arbitrary aspect ratio γ, Eq. (2.136)
or (2.138) can be used for the value of f Re l .

4.1.1.2 Nucleate boiling
The heat transfer coefficient for nucleate boiling of water can be empirically
expressed as (see Baehr and Stephan, 2004, Eq. (4.97))

α ¼ 1:95q 0:72 0:24 (4.10)
p