Page 133 - Mechanical Engineers' Handbook (Volume 4)

122 Exergy Analysis, Entropy Generation Minimization, and Constructal Theory

the environment. In other words, the nonflow exergy represents the exergy content of a given
closed system relative to the environment.
Associated with each of the streams entering or exiting an open system is the thermo-
mechanical or physical flow availability,
B H TS
0
b h Ts
0
At the restricted dead state, the nonflow availability of the stream is B H 0 T S . The
0 0
0
difference B B is known as the thermomechanical or physical flow exergy of the stream
0
E B B H H T (S S )
0
0
0
x
0
e b b h h T (s s )
0
x
0
0
0
The flow exergy represents the available work content of the stream relative to the restricted
dead state (T , P ). This work could be extracted in principle from a system that operates
0
0
reversibly in thermal communication only with the environment (T ), while receiving the
0
given stream ( , h , s) and discharging the same stream at the environmental pressure and˙m
temperature ( ˙m, h 0 , s ).
0
˙
In summary, exergy analysis means that the E W equation can be rewritten more simply
as
n
d
E ˙ me
˙
˙
E ˙ x me TS ˙
x
W
0gen
dt i 1 Q i in out
Examples of how these exergy concepts are used in the course of analyzing component by
component the performance of complex systems can be found in Refs. 1–4. Figure 2 shows
1
one such example. The upper part of the drawing shows the traditional description of the
four components of a simple Rankine cycle. The lower part shows the exergy streams that
enter and exit each component, with the important feature that the heater, the turbine, and
the cooler destroy significant portions (shaded, fading away) of the entering exergy streams.
˙
The numerical application of the E W equation to each component tells the analyst the exact
widths of the exergy streams to be drawn in Fig. 2. In graphical or numerical terms, the
1
‘‘exergy wheel’’ diagram shows not only how much exergy is being destroyed but also
where. It tells the designer how to rank order the components as candidates for optimization
according to the method of entropy generation minimization (Sections 3–8).
˙
To complement the traditional (first-law) energy conversion efficiency, (W
t
˙
˙
W )/Q H in Fig. 2, exergy analysis recommends as figure of merit the second-law efficiency,
p
˙
˙
W W p
t

˙
II
E
Q H
˙
˙
˙
where W W p is the net power output (i.e., E W earlier in this section). The second-law
t
efficiency can have values between 0 and 1, where 1 corresponds to the reversible limit.
Because of this limit, describes very well the fundamental difference between the method
II
of exergy analysis and the method of entropy generation minimization (EGM), because in
EGM the system always operates irreversibly. The question in EGM is how to change the
system such that its S ˙ gen value (always finite) approaches the minimum S ˙ gen allowed by the
system constraints.
Consider next a nonflow system that can experience heat, work, and mass transfer in
communication with the environment. The environment is represented by T , P , and the n
0
0