Mathematical model of a rotary 3D format photo electric energy device

This article provides a theoretical analysis of the mechanical and energy issues of a newly developed 3D rotating photovoltaic device. In addition, a 3D model of the photovoltaic device has been developed. Also, a digital modeling program has been developed to study the mechanical parameters and external influences on the surface temperature of a photovoltaic device. The results obtained in new program are presented.


Introduction
Solar panels exchange heat energy with the environment through radiation. However, the heat energy coming from the sun and falling on the surface of the solar panel is greater than the heat radiation energy of the solar panel to the environment so the surface temperature of the solar panel is higher than that of the environment [1][2]. According to the experimental results, the surface temperature of the solar panel rises to a value 63% higher than the ambient temperature. For example, when the ambient temperature is 35 0 C, the surface temperature of the solar panel rises to 57 0 C [3][4][5][6]. Another method of heat transfer available is convection heat transfer [8][9]. If the air layers around the solar panel move, it will cause the heat energy on the surface of the solar panel to be transferred to the environment. This ensures that the surface temperature of the solar panel does not differ significantly from that of the environment. Of course the question arises here, isn't there always wind? The solution to this is simple, if there is no wind, if we move the device itself, we can move the molecules with high temperature around it and exchange them with the molecules with low temperature. This causes forced convection. Since this process is continuous, the surface temperature of the device is approximately equal to the ambient temperature [14].

Theory
Suppose there is a connection between the intensity of light falling on a solar panel and the power of electricity as follows.

Pc -electrical power
Pin -power that is incident to surface of solar panel

Pdis -dissipative power
The dependence of light intensity and temperature is as follows: If we find Tc here UL·(Tc-Ta) = I(α-η) Tc-Ta =I/ UL(α-η) Tc=Ta + I·α / UL(1-η/α) If we calculate UL in NOCT, we say η = 0 So, The convection coefficient due to wind was studied empirically by Skoplaki and the following formula was determined for the forced convection coefficient of solar panels made of polycrystalline silicon [4].
When there is a difference between the surface of the solar panel and the ambient temperature, the process of energy exchange due to radiation also occurs [10][11][12][13].
Since the device we have developed is in the form of a pyramid, let us see that its mechanical properties i.e. the rotational speed of the device depend on the installed motor power, the moment of inertia of the device and the air resistance.
The moment of force applied by the motor to the device is used to give the device a certain acceleration and to overcome the frictional force of the air. Mt=M+Mish The solution of the differential equation is as follows.
If we say ω = 0 at initial time t = 0, then the solution in the view occurs.
From this formula we can draw the following conclusions. The device moves with acceleration during the initial times of movement, and after a certain time it reaches a constant speed. This is because the moment of friction is equal to the moment of force that the motor gives to the device. This event occurs in about 1-2 seconds. This phenomenon depends on the moment of inertia of the device, the resistance of the air, and the power of the motor.
Here the moment of inertia is determined as follows.

Graph 2 Dependence of the moment of inertia of a photoelectric device on the lower radius of the device
According to the theory developed above, a program called STVertical was created in the C # 9.0 programming language. In the program, the differential equation of the above formula (36) was solved by the numerical method. A 3D model has also been developed to provide a better understanding of the structure and operation of the device [14].

Graph 3
The dependence of the surface temperature of a photoelectric device on the speed of rotation.

Discussion
We know that due to the presence of air resistance, the angular velocity of the proposed device increases exponentially in 2 seconds (Graph 1). Then, the device starts spinning at the same speed. This is because the moment of resistance of the air is equal to the moment of force applied by the motor to the device.
By changing the height, top and bottom radii of the device, we can develop a technically better version of the device. It is known from the dynamics of solids that a change in the height, top and bottom radii of a pyramid causes a change in its inertia. A change in inertia, in turn, causes a change in the speed of the device. This means that the surface temperature of the solar cells also changes.
The program based on all developed theories was registered by the Intellectual Property Agency of the Republic of Uzbekistan under the name DGU09198 "STVertical" on 24.09.2020 [15][16][17]. The possibilities of this program are wide and it is possible to process the results and compare them with the results obtained in practice.

Conclusion
According to scientific studies, the surface temperature of solar panels has changed due to wind. Let's say there's no wind, but we can move the device. That's why we decided to turn the device on. We tried to find a technical and theoretical solution to it above. The results show that the surface temperature of the device does not change partially when the angular velocity is 8 rad / s. The above theoretical solutions show that the surface temperature of the device does not increase over time.