# A Validated Thermal Computational Fluid Dynamics Model of Wine Warming in a Glass
## 4 Validation
The convection of water affects the warming the least, whereas the convection of the air has a more significant influence. Without considering the water convection, the temperature increase after 40 min is \(0.3\,\mathrm{\SIUnitSymbolCelsius}\) lower compared to the experiment. This corresponds to a relative error of 6.0% in relation to the absolute temperature change. For the air convection, the error is 19.7% or \(1.0\,\mathrm{\SIUnitSymbolCelsius}\). Surprisingly, radiation has a relatively large influence and affects warming more than convection. Not including radiation in the simulation results in a \(1.7\,\mathrm{\SIUnitSymbolCelsius}\) lower temperature, corresponding to a relative error of 33.6%. This is unexpected, since most practitioners probably consider the influence of radiation negligible at relatively low present temperatures. However, the result is well in agreement with the standard literature, compared to example 16.5-2 in [37], which features comparable absolute temperatures, temperature differences, and emissivities. Without simulating radiation and convection of the room air, the predicted temperature is off by 66.3% or \(3.3\,\mathrm{\SIUnitSymbolCelsius}\). These results show that the numerical simulation has to account for the convection and, especially, the radiation to appropriately model the heat transfer for liquid warming in a glass. A simple heat transfer model considering only the heat conduction would not be sufficient to depict the complex physical process. The local and temporal effects of the physical heating mechanisms are discussed more closely in Section 5. Now, the simulation for red wine warming in the glass was evaluated with the average wine temperature in Figure 7(a). The simulation agrees very closely with the experiment, as before for water. The difference after 40 min is only \(0.07\,\mathrm{\SIUnitSymbolCelsius}\) for both initial temperatures, which corresponds to a relative error of 1.4% or 1.0%, respectively. The largest error is only \(0.18\,\mathrm{\SIUnitSymbolCelsius}\), or \(2.6\%\), for \(T_{0}=8\,\mathrm{\SIUnitSymbolCelsius}\) after 20 min. Figure 7(b) compares the simulation results for water and wine. Hardly any difference in the average temperature can be observed. The temperature after 40 min differs only by \(0.07\,\mathrm{\SIUnitSymbolCelsius}\) for both initial temperatures. The experimental data support the simulation results since the temperature for water and wine were also nearly the same in the experiments. The comparison of the material properties of the examined water and aqueous ethanol solution at \(20\,\mathrm{\SIUnitSymbolCelsius}\) yields a deviation of about 0.9% for the density, 2.2% for the specific  
Figure 6: Validating the simulation for water warming at \(T_{R}=23\,\mathrm{\SIUnitSymbolCelsius}\) with the temperature at three positions (\(y_{1}\), \(y_{2}\), and \(y_{3}\)) in the water (\(T_{0}=12\,\mathrm{\SIUnitSymbolCelsius}\)) and the average water temperature for \(T_{0}=8\,\mathrm{\SIUnitSymbolCelsius}\) and \(T_{0}=12\,\mathrm{\SIUnitSymbolCelsiusius}\). (**a**) Temperature at three positions. (**b**) Average temperature. heat capacity, and 11.5% for the heat conductivity. The investigated wine has a relatively high alcohol content of 13.5%. Since wine usually does not exceed 15.0%, no significant deviating simulation results are expected for other wines. For wines with lower alcohol content, the temperature difference between the wine and water simulation is even more negligible. Consequently, one can assume that deviating fluid properties of wine due to the alcohol content do not significantly affect the heat transfer. Simulation results are therefore valid for all types of non-sparkling wine with negligible or moderate sugar levels. The possible impact of the sugar content was already discussed in Section 2.2. Furthermore, it would be sufficient to model wine as water. The simulation approach can be applied to comparable non-sparkling beverages with similar properties.