Polynomial Expressions for the Thermal Efficiency of the Parabolic Trough Solar Collector

The parabolic trough solar collector (PTC) is the most mature solar concentrating technology, and this technology is applied in numerous thermal applications. Usually, the thermal efficiency of the PTC is expressed with the aid of polynomial expressions. However, there is not a universal expression that is applied in all cases with high accuracy. Many studies use expressions with the first-degree polynomial, second-degree, or fourth-degree polynomial expressions. In this direction, this work is a study that investigates different expressions about the thermal efficiency of a PTC with a systematic approach. The LS-2 PTC module is examined with a developed numerical model in the Engineering Equation Solver for different operating temperatures and solar beam irradiation levels. This model is validated using experimental literature data. The found data are approximated with various polynomial expressions with up to six unknown parameters in every case. In every case, the mean absolute percentage error and the R² are calculated. According to the final results, the use of the third power term leads to the best fitting results, as well as the use of the temperature difference term (ΔΤ), something that is new according to the existing literature. More specifically, the final suggested formula has the following format: “η_col = a₀ + a₃∙ΔT³/G_b + b∙ΔΤ”. The results of this work can be used by the scientists for the optimum fitting of the PTC efficiency curves and for applying the best formulas in performance determination studies.