# New Physically-Based Mathematical Model and Experiments for a Recently Invented Solar Pot
## 1 Introduction
The energy efficiency of the entire system increases by 20.08% in the case of a particle concentration of 0.5% by mass and a flow rate of 0.25 \(\frac{\mathrm{L}}{\mathrm{min}}\), and 2 litres of water at 30 \({}^{\circ}\)C could be heated to boiling point in 31.51% less time as in the case of the version using oil only. In [11] an indirect-type solar cooker is prepared in Egypt with flat plate collectors equipped with reflectors. They used phase change material, magnesium nitrate hexahydrate, mixed with steel shavings as heat storage material. The equipment is capable of cooking general meals in the midday and afternoon hours. In the evening it can be used to prepare special dishes that can be cooked at low temperatures for a long time (e.g., beans). In the night and morning hours it can be used to keep or reheat food. In [12] it was investigated how the performance of the system changes when the collector is supplemented with reflectors in an indirect solar food processing system equipped with a flat plate collector with water as working medium and supplemented with a heat storage tank containing a phase change material. They found that without a reflector, the highest average temperature of the absorber is 92 \({}^{\circ}\)C, the highest temperature of the outlet working medium is 71 \({}^{\circ}\)C, and the highest energy efficiency is 63%. It can be stated that the system is not suitable for cooking as the minimum safe temperature for cooking is 73.9 \({}^{\circ}\)C according to [5]. On the other hand, thanks to the addition of reflectors, these values were respectively 130 \({}^{\circ}\)C, 103.65 \({}^{\circ}\)C and 79%. The device was used to cook 1 kg of rice and 1 kg of pasta in 1.5 L of water. In both cases they were successful. It should be mentioned that the additions made in order to increase the performance of the equipment significantly increased the complexity of the system. The system examined in this paper has a simpler design and does not contain phase change material. In [13] a solar pressure cooker is investigated, which is connected to an evacuated tube solar collector to provide the necessary energy for operation. The water heated in the collector flows directly into the cooking chamber (under pressure) without the intervention of a heat exchanger. Thus, during operation, the condition of the heat-treated raw material/food must be difficult to check. The system we are examining is more practical, the cooking space is accessible during operation too, as it is hydraulically separated from the collector circuit under pressure. In [13] they used experiments to investigate the thermal behaviour of the equipment, under different weather conditions (radiation intensity, ambient temperature), regarding the boiling of different masses of water. Based on their results, a larger mass of water boils proportionally in less time, so the efficiency of the system improves when larger quantities are boiled. In [14] a large-scale cooking system was made capable of supplying energy to several cooking units at the same time. The flat plate collector system also includes a heat storage tank made of oil and stone, in addition to the cooking units. The flow of the working medium is not forced, no pump is needed. The system has been successfully used for food preparation in several developing countries (e.g., Mali, India). The system, that is the subject of this paper's research, works with a pump, so its placement/implementation can be done in a less constrained manner, it is also simpler and does not contain heat storage. The main elements of the system examined in this paper are the solar collector and the so-called solar pot. In the literature, there are mathematical models for collectors and solar heating systems [15; 16], however, as it is a new invention, no model has yet been worked out for the solar pot. In terms of design, the solar pot is similar to a tube-in-tube heat exchanger or a solar storage tank. Models for those are already available in the literature. There are two main types of models.