Page 372 - Design and Operation of Heat Exchangers and their Networks

356
(7.167)
(7.166)
(7.168)
MÞ
…,
MÞ
2,
¼ 1,
…,
2,
j
i,
¼ 1,
ð
3
7
7
5
7
δ jn X U mk A ΔU nk 7
MÞ
j
i,
e
ð
…,
C7
13
C7
C7
X U mk A5
C7
C
1
C
C
C
2,
¼ 1,
U jk
^ jk
^
m¼1
U
M
M
j
i,
ð
7
5
3
7
7
δ nj
! 7
10
X U mk A@
CB
CB
CB
CB
X U mk @
0
B
B
B
B
X U ik
k¼1
M w
U ik U nk
M
m¼1
M
+
U ik
+
sC i
+
sC w,k
sC w,k
δ ij Design and operation of heat exchangers and their networks m¼1 m¼1 respectively. parameters, transfer heat and rates flow thermal form: matrix the in expressed be can i ^ (7.169) TðÞ x 00 TðÞ G 0 ^ 0 G ^ T x 0 GTðÞ 1 h x 00 + Δ e s 1 h ^ ^0 ^ ^ (7.170) x 00 i G 00 G 00 ^ T
X
n¼1
M
X U mk 0 B B δ in B @ 1 _ the of conditions G
U ik U jk M + m¼1 M n¼1 1 C C C X U mk A C i C e ΘðÞ + Δ e 0 T 0 x 00 G
sC w,k 1 C C C X U mk A X B C ^ jk U M ^ m¼1 transforms boundary + G e ΘðÞ + Δ e 000 T 0
M w X k¼1 U jk Θ x 00
¼ C i 6 _ ! B of + G
2 6 6 6 4 M m¼1 δ ij Laplace the e 0 e 0 e 00 e
1 0 B B B @
Δ e i U ik B U ik U ik are transform ¼ G
a ij 0 B B δ ij B @ ^ ^ i _ C the e ΘðÞ ¼ G x 0 e 000 e 0 Θ
_ C _ C i _ C i e U
2 6 6 6 4 2 6 6 6 4 and e 00 Θ
M w X 6 k¼1 M w k¼1 e _ C Laplace
¼ C i which The
1 _ ¼ 1 X 6 s
b ij c ij
in