Biomedical Engineering Reference
In-Depth Information
which is a direct translation Eqn
(3.120)
based on the mass in the system rather than number
of moles. Therefore:
m
j
H
j;
out
H
j;
in
X
N
S
0 ¼
_
j
¼1
Because there are no changes in flow rates. (1) no phase change and (2) no reaction
occurring.
Z
C
P
d
T
m
j
C
Pj
T
j;
out
T
j;
in
X
N
S
Since
DH
¼
¼
C
P
DT
;00 ¼
_
j
¼1
Thus,
m
H
C
PH
T
H
;
out
T
H
;
in
þ
_
m
C
C
PC
T
C
;
out
T
C
;
in
¼ 0
_
m
H
C
PH
T
H
;
in
T
H
;
out
¼
_
m
C
C
PC
T
C
;
out
T
C
;
in
¼
q
H
¼
_
q
C
For example, q
H
can be understood by performing an energy balance just over the hot stream
(in the heat exchanger) as illustrated in
Fig. E3-6a
.
⎡
N
⎤
⎡
N
⎤
d
(
U
⋅
m
)
S
S
∑
=1
∑
=1
=
Q
−
W
+
m
H
−
m
H
⎣
⎦
⎣
⎦
j
j
s
j
j
dt
j
j
in
out
0
-q
H
0
Steady state
heat loss to cold stream
no work done
Therefore:
m
H
H
H
;
in
H
H
;
out
¼ 0
q
H
þ
_
W
s
= 0
1000 kg/h at 121°C
Fermentation medium leaving at 30°C
Wastewater
85°C
Cold-water: at 20°C
q
H
FIGURE E3-6A
Schematic diagram of a control volume (or system) around the hot stream passing through the
heat exchanger.
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