Page 370 - Design and Operation of Heat Exchangers and their Networks

(7.164)
(7.165)
MÞ
t j
…,
5
7
7
X U mk A ΔU nk 7
2,
e
i ¼ 1,
C
C
ð
^ j
t
m¼1
M
C7
C7
C7
C7
X U mk A5
13
! 7
3
δ nj
^ jk
^
CB
CB
+ X U mk A@
U
m¼1
M
δ nj
m¼1
B
B
B
+ X U mk @
B
0
M
T
Θ + BT + C ^
sC w,k
m¼1
U ik U nk
M
as

form
sC w,k
U ik U jk M w 7 θ j 7e + X U ik sC i δ ij 7 M 5 k¼1 + X U mk m¼1 3 1 10 0 7 C CB C CB B U jk U ik Dynamic analysis of heat exchangers and their networks by given are (7.165) Eq. in C B,and A, matrices 355
δ ni
Θ ¼ A e
B
n¼1 B
@
sC w,k M M n¼1 matrix d e dx M M
M w X k¼1 1 C C C X U mk A X B C 1 C C C X U mk A X C the of
¼ X 6 M m¼1 M m¼1 (7.164) elements
2 6 6 6 4 U jk ^ jk ^ in
M j¼1 U
d e i θ dx δ ij δ ij
Δ e i U ik B i T .
C i 0 B B B @ 0 B B B @ Eq. The
_ ! B
_ C _ C i ^ express
2 6 6 4 _ U ik C i U ik ^ i _ C …, e M θ
M w + XX 6 k¼1 6 to
M j¼1 2 6 6 4 e 1 , e 2 , θ
M w k¼1 6 convenient h θ
M 1 XX 6 s j¼1 is It e Θ ¼ where