Page 135 - Mechanical Engineers' Handbook (Volume 4)

124 Exergy Analysis, Entropy Generation Minimization, and Constructal Theory

Figure 3 The relationship between the nonflow total (
t ), physical (
), and chemical (
ch ) exergies.
(From A. Bejan, Advanced Engineering Thermodynamics. 1997 John Wiley & Sons, Inc. Reprinted
by permission.)

occurs (in addition to heat and work transfer) and, in the end, the system reaches chemical
equilibrium with the environment, in addition to thermal and mechanical equilibrium. The
work made available during this second step is known as chemical exergy, 1

( * )N
n

ch
i 1 i 0,i i
The total exergy content of the original nonflow system (E, S, V, N ) relative to the environ-
i
mental dead state (T , P , ) represents the total nonflow exergy,
0
0,i
0

ch
t
˙
The total flow exergy of a mixture stream of total molal flow rate N (composed of n
˙
species, with flow rates N i ) and intensities T, P, and (i 1,..., n) is, on a mole of
i
mixture basis,
e e e
t x ch
where the physical flow exergy e x was defined above, and e ch is the chemical exergy per
mole of mixture,
e ( * ) N i
˙
n

ch
˙
i 1 i 0,i N
In the e expression * (i 1,..., n) are the chemical potentials of the stream constituents
ch i
at the restricted dead state (T , P ). The chemical exergy is the additional work that could
0 0
be extracted (reversibly) as the stream evolves from the restricted dead state to the dead state
(T , P , ) while in thermal, mechanical, and chemical communication with the environ-
0 0 0,i
ment.
3 ENTROPY GENERATION MINIMIZATION
The EGM method 3,4 is distinct from exergy analysis, because in exergy analysis the analyst
needs only the first law, the second law, and a convention regarding the values of the intensive
properties of the environment. The critically new aspects of the EGM method are the mod-
eling of the system, the development of S gen as a function of the physical parameters of the
model, and the minimization of the calculated entropy generation rate. To minimize the
irreversibility of a proposed design, the engineer must use the relations between temperature
differences and heat transfer rates, and between pressure differences and mass flow rates.