Material properties included in the model have been previously described [Incropera & Dewitt, 1996]. Nevertheless, these values can vary from the real ones (i. e. the cooper on the absorber, or the crystal of the covering) depending on the manufacturing processes. In this sense after eq. (8) and (11) solving, results are not satisfactory enough. In fact, convection parameters associated to heat transmission to water vary drastically in each case. For this reason, parameter optimization technique is used to determine those real values. In this case, the parameters that need to be optimized can be divided into two categories:

— Material properties, such as crystal extinction coefficient ke (m-1), crystal refraction index n2 (dimensionless), directional absorbance of cooper black plate ae (dimensionless), plate emmitance £p (dimensionless), crystal emmitance £p (dimensionless), conduction coefficient of the isolator (aluminium sandwich model) KiT (W/mK), and conduction coefficient of cooper kp (W/mK)

-Heat transfer properties, such as convection coefficient pipe-fluid h (W/m2 K) (where Kh is optimized), and convection factor through working fluid Uo (w/m3 K) (where KuO is optimized).

The optimization process consists of minimizing an objective function V, obtained from the sum of squares of the differences between the model values and the empirical values [Gill et al., 1981]. The system supplies two values of the temperature: the output temperature of the fluid, Tfo, and the plate temperature at the measurement point, Tp, near the top of the absorber, by means of a bulb thermometer. The optimization process makes possible to find the minimum value of the objective function.

^ = lTfo — Tfo f+lTp — TP ) (12)

At any step of the optimization process, the previous equations set (eq. (8) and (11)) is evaluated and the temperatures distribution is obtained. Two of those values are used to determine V next to the other two real ones. The optimization algorithm changes the parameter values, and repeats the process with the new ones, until the objective function reaches a minimum. This process is based on a Taylor series expansion of V, where the parameters are modified with the gradient descendent method [Gill et al., 1981]. At this point, modelled and real values are almost the same, and the temperature distribution is considered to be correct, and close to reality.