# MATHEMATICAL SIMULATION OF THE MOTION OF A SOLAR SPOT ON THE SURFACE OF A STIRLING ENGINE RECEIVER

### Abstract

*One example of an autonomous solar thermodynamic system is the use of a Stirling engine to generate electricity. The idea and implementation of such systems is not new, and during the twentieth and twenty-first centuries, systems were developed that used solar concentrators to direct the flow of solar radiation to the receiver of a Stirling engine. The receiver in this case is placed in the focus of the hub, but other configurations of such systems are possible. One idea is to use lenses as an element that concentrates radiation on the receiver.*

*A mathematical model was developed in this work, which makes it possible to determine the focusing surface of solar radiation with the help of a lens on a Stirling engine receiver.*

*To find the surface, it is proposed to divide the process into two main tasks: determining the course of the radiation concentrated by the lens on a horizontal surface and directly calculating the focusing surface. The first problem was solved by calculating the dependence of the coordinates of concentrated radiation at each time depending on such solar angles as: azimuthal angle of the Sun, the angle of inclination of the sun's rays to the horizontal plane, the angle of inclination of the Sun. The solution of the second problem was to find a surface, each point of which is equidistant from the lens.*

*Fixed at a distance of 1 m from the horizontal surface of the lens, with a focal length of 2.78 m during October, forms a surface bounded on the X axis by coordinates -2.15 and 2.15, on the Y axis by coordinates 2.7 and 3.6, by Z axis coordinates -0.2 and -0.8. The surface at each of its points is equidistant from the lens, the distance to the lens is the focal length. Thus, the surface is an array of focal points of the lens when changing the position of the Sun during the month.*

*The use of the model allows you to design a motor receiver for use in solar autonomous installations using lenses. Execution of the motor receiver in the form repeating a surface of focus during time of use of installation allows to maximize time of stay of the receiver in focus of a concentration lens and, as a result, to increase total size of receipt and use of solar radiation. Bibl. 4, fig. 6*

### References

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3. Strebkov D., Tveryanovich Ye. Kontsentratory solnechnogo izlucheniya. Pod red. akademika Raskhn D.S. Strebkova. M. GNU VIESKH. 2007. 316 p. [in Ukrainian].

4. Mkhitaryan N.M.. Gelioyenergetika: sistemi, tekhnologii, vikoristannya. Kyiv. Naukova dumka 2002. 315 p. [in Ukrainian].

*Vidnovluvana Energetika*, (4(67), 44-49. https://doi.org/10.36296/1819-8058.2021.4(67).44-49