Derivation of efficiency factors for uneven irradiation on a fin absorber

摘要

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'{sub}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'{sub}c(x), where x is the distance from the edge of the absorber. Close to the edge, F'{sub}c(x) < F' and close to the pipe, F'{sub}c(x) > F'. In this paper formulas are derived for calculating F'{sub}c(.x) for a fin absorber with constant fin thickness. By weighting F'{sub}c(.x) with the absorbed irradiance, S'{sub}c(x), and integrating across the absorber, an absorber average optical efficiency factor, F'{sub}(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'{sub}(c,a) can be used for calculating a corresponding heat removal factor for uneven irradiation, FR)C. Formulas for calculating the temperature distribution across the absorber for the case of uneven irradiation are also derived.