The non-black-body converter we considered must have some special properties in order to give the best performance. Indeed, let us divide the whole domain of frequencies (0, go) into two subdomains C/Tc and f/y in such a way that the difference between the energy of the radiation incoming within &T and the energy of the radiation emitted within C/ T be maximized. For good performance the reflectance of the absorber surface must be small for the domain and high for &r[12]. We will make two hypotheses: (1) the domains and contain the greatest part of the energy of the incoming and emitted radiation, respectively, and (2) the absorber reflectance is independent of frequency within -^'t^ and &t, respectively. Under such circumstances the emitted radiation can be considered as diluted radiation and the theory of Landsberg & Tonge [7] applies. The two hypotheses are well verified in the case of selective solar converters, if the temperatures Tc and T are sufficiently far apart [12]. The spectrally averaged absorbtance and emittance of the selective converter will be noted with a and e, respectively (for details of computation see [12]). The converter emits diluted radiation over the solid angle w* = 2n with dilution factor e. We will note Te, T* or P, P* are the effective temperatures and the corresponding quantities of incoming and emitted radiation, respectively. Then, from (7) and (9-12) we can write: In order to determine the maximum of i] we must first obtain the optimal converter temperature, from di]/dT — 0. But the dependence of a and e on T is influenced in a complicated manner by the structure of the selective absorber surface (see, e.g., [12]). Consequently, it is difficult to obtain a simple general procedure for maximizing t], unless the case of a black-body converter is considered. 3. Upper Bounds Formulae for the Conversion Efficiency Let us introduce some notation: The maximal converter temperature Tmax = Te can be reached through effective equilibrium, for which we suppose <!>,, = [7]. Consequently, from (13) and (15) we see that:
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