Page 381 - Design and Operation of Heat Exchangers and their Networks

364 Design and operation of heat exchangers and their networks

The system is initially at a nonoperational state with a uniform initial
temperature t 0 . The nonzero heat transfer parameters are given as

U 11 ¼ U 22 ¼ 2W=K, U 31 ¼ U 42 ¼ 12W=K, U 53 ¼ U 64 ¼ 1W=K
Other values of U ij are zero. The thermal capacities and thermal capacity
rates are

C 1 ¼ C 2 ¼ 0:25 W=K, C 3 ¼ C 4 ¼ C 5 ¼ C 6 ¼ 1W=K,
_
_

_

_

_

_
C 1 ¼ C 2 ¼ 0J=K, C 3 ¼ C 4 ¼ 1J=K, C 5 ¼ C 6 ¼ 10 J=K,
C w,1 ¼ C w,2 ¼ 1:25 J=K, C w,3 ¼ C w,4 ¼ 1J=K
The connecting matrices are given as
2 3 2 3
0 00000 10
6 0 00000 7 6 01 7
6 7 6 7
6 0 00010 7 6 00 7 10 0000
00
000
0
G ¼ 6 7 , G ¼ 6 7 , G ¼ , G ¼ 0,
6 0 00001 7 6 00 7 01 0000
6 7 6 7
0 00100 00
4 5 4 5
0 01000 00
0 T 00 T
½
x ¼ 1 0010 1Š , x ¼ 0 1101 0Š
½
The temperature responses of the system to a unit step disturbance in the
inlet temperature of stream 1 are shown in Fig. 7.7.
0.6
0.5
q
1
q
0.4 2
q 0.3
0.2
0.1

0.0
0 100 200 300 400
t
Fig. 7.7 System responses to a unit step disturbance in the inlet temperature of
stream 1 (θ 1 (τ)¼1).
0