Page 368 - Design and Operation of Heat Exchangers and their Networks

354
(7.162)
(7.161)
into
(7.148)
(7.124),
k X Δe 00 ðÞt i
x 00
i
Eqs.
s
substituting
g li
X U mk ^ mC7
13
C7
j¼1
i¼1
M
t
MÞ
^
s X Δe 000 ðÞt 0
N 00 Þ
…,
by
M
s
obtained
2,
g lk
…,
i ¼ 1,
k¼1
0
B
k¼1
2,
N 0
¼ 1,
ð
s
be
¼ 0
l
ð
can
x 00 ,
C ΔU nk
i
#
¼ 0
k ðÞ X g ij e Δτ ij s e j M t k X g ij ^ j t j¼1 k ðÞ X g 00 e Δτ 00 s e i li x 00 li t X U mk t mC X U mk
θ M N 0 x 00 s g g ik ðÞt 0 s X Δe 0 s x 00 , j k X Δe ij ðÞt j j Design and operation of heat exchangers and their networks U nk B C7 B C e ^ n m¼1 (7.163) M w Þ …, 2, k ¼ 1, ð t + C7 B C M X U mk A5 @ A ^ m¼1 yields (7.159) Eq. into
x 00
domain
θ
j
1
#
li
M j¼1 M i¼1 M lk t k X g 00 ^ i ðÞ i¼1 Laplace M M m¼1 (7.163)
s ik ^ 0 s t n m¼1
e the 0 B B B @ (7.148),
ik s θ 0 N 0 k¼1 e lk in + B
ik e Δτ 0 ^ i X g 0 x 0 i N 0 ^ 00 X g 000 ^ 0 k¼1 walls U nk e n θ
s X g 0 + 1 s N 0 k¼1 " + 1 s M X 6 n¼1 Eqs.
N 0 k¼1 " t θ 00 ðÞ X g 000 e Δτ 000 s θ 0 lk t l of 2 6 6 6 4 (7.124),
x 0 , i e s l temperature X U mk of
e i θ 1 M + m¼1
excess sC w,k substitution
The (7.160): e w,k ¼ The
Eq. θ