[Luyben] Process Mod.. - Student subdomain for University of Bath

50 MATHEMATICAL MODELS OF CHEMICAL ENGINEERING SYSTEMS
Q4-M TJ~
4
*
Q3-- TJ~
I
Q2** 7~2 !
4 i’
QI-- TJI -
F~
TJO
t
FIGURE 3.4
Lumped jacket model.
D. S-CANT METAL WA&s In -.-- some reactors, particularly
m-pressure v& or smaller-scale equipment, the mass of the metal walls and
its effects on the thermal dynamics m be considered. To be rigorous, the
energy equation for the wall should be a partial differential equation in time and
radial position. A less rinorous but frequently used approximation is to “hunp”
the mass of the metal and assume the metal is all at one temperature I’,‘,. This
assumption is a fairly ed one when the wall is not too sand the thermal
-
conductivity of the metal is large.
Then effective i@ide and @e film coefficients h, and h, are used as
in Fig. 3.5.
P
The three energy equations for the process are: ,
PC 4v”r)
* at
= pCkF, To - FT) - AV(CA)“ae-E’RT - h,AXT - TM)
is-
PJ vJ cJ dt - FJ PJ CJ~%I - r,) + ho ‘%(TM - TJ)
.-
where hi - inside heat transfer film coefficient
h, = outside heat transfer film coefficient
(3.33)
FIGURE 3.5
Lumped metal model.