**6. Conclusions**

A strategy was established to improve computational time, as described below. The first analysis shown in Figure 3a, was computed using properties of water to simulate this fluid inside of the cell. For the simulations shown in Figure 3b–e, a thermal diffusivity of value 1 was used to reduce computational time. The time is only 3 s, in contrast with Figure 3a, where time is 3000 s.

The maximum error obtained in this work among the analytical results and the numerical method was around 0.86% for an increase of 10 ◦C and the minimum was 0.075% for an increase of 1 ◦C. These results show that there is a good agreemen<sup>t</sup> with the finite-element method.

The cylinder of a 1.5 cm radius and a height of 9.9 cm reached in a period time of 1.5 s a uniform temperature inside of the entire cell, which is half the time with respect to other dimensions evaluated. This is because the evaluated cylinders have a smaller radius with respect to the sphere. However, other parameters such as temperature sensor location, the cell material, and the inlets and outlets for fluid to the cell need to be evaluated.

The spherical geometry has better thermal performance than the cylindrical, because the temperature gradients are smaller. The results obtained are that the maximum gradient for a spherical cell is 0.104 ◦C, and the maximum gradient for a cylindrical cell is 0.208 ◦C; therefore, geometry affects thermal behavior, as reported by [2]. In real applications, the system in a sphere responds with greater thermal speed than in a system contained within a cylinder. However, the homogeneity in the fluid contained in the cell is the most important variable because accuracy measurements affect the heat capacity value.

When heat is added to a system, increasing the temperature from 23 ◦C to 25 ◦C, the difference in temperature between the analytical solution and the numerical solution is 0 as seen in Figure 3a. The maximum temperature variation between the cylinder and the sphere obtained from the simulation occurred at the time of extracting heat from the system, causing a decrease in temperature from 30 ◦C to 29 ◦C, generating a temperature variation of 0.08 ◦C according to Figure 3e.

The error among analytical and numerical results increases with increasing temperature and decreases as the steady state is reached.

**Author Contributions:** Conceptualization, J.E.E.G.-D. and J.M.O.R.; methodology, J.E.E.G.-D., J.M.O.R., and M.A.Z.-A.; software, M.A.Z.-A., J.M.O.R., and J.E.E.G.-D.; validation, J.E.E.G.-D., J.R.-R., M.A.Z.-A., J.M.O.R., and L.L.-C.; formal analysis, L.L.-C., J.E.E.G.-D., J.R.-R., and M.A.Z.-A.; writing—original draft preparation, M.A.Z.-A., L.L.-C., and J.R.-R.; writing—review and editing, M.A.Z.-A.; supervision, M.A.Z.-A., J.R.-R., and L.L.-C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Consejo Nacional de Ciencia y Tecnología (CONACYT) and PRODEP.

**Conflicts of Interest:** The authors declare that there is no conflict of interest. *Energies* **2020**, *13*, 2300
