# New Physically-Based Mathematical Model and Experiments for a Recently Invented Solar Pot
## 3 Mathematical Modelling
### Simulation Results
Convective heat transfer between the inside of the mantle and the outer surface of the cooking tank's wall. Taking into account the liquid in the mantle (water) and the material of the cooking tank wall (stainless steel), and assuming forced convective heat transfer along the surface of the wall, the heat transfer coefficient is 850 \(\frac{W}{m^{2}K}\), which is an average value according to [34]. 2. Thermal conduction inside the mantle's wall. (For more details, see Note 2 above.) 3. Convective heat transfer between the inner surface of the cooking tank's wall and the inside of the cooking tank. Taking into account the material of the wall (stainless steel) and the liquid in the cooking tank (water), and assuming free convective heat transfer along the surface of the wall, the heat transfer coefficient is 650 \(\frac{W}{m^{2}K}\), which is an average value according to [34]. The above details were fed into the [35] online program, which made the necessary calculations for the overall heat transfer coefficient. The result is U\({}_{p,in}=351\)\(\frac{W}{m^{2}K}\). T\({}_{p,e}\)(t) is assumed to be constant as the solar pot is located in an air-conditioned mobile container, so T\({}_{p,e}:\) T\({}_{p,e}(t):25\)\({}^{\circ}\)C, in accordance with the temperature set inside the container. The initial values of the model are also set to this value, so T\({}_{m,out}(0):25\)\({}^{\circ}\)C and T\({}_{t}(0):25\)\({}^{\circ}\)C. (Accordingly, our model can be applied for a solar pot inside a building, which is a rather general situation, since the outside effects, like the effect of sky, solar irradiance, wind speed etc. are not considered.) For the sake of simplicity, T\({}_{m,in}\)(t)(\(=\) T\({}_{c,out}\)(t)) is set constant in the simulations, 80 \({}^{\circ}\)C. Choosing this temperature value, it was taken into consideration that it can easily be reached and maintained for a longer time on a typical day in May in Hungary and that this inlet temperature is probably high enough for the cooking tank to reach the minimum temperature for sterilizing foods--based on our preliminary assumption. This minimum temperature is 73.9 \({}^{\circ}\)C, but in this work 75 \({}^{\circ}\)C is aimed due to safety purposes. The simulations were carried out with two different volumetric flow rate (v) values, which can be realized in the experimental system as well. The results of the simulations are presented in Figures 5 and 6. More specifically, Figure 5 presents the modelled T\({}_{m,out}\) and T\({}_{t}\) temperatures in case of v = 100 \(\frac{L}{h}\)(\(=2.78\cdot 10^{-5}\)\(\frac{m^{3}}{s}\)), while Figure 6 presents them in case of v = 200 \(\frac{L}{h}\)(\(=5.56\cdot 10^{-5}\)\(\frac{m^{3}}{s}\)). The running time of the simulations was 1 h in both cases. In Figures 5 and 6, it can be seen that the cooking tank temperature reaches 75 \({}^{\circ}\)C, which is normally enough for the sterilization of foods. It can also be stated that this temperature is reached in less time with higher flow rate. With 100 \(\frac{\text{L}}{\text{h}}\), it took 38 min (see Figure 5), while with 200 \(\frac{\text{L}}{\text{h}}\), it required 28 min (see Figure 6). In addition, the maximum (final) tank temperature was 76.5 \({}^{\circ}\)C in case of 100 \(\frac{\text{L}}{\text{h}}\) and 77.7 \({}^{\circ}\)C with 200 \(\frac{\text{L}}{\text{h}}\). Figure 5: Result of the simulation in case of \(\text{v}=100\)\(\frac{\text{L}}{\text{h}}\). Figure 6: Result of the simulation in case of \(\text{v}=200\)\(\frac{\text{L}}{\text{h}}\).