Solar Energy Vol. 21. pp. 129-138 003g-092xf'/81~01-0129/$02.00/0 © Pergamon Press Ltd., 1978. Printed in Great Britain THERMAL CONVERSION OF SOLAR RADIATION THEORETICAL PERFORMANCE OF COLLECTORS FURNISHED WITH AN ABSORBENT SELECTIVE SURFACE~f R. PASQUETT1and F. PAPINI Universit~ de Provence, D~partement d'H61iophysique, ERA CNRS No. 538, Centre de Saint J~r6me, 13397 MarseilleCedex 4, France (Received 14 January 1977; in revised /orm 22 July 1977; received /or publication 1 March 1978) Abstract--The present study is concerned with the determinationof the behavior of selective surfaces in thermal convertors of solar energy. By means of an idealizedmodel, the influenceof various parameters such as selectivity, concentrationratio and working temperatureon the efficiency of the collectoris thus broughtout. The study leadsto an optimisedselective surface for each conditionof use, either by considering the instantaneousefficiency or, in a more realistic way, by introducing the daily efficiencyof an installation. Furthermore, a "temperature-concentration" diagram allows us to make an a priori estimation of the suitable value of the selectivityif the temperature and the concentration ratio are externally determined. It is also shown how convective phenomena have to be taken into account in the establishmentof the characteristicsof the collector. I. INTRCq~CTION In a thermal solar energy collector, the use of a hot selective surface can allow a sizeable increase in the efficiency of the collector. The essential properties of such a surface is its high absorptance of solar radiation, together with low emittance at working temperature. However, the use of a particular selective surface is not always justified, e.g. if the surface is to function at a very low temperature. Also with a large concentration of solar radiation, a black surface is preferable. The problem is more complex in situations which differ from these two extremes. In a specific situation, the solution demands a study of the variation of the thermal energy balance on the absorbing surface, in terms of the optical properties of this surface; in a general one, the introduction of simplifying hypotheses becomes indispensable. Thus idealized surfaces, for which the monochromatic emit- tance was equal to zero above a certain wavelength, have been studied elsewhere[l-4]. The study undertaken here is less restrictive; in particular it enables one to pre- determine the characteristics of the absorbing surface best adapted to a collector of known concentration ratio and working temperature. The following hypotheses have enabled us to general- ize our analysis: The selective surface of the collector is characterized by three omnidirectional parameters: the cutoff wavelength Ac; in the waveband (0,At) the monoch- romatic absorptance constant A; in the waveband (Ac,no) the monochromatic emittance constant E. Two additional parameters define the collector when it is in operation: the working temperature T of the ab- sorbing surface, taken as constant, and the geometrical concentration ratio C of the incident radiation; the value of C is equal to the ratio of the apertures of the receiver and of the absorber. tTranslated from the French. The effects of thermal mass are negligible, i.e. the time constant of the collector is considered to be zero. The spectral distribution of the incident energy is similar to that of a blackbody which is at a temperature of 5880 K. The surroundings, which radiate directly on the ideal- ized surfaces, are comparable to a blackbody which is at a temperature To of 293 K. Therefore, the object of the study is mainly the determination of a selective surface used in given condi- tions of temperature, incident radiation, or concentra- tion. The technical difficulties of realization of the sur- face will be defined by the ratio AlE which will be called "the selectivity factor". Since these difficulties grow with the parameter, we shall try to evaluate the value of AlE above which the efficiency of the machine practically no longer increases. Furthermore, we shall show how the convective phenomena influence the formulation of this efficiency. The latter will be defined for not only an instantaneous incident power but also for an average daily incident power; thus we shall get a more exact idea of the real possibilities of the collector. z TH IO, DO, TIW s ~ c E ON THE J~k~asJ~rr ~,FAC¢. The radiative efficiency, per unit area of aperture, can be well approximated [5] (see nomenclature) ~}u D ~ = ~ - A W(1 - Y) with i E W(AIE, Ac)=E + (I--~)ks • AW=a 129