Page 369 - Design and Operation of Heat Exchangers and their Networks

354 Design and operation of heat exchangers and their networks

(7.161) (7.162) into (7.163)

(7.148) M w Þ

(7.124), …,
x 00 j x 00 i 2,

k X Δe ij ðÞt j 13 C7 C7 C7 A5
s s Eqs. k ¼ 1, ð
g g li k X Δe 00 ðÞt i
M j¼1 M i¼1 substituting X U mk ^ mC7 t ^

g ik ðÞt 0 s MÞ …, s N 00 Þ by M ^ ^ n m¼1 M X U mk m¼1

X Δe 0 2, s X Δe 000 ðÞt 0 g lk …, obtained t yields
N 0 k¼1 i ¼ 1, N 0 k¼1 2, 0 B B B @

ð ¼ 1, U nk B s
s ¼ 0 be + (7.159)
x 00 , j x 00 , i l ð
can e
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 # x 00 j li θ # ¼ 0 domain 1 C ΔU nk C C A Eq. into

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
ik s θ 0 N 0 k¼1 e lk in + B
e the 0 B B B @ (7.148),
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