Page 150 - Entrophy Analysis in Thermal Engineering Systems

144 Entropy Analysis in Thermal Engineering Systems

Next, we evaluate the entropy generation rate of the SOFC. The total
entropy flow at the fuel cell inlet is

ð s Þ (9.38)
S 2 ¼ _n H 2 H 2 + _n O 2 O 2 + _n N 2 N 2 2
s
s
Likewise, the total enthalpy flow of the reaction products at state 3 is

+ _n H 2 O s H 2 O (9.39)
S 3 ¼ _n H 2 1 U f s H 2 + _n O 2 O 2 + _n N 2 N 2
3
s
s
The specific entropy of the individual species in Eq. (9.39) should be calcu-
lated at temperature T 3 and their partial pressure, p i , at state 3, where

i : H 2 ,O 2 ,N 2 ,H 2 O (9.40)
_ n i
p i ¼ p 3
3
_ n tot
The entropy generation rate of the SOFC is determined by
_
Φ SOFC ¼ S 3 S 2 (9.41)
The total molar flowrate of the SOFC products flowing to the combustor
can be determined using Eq. (9.33) through Eq. (9.37). Hence,

1 4:76 1
ð _ n tot Þ ¼ IN c + (9.42)
3
2F U f 2U a 2
The unburned portion of the hydrogen is assumed to completely oxidize
within the combustor.

9.5.2 Illustrative example
A numerical example is now presented to examine the performance of the
hybrid system of Fig. 9.8 using the following operating parameters. The
2
SOFC stack consists of two cells each with a surface area of 1000cm .
The operating voltage, current density, and temperature are 0.68V,
2
300mA/cm , and 1173K, respectively. The fuel utilization factor is assumed
to be 0.8. The isentropic efficiencies of the gas turbine and compressors are
0.90 and 0.85, respectively. Both the hydrogen and air are supplied to the
cycle at 298.15K and 1bar.
The net power generation and the thermal efficiency of the hybrid cycle
are obtained as follows.
_ _ _ _ _ (9.43)
W net ¼ W FC,ac + W t W c W fc