Mathematical model for determining of hourly average total solar radiation on tilted surface of two different cities (Mansoura and Riyadh).

The main drawback of solar energy utilization in any application based on calculated hourly average solar radiation flux incident on a horizontal plane is the clearness index of the specific location. A mathematical model using MATLAB program was functioned to compute the hourly average solar radiation flux incident on a horizontal surface of Mansoura University (latitude and longitude angles, and altitude above the sea level, respectively, are 31.045oN, 31.365oE, and 6.0 m) and King Saud University (24.725N, 46.617E, and 611 m). The hourly average solar radiation measured on a horizontal surface at the same locations and times was used with that calculated for the average day of each month throughout a whole year in order to determine the clearness index (KT). The split of total solar radiation measured on a horizontal surface into its beam and diffuse components is of interest in two contexts. Firstly, methods for calculating total solar radiation on surfaces of other orientation from data on a horizontal surface require separate treatments of beam and diffuse solar radiation. Secondly, estimates of the longtime thermal performance of most concentrating solar collectors must be based on estimates of availability of beam solar radiation. The measured data of hourly average solar radiation on tilted surface was validated against that computed by Duffie and Beckman model using coefficient of determination (R2), correlation coefficient (r), and root mean square error (RMSE). The obtained results revealed that, the validation between the measure and calculated data was highly agreement as the (R2) and (r) were high and the (RMSE) was low.