Page 65 - Design and Operation of Heat Exchangers and their Networks

52 Design and operation of heat exchangers and their networks

t h,w ¼ t h k i Δt d =α h
where Δt d is the true temperature difference for dispersive flow at the
reference point calculated from Eq. (2.113):

0 00 00 0
h
c
c
h
Δt d t t =Pe h + t t =Pe c
C ¼ ¼ 1
0
00
0
00
00
t h t c t t 00 t t 0 = ln t t = t t 0
h c h c h c h c
ð
ð 100 80Þ=∞ +70 20Þ=12
¼1 ¼ 0:9037
ð
ð ½ 100 70Þ 80 20ފ= ln 100 70Þ= 80 20ފ
ð
ð
½
The mean wall temperature is determined by
ð
t h,w,m ¼ t h,m Ct h,m t c,m Þk i =α h

100 + 80 70 + 20
¼ 90 0:9037 1131=3728 ¼ 77:66°C
2 2
With the newly calculated tube length L and wall temperature at the
tube inside t h,w,m for the calculation of Pr w , we can recalculate the
Gnielinski correlation and repeat the earlier steps. After several iterations,
the calculation converges to L¼2.99m.
The detailed calculation procedure can be found in the MatLab code for
Example 2.7 in the appendix.
2.1.6 Application of the dispersion model to axial wall heat
conduction
The dispersion model can also be applied to the approximate consideration
of axial wall heat conduction that has a similar negative effect on efficiency as
fluid dispersion. One effective dispersive Peclet number
Pe eff ¼Pe h ¼Pe c ¼Pe for both fluids is defined and has to be determined
from the construction and heat transfer data at the operation point, with
which the correct outlet temperatures can be calculated. The axial wall heat
conduction in the separating wall and in the outer wall is taken into account
under the assumption of adiabatic outside surface of the heat exchanger.
Simple correlations are developed of the effective Peclet number for coun-
terflow, parallel flow, and mixed-mixed crossflow (Roetzel and Na
Ranong, 2018b; Roetzel and Spang, 2019).
The heat conduction in the walls is expressed with wall Peclet numbers.
For the separating wall, it is defined as

_ L h _ L c
Pe w,h ¼ C h ,Pe w,c ¼ C c (2.116)
λ w A c,w,h λ w A c,w,c