A novel analytical solution for the transmissivity of curved transparent surfaces with application to solar radiation

• A novel method to calculate transmissivity of curved transparent surfaces is developed.
• Transmissivity is calculated as a function of geographical location and surface geometry.
• The novel analytical method derives direct and diffuse radiation coefficients.
• Total transmitted solar energy through a curved surface can be directly calculated.

In this article, a novel mathematical expression for calculating the transmissivity of curved transparent surfaces due to sun rays for both direct and diffuse radiation is presented. An analytical solution is performed for the transmissivities of both direct and diffuse radiation – τgnτgn and τgdτgd – as functions of the latitude (ϕ), orientation (γ), and the curved surface aspect ratio (P = b/a  ) to derive new parameters that are defined as direct and diffuse radiation coefficients (Γn¯ and Γd¯). Hence, such parameters can be directly used to evaluate the total transmitted solar energy through curved transparent surfaces that are widely used in greenhouses as well as new designs of solar collectors with curved glass covers. The proposed mathematical expression should be of significant value to the design of solar equipment in a wide range of applications.