###### Abstract  
Thermal energy stored within a rock bed thermal storage system, which is mostly used in agriculture, can be identified during the storage phase using mathematical models based on heat transfer, which concerns batteries running in a vertical setting. However, this requires the conversion of differential equations into algebraic equations, as well as knowledge about the initial and boundary conditions. Furthermore, a lack of information or incomplete information about the initial conditions makes it difficult or impossible to evaluate the volume of stored energy, or can cause significant errors during evaluation. Such situations occur in systems equipped with a rock battery, in which solar collectors act as source of energy. Considering the above, as well as the lack of a model for batteries in a vertical setting, we identified the need for research into the storage phase of rock bed thermal storage systems, working in a horizontal setting, and generating MLP-type neural models. Among these models, MLP 4-7-1 turned out to be the best both in terms of the values of regression statistics and possibilities of generalization. According to the authors, artificial neural models depicting temperature changeability in storage phase will be helpful in the development of a new methodology that can predict the heat volume in rock bed thermal storage systems. r +
Footnote †: : 2021: 11, 10711. [[https://doi.org/10.3390/app112210711](https://doi.org/10.3390/app112210711)]([https://doi.org/10.3390/app112210711](https://doi.org/10.3390/app112210711))
temperatures, assuming an identical rock bed and air temperature), we shall focus on the two-temperature model, as it bears more similarity to the empirical system. This model consists of several equations of flow continuity and momentum, and two equations of energy balance for the air and the deposit, as appropriate (Equations (1)-(4)). A flow continuity equation:  
\[\
abla\cdot\mathbf{U}=0 \tag{1}\]  
where \(\mathbf{U}\)--averaged air velocity in an elementary volume [m\(\cdot\)s\({}^{-1}\)]. A momentum equation:  
\[a\mu\psi\mathbf{U}+b\rho_{f}\psi^{2}|\mathbf{U}|\mathbf{U}=-\
abla p_{T}+\rho_{f\theta}\beta \Big{(}T_{f}-T_{o}\Big{)}g\mathbf{k} \tag{2}\]  
where:  
\(\alpha\)--Darcy's constant [m\({}^{-2}\)];  
\(\mu\)--dynamic viscosity [kg\(\cdot\)(m\(\cdot\)s)\({}^{-1}\)];  
\(\psi\)--porosity;  
\(\rho_{f}\)--fluid density [kg\(\cdot\)m\({}^{-3}\)];  
\(\rho_{f\theta}\)--fluid density at the reference temperature [kg\(\cdot\)m\({}^{-3}\)];  
\(b\)--Forchheimer's constant [m\({}^{-1}\)];  
\(p_{T}\)--dynamic pressure [Pa];  
\(\beta\)--volumetric temperature expansion coefficient [K\({}^{-1}\)];  
\(T_{f}\)--air temperature [K];  
\(T_{o}\)--reference temperature [K];  
\(g\)--acceleration due to gravity [m\(\cdot\)s\({}^{-2}\)];  
\(k\)--vertical unit vector. The equation for fluid energy balance:  
\[\Big{(}\rho_{f}c_{fp}\Big{)}\psi\frac{\partial T_{f}}{\partial t}+\Big{(}\rho _{f}c_{fp}\Big{)}\psi\mathbf{U}\cdot\
abla T_{f}=k_{f}\
abla^{2}T_{f}+\frac{hA_{sf }}{\forall}\Big{(}T_{s}-T_{f}\Big{)} \tag{3}\]  
where:  
\(A_{sf}\)--interface surface [m\({}^{2}\)];  
\(c_{fp}\)--fluid specific heat [J\(\cdot\)(kg\(\cdot\)K)\({}^{-1}\)];  
\(k_{f}\)--effective thermal conductivity of fluid [W\(\cdot\)(m\(\cdot\)K)\({}^{-1}\)];  
\(h\)--convective heat transfer coefficient [W\(\cdot\)(m\({}^{2}\).K)\({}^{-1}\)];  
\(T_{s}\)--deposit temperature [K];  
\(t\)--time [s];  
\(\forall\)--volume deposit [m\({}^{3}\)]. Rock bed energy balance equation:  
\[\big{(}\rho_{s}c_{sp}\big{)}(1-\psi)\frac{\partial T_{s}}{\partial t}=k_{s} \
abla^{2}T_{s}+\frac{hA_{sf}}{\forall}\Big{(}T_{f}-T_{s}\Big{)} \tag{4}\]  
where:  
\(c_{sp}\)--rock-bed-specific heat [J\(\cdot\)(kg\(\cdot\)K)\({}^{-1}\)];  
\(k_{s}\)--effective thermal conductivity of rock bed [W\(\cdot\)(m\(\cdot\)K)\({}^{-1}\)];  
\(\rho_{s}\)--rock bed density [kg\(\cdot\)m\({}^{-3}\)].