Page 371 - Design and Operation of Heat Exchangers and their Networks

Dynamic analysis of heat exchangers and their networks 355

(7.164) (7.165)

MÞ
t j
3 7 7 7 5 …, by
e 2,
1 C C C X U mk A ΔU nk 7 C i ¼ 1, ð given
U jk M m¼1 ^ j t are

! 7 δ nj ^ jk X U mk A5 ^
3 7 θ j 7e 7 5 13 C7 C7 C7 C7 (7.165)
+ X U ik 10 CB CB CB CB U M m¼1 Eq.

M w k¼1 in C

sC i M + X U mk A@ m¼1 0 B B B δ nj B
U ik T B,and
δ ij sC w,k U ik U nk M + X U mk @ m¼1 as Θ + BT + C ^ A,

U ik U jk M + X U mk m¼1 0 B B δ ni @ n¼1 B sC w,k form Θ ¼ A e matrices

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