Numerical calculation of the intercept factor for parabolic trough solar collector with secondary mirror

Abstract The intercept factor is the most complex parameter involved in determining the optical efficiency of a parabolic trough solar collector. A numerical algorithm method was proposed to calculate the intercept factors of a parabolic trough solar collector using the Gauss error function and a Python program. The results indicate that the intercept factors can be calculated quickly and conveniently using the proposed method. We also introduced a numerical solution to calculate the intercept factor of the parabolic trough solar collector, which can provide accurate interception factors for different types of secondary reflection concentrators. The new analytical method was validated and benchmarked against a Gauss error function and Python program, demonstrating that the deviations were below 0.0015% for most cases studied. The primary goals of this study were to determine an appropriate numerical method to solve the intercept factors and errors for different secondary mirror types and to incorporate the selected intercept factor calculation into a secondary mirror design for a parabolic trough solar collector under various conditions.