# New Physically-Based Mathematical Model and Experiments for a Recently Invented Solar Pot
## 1 Introduction  
The thermal energy provided by the sun is used to treat food in different ways. Examples include drying [1], baking and cooking [2]. Solar food preparation devices operated with solar energy are known, in which solar energy directly heats a surface or air along it in a closed box, and the heat is transferred from there to the closed vessel placed in the box [3]. With this solution, the preparation of food by cooking cannot be solved in many cases [4]. However, there are solar cookers able to produce the temperature required for cooking, which is 73.9 \({}^{\circ}\)C according to [5]. Typical types are the reflective panel [6], the parabolic [7] and the evacuated tube solar cooker [8]. These are the so-called direct-type food processing devices. Indirect types use a solar collector to produce the thermal energy needed for food processing. In [9] a solar cooker with solar collector and heat storage is investigated in China that uses oil as heat transfer medium. The main elements of the system are the solar collector, the heat storage and the cooking plate, which can be converted into a traditional electric cooking plate when supplemented with a heating element, enabling cooking even when there is not enough solar energy available. The main goal of the research was to investigate the effect of the quartzite heat storage medium on the system. For this, a mathematical model describing the performance of the system was prepared. The design with heat storage was compared with a version with one and two heat storage tanks. Based on the results, the version with quartzite heat storage increases the performance of the system, and the investment cost also decreases. The solar share was 71% which clearly means a significant reduction in the carbon dioxide emission with regard to the cooking activity. In the investigations of the present paper on a mantle-pot equipment that we call solarpot, working with only solar heat, the solar share is even higher, 100%. Nevertheless, the completion of the pot with some auxiliary heating may come into consideration in the future, as it is mentioned in the Conclusions. (It would decrease the solar share but increase the operating period of the pot.) In [10] a research is conducted on an indirect type solar food processing device with nanofluid working medium. One of the main elements of the system is the parabolic solar collector, at the focal point of which the working medium is heated by flowing through it. The other important element is the cooking unit, which consists of a copper pot and the copper pipe that surrounds it (wrapped around it). The heated working medium flows in this pipe, thus transferring the heat to the cooking space. A separate tank was also installed between the cooking unit and the collector, through which the working medium also flows. Due to the parabolic collector, the spiral heat exchanger and the additional tank, the structure of the system is more complex and thus its implementation is obviously more expensive than the system of the solar pot of this paper, which uses a more conventional evacuated tube collector and the solar pot similar to a simple, jacketed heat exchanger. The authors investigated the effect of mixing nano-sized particles with the oil serving as the working medium, how the mass fraction of the particles and the volumetric flow rate of the medium affect the development of the system's energy efficiency. The mass fraction was varied between 0 and 0.5% by mass, and the flow rate between 0.25 and 0.55 \(\frac{\mathrm{L}}{\mathrm{min}}\). Based on their tests, it was found that while the efficiency of the collector increases continuously with the increase in volumetric flow rate, the highest efficiency is achieved in the case of the cooking unit at 0.25 \(\frac{\mathrm{L}}{\mathrm{min}}\). Increasing the mass ratio increases the energy efficiency of both main units.