Derivation of efficiency factors for uneven irradiation on a fin absorber

Abstract

In the equation for thermal energy output from a flat-plate solar collector (written as a function of the collector mean heat carrier temperature), both the gain and the loss terms are multiplied by the collector efficiency factor, F ′. For a concentrating collector with an uneven (non-uniform) irradiation on the absorber, the efficiency factor for the gain term, here called the optical efficiency factor, F ′ c, is different from F ′ and is a function of the irradiation distribution on the absorber. If the heat loss coefficient is assumed to be constant across the fin, the optical efficiency factor for absorbed irradiation at a certain distance from the edge of the absorber is independent of absorbed irradiation at other locations and can therefore be expressed F ′ c( x), where x is the distance from the edge of the absorber. Close to the edge, F ′ c( x)< F ′ and close to the pipe, F ′ c( x)> F ′. In this paper formulas are derived for calculating F ′ c( x) for a fin absorber with constant fin thickness. By weighting F ′ c( x) with the absorbed irradiance, S c( x), and integrating across the absorber, an absorber average optical efficiency factor, F ′ c,a, is obtained. This value replaces F ′ in the gain term of the equation for thermal energy output. If, instead, the energy output equation is expressed as a function of the inlet temperature, F ′ c,a can be used for calculating a corresponding heat removal factor for uneven irradiation, F R, c . Formulas for calculating the temperature distribution across the absorber for the case of uneven irradiation are also derived.