Page 136 - Advanced thermodynamics for engineers

122 CHAPTER 6 FINITE TIME (OR ENDOREVERSIBLE) THERMODYNAMICS

0.8
Q
U A /U A C
C
H H
W
0.7 =1.0
Q
U A /U A C
H H
C
W η =2.0
Non-dimensional heat flux and power Engine thermal efficiency 0.5
0.6
0.553
0.4

0.3

0.2

0.1

0.447
0
0 0.2 0.4 0.6 0.8 1.0
Temperature across heat engine, τ

FIGURE 6.2
Variation of heat flux, power output and thermal efficiency for an endoreversible engine operating with
T H /T C ¼ 5.0.

6.2 EFFICIENCY AT MAXIMUM POWER
It is shown in Fig. 6.2 that the rate of work output (power) is a function of the ratio of temperatures of
the hot and cold reservoirs, the ratio of temperatures across the engine and the thermal resistances. The
optimum temperature ratio across the engine (s) to give maximum power output is obtained when
vW _
¼ 0:
vs
Differentiating Eqn (6.11) with respect to s gives.
0 1
vW _ B 1 C ð1 sÞ ðs T C =T H Þ ðs T C =T H Þð1 sÞ

¼ B C
vs @ U H A H A s s s 2
1 þ
U C A C
0 1
1
1 B C 1 T C
¼ B C s þ : (6.12)
s @ U H A H A s T H
1 þ
U C A C