Derivation of efficiency factors for uneven irradiation on a fin absorber

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 0. 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 0 c , is different from F 0 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 0 c ðxÞ, where x is the distance from the edge of the absorber. Close to the edge, F 0 c ðxÞ < F 0 and close to the pipe, F 0 c ðxÞ > F 0. In this paper formulas are derived for calculating F 0 c ðxÞ for a fin absorber with constant fin thickness. By weighting F 0 c ðxÞ with the absorbed irradiance, ScðxÞ, and integrating across the absorber, an absorber average optical efficiency factor, F 0 c;a, is obtained. This value replaces F 0 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 0 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. 2004 Elsevier Ltd. All rights reserved