Page 89 - Entrophy Analysis in Thermal Engineering Systems

Endoreversible heat engines 81

constant. In the case of constant heat input, optimization of any model of
engine that interacts with two thermal sources, based on maximum thermal
efficiency, maximum power output and minimum entropy production
would result in an identical design [5].
From practical viewpoint, optimization of an engine with a fixed heat
input is irrelevant. A given heat input is equivalent to a fixed mass of fuel
to be burnt in furnace. Once the problem is reduced to a fixed amount
of burning fuel, an important ability of varying mass of fuel at other oper-
ational conditions (such as at part-load operation) is taken away. So, a, more
general case would be to treat this parameter as a variable together with many
other parameters, which may directly or indirectly influence the thermal
efficiency of an engine.
Let us now consider a Carnot vapor cycle with varying heat input. For
_
this, we assume that C h is the design parameter, and all other parameters,
including T EH are constant. Similar to the case with varying T EH , it can
_
be inferred from Eq. (6.28) that there is an optimum C h given by
Eq. (6.34), which maximizes the power output.

p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
_ _ T EH T EH T l,in (6.34)

C h
opt ¼ C l T h,in T EH
Substituting Eq. (6.34) into Eq. (6.28), the maximum power output at opti-
mum heat capacity of the hot stream is obtained as

p ffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffi 2
_ T EH T l,in (6.35)

_ W max ¼ C l
_
Eq. (6.35) reveals that when the power optimization is performed with C h ,
the maximum power depends only on three parameters: the heat capacity
and the inlet temperature of the cold stream, and the highest temperature
of the engine T EH . On the other hand, the thermal efficiency of the cycle
at maximum power is

r
ffiffiffiffiffiffiffiffiffi
T l,in
η ð th W max ¼ 1 T EH T h,in T EH (6.36)
Þ _
T h,in T l,in
It can be implied from Eq. (6.36) that the thermal efficiency at maximum
power is independent of the heat capacities of the cold and hot streams,
but it depends on their inlet temperatures as well as the highest temperature
of the engine.