A mathematical model to develop a Scheffler-type solar concentrator coupled with a Stirling engine

This study develops and applies a new mathematical model for estimating the intercept factor of a Scheffler-type solar concentrator (STSC) based on the geometric and optical behaviour of the concentrator in Cartesian coordinates, and the incorporation of a thermal model of the receptor is performed using numerical examinations to determine the technical feasibility of attaching the STSC to a 3kWe Stirling engine. A numerical validation of the mathematical model is determined based on the experimental results reported for the WGA500 concentrator and the CNRS-PROMES system receiver. The numerical results allow for the design of the STSC and a comparison with a parabolic dish that provides the same thermal demand. Our findings show that the highest concentration was obtained with an edge angle of 45°, which was observed in the parabolic dish as well, but the STSC receiver shows a 7% increase in the thermal efficiency compared with the efficiency of the parabolic dish receiver. Finally, the STSC is appropriate for regions where the solar height allows for a reduction of convective thermal loss.

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