Page 139 - Advanced Thermodynamics for Engineers, Second Edition

126 CHAPTER 6 FINITE TIME (OR ENDOREVERSIBLE) THERMODYNAMICS

If the resistance to the low-temperature reservoir is high, i.e. U H A H /U C A C ¼ 2, the situation
changes, as shown below.
First,
2 2 4
U H A H ¼ ¼ ¼
1 þ 1=2 3=2 3
giving
W _ ð1=2 1=4Þð1 1=2Þ
_
¼ 1600 ¼ 133 units; which results in W ¼ 177:8kW;
U H A H ð1 þ 2Þ=2
and
Q _ H
_
¼ 267 units; or Q ¼ 355:6kW
U H A H
Then,
Q _ C 2Q _ C 2
_
_
_
¼ ¼ Q W ¼ 267 units; giving Q ¼ 177:8kW:
C
H
U C A C U H A H U H A H
Hence,
( )
1 Q _ C
T 1 ¼ þ T C ¼ 2ð267 þ 400Þ¼ 1334 K; and T 2 ¼ 667 K:
s U C A C
These results are shown graphically in Fig. 6.4.
UA UA UA
____
____
____
UA = 1 UA = 1/2 UA = 2
T = 1600 K
1334 K
T 1200 K
1067 K
E R
E R
E
R
T 667 K
600 K
533 K
T = 400 K

FIGURE 6.4
The effect of heat transfer parameters on engine temperatures for a heat engine operating between reservoirs
at T H ¼ 1600 K and T C ¼ 400 K.