# New Physically-Based Mathematical Model and Experiments for a Recently Invented Solar Pot
## 2 System Description  
The solar pot (shown in Figure 1) is a recent invention, which gained a utility model protection in 2021 from the Hungarian Intellectual Property Office under patent number 5489 [33]. Currently, the pot is in prototype status, that is, a single specimen of it has been produced, from stainless steel (AISI 304) with a thickness of 2 mm, so far, for research purposes. However, it is already published by means of the mentioned patent, so it could be produced by a proper manufacturer commercially, in compliance with the related legal regulations. The device is made for environmentally friendly cooking or heating of foods and liquids. Its structure is similar to a double pipe heat exchanger. It has an outer mantle and an inner cooking tank. Cooking or heating is done as follows. The mantle heats the cooking  
Figure 1: Photos of the solar pot. tank by circulating working medium (water or else) along the cooking tank's outer surface. The mantle forms a closed hydraulic circuit with a solar collector. The working medium in the mantle and the interior of the cooking tank are hydraulically separated from each other, which implies heating and cooking can be executed hygiically. The pot can also be used for reheating foods or heating liquids not only in connection with food preparation. Using the device, heating and cooking can be made with the utilization of renewable solar energy. The solar pot has the advantage that it can be connected to an existing solar heating system. It is an indirect-type food processing equipment, which can be used with any collector using liquid as working fluid. If there is insufficient solar energy, one can heat the pot with a stove or a cooking plate as well. In the experimental system of this paper, the solar pot is connected to an evacuated tube solar collector. Figure 2 presents the sketch of the pot containing the main geometric sizes and measuring points (for three temperatures) on it. The experimental solar heating system with the solar pot and the time-dependent variables along with the parameters of the system are shown in Figure 3.  
Figure 3: The solar pot and the experimental system. Figure 2: Sizes and measuring points of the solar pot. In Figure 3, t denotes the time dependence of the variables. These variables are the following:  
* \(\mathrm{T_{c,e}}\): temperature of the solar collectors's environment (outdoors), \({}^{\circ}\)C,
* \(\mathrm{T_{c,in}}\): solar collector inlet (water) temperature, \({}^{\circ}\)C,
* \(\mathrm{T_{c,out}}\): solar collector outlet (water) temperature, \({}^{\circ}\)C,
* \(\mathrm{T_{t}}\): temperature in the cooking tank, \({}^{\circ}\)C,
* \(\mathrm{T_{p,e}}\): temperature of the solar pot's environment (indoors), \({}^{\circ}\)C,
* \(\mathrm{T_{m,in}}\): mantle inlet (water) temperature, \({}^{\circ}\)C,
* \(\mathrm{T_{m,out}}\): mantle outlet (water) temperature, \({}^{\circ}\)C.  
As the fluid in the mantle is considered mixed, the (homogeneous) temperature inside the mantle is (consequently) considered the same as the mantle outlet temperature. (Basically, this temperature also corresponds to the, geometrically, mean fluid temperature in the mantle.) As the pipes connecting the solar pot and the collector are insulated and their volume is neglected, we consider the solar collector outlet temperature and the mantle inlet temperature equal (\(\mathrm{T_{c,out}}=\mathrm{T_{m,in}}\)). The same holds for the solar collector inlet temperature and the mantle outlet temperature (\(\mathrm{T_{c,in}}=\mathrm{T_{m,out}}\)).