Derivation of the effective beam radiation incidence angle equations for diffuse and reflected solar radiation using a two dimensional approach

• Derives effective beam radiation incidence angle equations for diffuse and reflected radiation approaching cover.
• Uses two dimensional derivation approach.
• Derivation consistent with cover transmittance calculations.
• Reviews equations for collector cover transmittance, reflectance, and absorptance.

When calculating the performance of a flat plate solar collector, it is important to determine the amount of solar radiation that is transmitted through the cover to the absorber plate. The solar radiation transmitted to the absorber plate can be thought of as the fuel for the collector. Using the isotropic diffuse concept, solar radiation can be broken into three components: diffuse radiation, reflected radiation, and beam radiation. The diffuse and reflected radiation does not approach the collector from a single direction or at a specific angle. Rather, the diffuse and reflected radiation comes from many directions at several different angles. By using an effective beam radiation incidence angle, the transmittance of the diffuse and reflected radiation may be equated for a single angle rather than integrated over the entire range of incidence angles. The effective beam radiation incidence angles may be thought of as the initial angles at which the diffuse and reflected radiation is assumed to approach the collector cover.The effective beam radiation incidence angle equations for the diffuse and reflected radiation have been previously derived using a three dimensional approach. The work presented offers effective beam radiation incidence angle equations that were derived using a two dimensional approach. The two dimensional approach is consistent with the equations one typically uses to calculate the transmittance for a collector cover. Therefore, the equations derived in this work are consistent with the methodology one normally uses to calculate the transmittance of solar radiation through a collector cover.