The present stagnation temperature studies allow determining the heat loss coefficient and the heat capacity of a collector. In this approach the collector is not necessarily connected to an operating heat removal system (e. g. water). This implies that the absorbed solar irradiance AcIG (ra)e is equal to the heat loss Ac UL (Tabs, m — Ta) plus the change in internal energy Ac Ce(dTabs, m/dt) of the collector:

Ac is the active collector area, IG the global solar irradiance, (ra)e is the effective transmittance — absorptance product, UL the heat loss coefficient, Tabs, m the mean absorber temperature, Ta the ambient temperature and Ce is the effective heat capacity of the collector per unit area. In the following (Tabs, m — Ta) will be referred to as AT. The solar energy absorbed by the collector per unit area can also be written in terms of direct and diffuse components,

IG (Ta)e = Ig ( Ta)en [kbKe (db) + kdKe (6d )] (2)

The term (ra)e in Eqn. 2 has been replaced by the effective transmittance-absorptance product at normal incidence (ra)en multiplied with the incidence angular modifier K6(6). kb and kd are the fractions of the global irradiance related to direct beam radiation and diffuse radiation respectively. 6, is the incidence angle of the direct beam radiation, while 6d is the equivalent angle of the diffuse radiation. The incidence angle of the direct beam can be calculated for any time of a day from formulas given in [15]. Duffie and Beckman [15] also provide formulas for the effective incidence angle of the diffuse radiation. Rearranging Eqn. 1 and inserting Eqn. 2 gives:

Ul = [M6(6b) + к„Кб(б„)]- Ce ^ (3)

In general, the U-value is assumed to have a linear dependence on AT as shown in Eqn. 4.

Ul = U1 + U2 AT (4)

In order to predict the fraction of the solar irradiance that is absorbed in the collector, previous knowledge about (ra)e is used. This makes it possible to identify both U1 and U2 by plotting the right side of Eqn. 3 against AT. The only unknown parameter on the right side is the heat capacity. When the heat capacity term is set to zero, the U-value is apparently larger before solar noon than after solar noon. The heat capacity is chosen so that the derived U-values before and after solar noon coincide. This approach to graphically determine the heat capacity will be shown in Section 5. Ui and U2 are then determined by using a least square fit (minimizing the sum of the squared residuals).

It is emphasized that there is a difference between the coefficients U1 and U2 in the present paper and c1 and c2 in EN 12975 [16]. The relation between the two constants is c1 = F’ U1 where F’ is the collector’s efficiency factor. F’ is close to unity for the present collectors in the present study (and generally for most polymeric collectors), hence the difference disappears.