Page 373 - Design and Operation of Heat Exchangers and their Networks

356 Design and operation of heat exchangers and their networks

(7.166) MÞ (7.167) (7.168) (7.169) (7.170)

…,
2, MÞ respectively.
¼ 1, …,

j 2, x 00 i
i, ^
ð ¼ 1,
3 7 7 7 5 i T
MÞ e j i, ð parameters, TðÞ x 00 ^ G 00 G 00 ^
…, 1 C C C C 13 C7 C7 C7 C7
2, δ jn X U mk A ΔU nk 7 form:
¼ 1, U jk ^ jk X U mk A5 ^ transfer TðÞ G 0 ^ 0 G ^ T +

j M m¼1 U M m¼1 matrix ^0 T
i,
ð heat
3 7 7 7 5 δ nj the x 0 ^ G 000
! 7 10 CB CB CB CB 0 B B B B and in ^
X U ik X U mk A@ X U mk @ rates s G 000
M w k¼1 expressed GTðÞ 1 h 1 h
+ M m¼1 U ik U nk M m¼1 flow x 00 s
sC i U ik + + be + Δ e x 00

δ ij sC w,k M X n¼1 sC w,k thermal can + Δ e 00 TðÞ + G
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