Page 128 - Design and Operation of Heat Exchangers and their Networks

116 Design and operation of heat exchangers and their networks

in which

p ffiffiffiffi 1 p ffiffiffiffi p ffiffiffiffi
ln R + R 1= R
2
ERðÞ ¼ p ffiffiffiffi p ffiffiffiffi (3.224)
R 1= R
p ffiffiffiffi p ffiffiffiffi n

μ ¼ ERðÞ R 1= R (3.225)
2CN
2πnkhs
CN ¼ p ffiffiffiffiffiffiffiffiffiffiffiffi (3.226)
_ _
C h C c
_
C min
R ¼ _ (3.57), (3.227)
C max
We assume that the hot fluid has smaller thermal capacity rate,
_
_
C min ¼ C h . Then, the temperatures of the hot and cold fluids change with
the current radius r of a spiral heat exchanger according to
G μ xðÞ
t h x ðÞ ¼ 1 p ffiffiffiffiffiffi (3.228)
2CN R h =n + RG μ CNð Þ
G μ CNÞ G μ xðÞ
ð
t c xðÞ ¼ p ffiffiffiffiffiffi (3.229)
ð
2CN= n R h Þ + G μ CNð Þ
where
CN
x ¼ r (3.230)
ns
2 μ
ð 1+ x Þ 1
G μ xðÞ ¼ (3.231)
μ
3.4.3 Spiral heat exchanger with an open area at the center

To model and design a spiral heat exchanger with an open area at the
center (r 0 ≫ s), Bes (2001) proposed a method by which two hypothet-
ical spiral heat exchangers connected in series was supposed. The first spi-
ral heat exchanger has flow properties and a geometry as a real one, but
the channels are assumed to be extended up to the center of the appa-
ratus, and its parameters are denoted with the subscript “1.” The second
one has the same parameters but was fitted in the open space at the center
of real spiral heat exchanger, and its parameters are denoted with the
subscript “0.”