Biomedical Engineering Reference
In-Depth Information
FIGURE 2.6
Velocity distribution in a rectangular mixing channel (h
¼
0.14) with: (a) the same viscosity b ¼
1 and (b) different
viscosities b
¼
2.
b sinh 2 rq
cosh 2 rq
b cosh q
þð
b
1
Þ
cosh rq cosh q
þ
B 2 ¼
A 1
Þ :
cosh 2 rq
b sinh 2 rq
ð
b
Þ
sinh rq cosh rq cosh q
sinh q
ð
1
Figure 2.6 shows the typical velocity distribution in a rectangular channel for streams with different
flow rates. For streams with the same viscosity, the velocity distribution is flat.
2.1.2.3 Conservation of energy
The conservation of energy is governed by the first law of thermodynamics:
d Q
þ
d W
¼
d E total
(2.18)
which means, the change of the total energy in a system is equal to the sum of the heat and work added
to the system. The energy equation can then be formulated for the absolute temperature T as
D T
D t ¼
bT D p
rc p ¼
D t þ
div
ð
k
V
T
ÞþF
(2.19)
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