## Parabolic Solar Dish System

In what follows, we illustrate the benefits of solar power generation on sustain-ability, on reducing greenhouse gas emission and on reducing global warming by a case study. The study refers to a residential (single) unit for solar power conversion based on a paraboloidal mirror that is illustrated in Fig. 4.6. The solar dish concentrates the insolation on a glazed tube receiver that plays the role of desorber for an ammonia-water Rankine cycle. For expansion and work production, a scroll machine is capable of operating in a two-phase regime. The rejected heat of the heat engine may not in principle be "thrown out" in the environment, but rather is used for cogeneration through water heating.

Based on the insolation IT we summarize in Table 4.3 the relationships for relevant efficiencies (see also the Nomenclature). In the definition of efficiency for the system with cogeneration we assumed that the rejected heat to the cold reservoir, Q0, is a useful heat (e.g., for water heating).

 Parameter Definition Optical efficiency I T A a Thermal efficiency I c Aab Solar collector ncoll _ noptnth ii ab System without cogeneration I It A a

The first step in solar energy system modeling and its design calculations is to determine the solar collector geometry and characteristics for maximum performance. This, in fact, is to maximize the collector efficiency. The derivation of the collector's efficiency results from the energy balance stating

where Qloss = UAab (Tab — T0) represents the heat losses expressed in a linearized way. Dividing Eq. (4.3) with ITAa, extracting 1]opt as a common factor on the LHS, and identifying the concentration ratio one obtains

where we denoted with Fcoll = U(Tab — T0 ^(^pTCx) the collector factor depending on the solar absorber temperature (assumed at the average), the insolation and optical properties which are accounted for through the optical factor

Q = pTa including the shading and light blocking factor Z reflectivity p, transmissivity of receiver's glazing T and absorptivity aof the receiver's surface. In Eq. (4.4), the intercept factor y = ^JZpTa which represents the ratio between solar energy flux absorbed by the receiver and the concentrated energy flux focalized on it is introduced. The intercept factor is an important parameter of the optical system that depends on the concentration ratio, the rim angle / (i.e., the angle between the focal axis and a ray connecting the rim with the focal point), and the angular optical errors S (expressed in mrad). The optical error is due to the conjugated effect of mirror specularity, mirror slope errors, pointing error, and sun-shaped non-uniformities. Among several correlations for y summarized in Jaffe (1983b), we selected the one of Duff and Lameiro (1974) that gives less than 10% estimation error.

For the solar concentrator we introduce the optical efficiency defined by nopt = Qy and thermal efficiency defined by TJth = 1 — FcolJCy . From Eq.

(3.4) and the definitions of optical and thermal efficiencies it results the following expression 7]con/Q = f (, /, S, Fcoll) ,which can be maximized with respect to the concentration ratio C, and rim angle / for fixed angular error S and collector factor Fcoll. This optimization is demonstrated in the next section. Its physical interpretation is explained by the trade-off between the need of a larger spot for capturing all concentrated light and a smaller absorber area for minimizing the heat loses.

In Duffie and Beckman (2006), the receiver's heat losses through radiation can be expressed £abOAab i(l — T4 ) = Ab ^((b + T0 )b + T0 fc — T0 ) , or if one may assume an average temperature difference between the absorber and envi ronment as, Aab (4cT3 )ab - T0); this last expression identifies an equivalent radiation heat transfer coefficient hrad = 4cT3. Considering the other heat losses, U is

Here, an important observation regards the trade-off between the collector and the heat engine efficiencies: high receiver temperature means bad collector efficiency and good engine efficiency, and vice versa. This trade-off is a fundamental ther-modynamic problem, as pointed out by Bejan et al. (1981). In this respect, the stagnation temperature Tab,max defined as the solar receiver temperature for which all incident radiation is dissipated into the ambient as heat loss (this is the ideal maximum collector temperature). If the heat engine is Carnot, Bejan et al. (1981) demonstrate that the optimal collector temperature that maximizes the work output

We developed a numerical model for our heat engine that runs on a peculiar kind of Rankine cycle that, as mentioned above, uses ammonia-water as working fluid. Furthermore, the heated fluid is expanded just after the boiling is initiated using a scroll expander that operates completely in two phase. A detailed analysis of the cycle including its modeling and optimization is presented in Zamfirescu and Dincer (2008a, b) and omitted here for brevity. We used the model for optimization of the receiver temperature, which is the similar to the optimization of Fcoll for maximum system efficiency. 