Biomedical Engineering Reference
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Q
Feed
C A0 , C P0 = 0, T 0
T c
T c
Cooling luid out
Cooling luid in
Q
Eluent
C A , C P , T
FIGURE 16.9 A jacketed CSTR with a saturated vapor e liquid fluid coolant.
As we have learned, to solve a nonisothermal reactor problem, two equations are needed:
mass balance and energy balance. For a constant fluid level in the CSTR, the mole balance of
reactant A leads to [see also eqn (5.35)]
d ð VC A Þ
d t ¼ V d C A
QC A0 QC A þ r A V ¼
(16.1)
d t
Substituting the reaction rate and dividing the reactor volume V throughout Eqn (16.1) ,we
obtain
d C A
d t
DðC A0 C A Þr ¼
(16.13)
where D is the dilution rate.
We next look at energy balance for the reaction mixture. Noting that the volume and pres-
sure in the reactor are constant, we obtain from the first law of thermodynamics [see eqn
(3.113)],
X
N S
QC j0 ðH j H j0 ÞþVrDH R þ X
N S
d T
d t ¼ Q W s
C Pj VC j
(16.14)
j¼1
j¼1
W s 0 . Heat transfer into the
The energy of stirring is dissipated into the reaction mixture,
reactor is accomplished by the jacket:
Q ¼ UA H ðT c
(16.15)
Assuming that the heat capacities are constant, we have
H j H j 0 ¼ C Pj ðT T 0 Þ
(16.16)
Letting
V ðT T C ÞþðT T 0 ÞD X
N S
C j0 C Pj W s
V
UA H
H R ¼
j¼1
0
@
1
A T T 0 D X
(16.17)
V þD X
N S
N S
UA H T c W s
V
UA H
¼
C j0 C Pj
C j0 C Pj
j¼1
j¼1
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