# New Physically-Based Mathematical Model and Experiments for a Recently Invented Solar Pot
## 1 Introduction
One is the black-box type and the other one is the physically-based model. The physically-based model relies on the physical background of the modelled system or process, which is therefore often difficult to set up in the case of a complex system [17]. Black-box modelling does not take into account the physical background, it represents a more result-oriented approach, the creation of the model is typically simpler [18; 19]. The Hottel-Whillier-Biss physically-based mathematical model worked out for flat plate collectors [20] can be used to describe the temperature distribution of the working medium along the length of the collector as a function of place and time. In [21] a physically-based mathematical model was developed that can be used to describe the temporal behaviour of a flat plate collector. Estimation of the temperature of the outlet working medium is made possible by a differential equation formulated on the basis of the energy balance of the collector. Reference [22] presents several physically-based mathematical models describing the dynamic behaviour of unglazed flat plate collectors. In [23] the possibility of a device that can be used for heating and domestic hot water production was developed, in which the collector is equipped with a mirror. In connection with this, a physically-based model was worked out for evacuated tube solar collectors, which can be used to estimate the total solar radiation reaching the collector. In [24] a black-box type neural network model was made, which can be used to model the thermal behaviour of a flat plate collector. Knowing the intensity of solar radiation, the ambient temperature and the temperature of the working medium entering the collector, with a constant mass flow, the temperature of the outlet heat transfer medium can be predicted with the model. In [25] a black-box model based on multiple linear regression was developed for solar collectors. As a result, the appropriate temperature of the outlet working medium can be calculated. The identified and validated model was compared to the physically-based model of [21]. The results showed that the model in [25] was able to predict the temperature of the outlet working medium more accurately. The importance of the model, in addition to the appropriate accuracy (average accuracy better than 5%), is due to its simplicity. It requires little calculation and can be used for any type of collector (e.g., evacuated tube collector). There are several mixed storage models in the literature. In [15] a physically-based mathematical model was developed. An ordinary differential equation based on the energy balance of the tank allows the temperature of the tank to be calculated. The model does not take into account the heat capacity of the solar storage material. In [26] a physically-based mathematical model for a mixed storage was worked out, based on the heat balance of the storage, which can be used to calculate the temperature of the storage. A similar model can be found in [27]. In [28] a black-box model based on multiple linear regression was developed for mixed solar storages, which can be used to determine the geometric average temperature of the storage. When modelling tube-in-tube heat exchangers, energy balance is often assumed between the working media of the two sides, neglecting the environmental heat exchange [29; 30]. In [31] various mathematical models for tube-in-tube heat exchangers similar to the solar pot examined in this paper were developed. The physically-basedmodel takes into account the heat exchange with the environment, too. A black-box type mathematical model was also developed in [31] based on multiple linear regression, which also takes environmental heat exchange into account. The models were validated using measurements on a heat exchanger.