Page 211 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

Distributed Processes 185

7-4 Response of Tubular Heat Exchanger to Step
In Jacket Temperature
Let the jacket temperature be a step of size U, at time zero. Equation
(7-12) becomes

(7-13)

Appendix F shows that the inversion of Eq. (7-13) gives

(7-14)

Appendix F also explains the nature of the unit step function U(t).
7-4-1 Tlle Large-Diameter case
Figure 7-3 shows the behavior of T(L,t) for the case where U,= 1, L = 1,
'rr = 1, t = 1, and v = 1. Note for t > tD' the outlet temperature is con-
0
stant at

0.7 ......-----,---,---,.------r--,--,.------r---r--.....------.

0.6
I I I I
l!c = 1 ~ = 1 ~ = 1 :
....................
• • 0 0
. ·.· ... ·.· ... : ... ·.· ...
I
I
I
I
. . · .... : .... ~ .... · ....
I I o 1
0.1 • t 0 ••• ••••••••••••••••• t 0 ••• ••••••
•
•
•
•
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Ttme
F1auRE 7-3 Response of largtH:tiameter tubular heat exchanger to step in
jacket temperature.