Unformatted text preview: stagnation
temperature Tmax is given by:
gamma.Ainqin = U.Arec(Tmax - Ta). For example, if the optical efficiency is gamma = 0.8,
the incident solar irradiation is qin = 800W/m2, the
ambient temperature is Ta = 30°C, and the heat loss
coefficient is U = 10W/m2K, then a concentration ratio
Ain/Arec = 1 (no concentration) gives Tmax = 94°C, and a
concentration ratio Ain/Arec = 10 gives Tmax = 670°C.
concentration The collector efficiency etac at operating temperature T is
etac=Qout/Ainqin = F'[gamma-U.Arec(T -Ta)/Ainqin]
= F''gamma(Tmax - T)/(Tmax - Ta).
The available mechanical power from the thermal power
output of the collector that would be obtained using a Carnot
cycle is Qout(1 - Ta/T), where the temperatures are absolute
temperatures. The second law efficiency eta2 of a heat engine is
eta2=(mechanical power delivered)
/(available mechanical power).
Suppose a heat engine with second law efficiency eta2
uses as input the thermal power Qout from the solar
collector. The first law efficiency of the engine is
eta1 = (mechanical power delivered)/Qout = eta2(1 - Ta/T),
eta where Tmax depends on the design of the collector and
on the solar radiation input qin. Now, given F', gamma,
eta2, Ta, and Tmax, we can find the maximum efficiency
obtainable, and the optimum operating temperature Topt
from the condition d(eta)/dT = 0. This occurs at the
Topt = [TmaxTa],,
and the maximum efficiency is obtained by putting
T = Topt in the equation
eta = etac.eta1.
eta For example, putting F' = 0.9, gamma = 0.8, eta2 = 0.6,
Ta = 30°C = 303K, we get the efficiencies etamax for
different degrees of concentration shown in Table 6.1.
Very low overall efficiencies are obtained unless
operating temperatures greater than 500°C are used.
Expensive concentrating systems are needed to reach
these high temperatures, so commercial viability is
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- Spring '14
- ........., Concentrating solar power, power tower