Page 104 - Design and Operation of Heat Exchangers and their Networks

92 Design and operation of heat exchangers and their networks

For a rating problem, it is not difficult to calculate Eq. (3.121) with com-
puter. However, this expression is not suitable for sizing problems. For a siz-
ing problem, we can use Eq. (2.77) to determine the required exchanger
area:

t t 00 t t 0
0
00
Q ¼ FkAΔt LM ¼ FkA h c h c (3.123)
0
00
ln t t = t t 0
00
h c h c
where F is the correction factor for the logarithmic mean temperature dif-
ference and can be approximately evaluated by
h i c
b
d
F ¼ 1+ aR NTU h (3.124)
h
The coefficients in Eq. (3.124) for many commonly used flow arrange-
ments are given by Roetzel and Spang (2010, 2013, Table 1). For the pure
crossflow,
a ¼ 0:433, b ¼ 1:6, c ¼ 0:267, and d ¼ 0:5
For an accurate design calculation, we can use Eq. (3.124) to get the ini-
tial design and then use Eq. (3.121) to check the design. The design can be
modified by means of Newton’s method until the calculated outlet fluid
temperatures agree with the design requirement.

3.3.2 Crossflow with one fluid unmixed and the other mixed

A typical crossflow with one fluid unmixed and the other mixed is the
crossflow through a tube bundle, in which the fluid flowing through the
tube bundle is laterally well mixed, but inside the tubes, the fluid flows
through each tube without mixing with the fluid flowing in other tubes.
Another example is the crossflow over one tube, in which the outside flow
can be considered as unmixed laterally along the tube, and the tube flow is a
plug flow, that is, laterally well mixed. For convenience, we denote the
unmixed fluid as the “hot” fluid and the other as the “cold” fluid.
The dimensionless energy equations for the crossflow with one fluid (hot
fluid) unmixed and the other (cold fluid) mixed reduces to

∂t h x, yÞ
ð
¼ t c yðÞ t h x, yð Þ (3.125)
∂x
ð
dt c yðÞ 1 NTU h
ð
¼ ½ t h x, yÞ t c yðފdx (3.126)
dy NTU h 0