Demonstration of the Geometrical Equations and Optical Parameters of the Conical Solar Concentrator for Solar Energy Applications

Abstract: This short communication presents the geometrical equations and optical parameters of a conical solar concentrator, enabling its integration into innovative solar energy applications. Demonstrating these expressions supports researchers in incorporating conical solar concentrators into CSP systems for generating clean electricity. Using numerical sequences and trigonometric identities, the equations for the focal distance and height are derived to represent the concentration of incident solar radiation along the entire focal line. Identifying the surface area of the conical solar concentrator further facilitates the estimation of absorbed solar power for solar energy applications. To analyze the influence of the concentrator parameters on those of the receiver, this short communication introduces a theoretical approach that relates the height and diameter of the conical solar concentrator to the absorber diameter. The demonstrated parameters, equations, and approaches enable proper dimensioning of the entire system (the conical solar concentrator and absorber tube), allowing subsequent evaluation of temperature or other required parameters such as pressure, volumetric flow rate, heat losses, and output power. To maximize concentrated solar radiation, the cone angle of the solar concentrator must be 45°. Overall, this work encourages mathematical modeling experts in the energy sector to develop additional characteristic equations for conical solar concentrators, promoting energy affordability through integration into organic Rankine cycles and supporting energy needs, particularly in isolated areas.