# A Validated Thermal Computational Fluid Dynamics Model of Wine Warming in a Glass
## 5 Results and Discussion
### Spatial and Temporal Heat Flux Analysis  
After describing the physical heating effects during the warming process, this section provides answers concerning where and when these effects occur. Figure 13a,b depict the heat intake \(Q\) from the surrounding air domain. At the liquid surface, convective and radiative heat fluxes add up to the total heat intake. The dominance of radiative heat flux and the overall low magnitude of heat transfer by convection can be explained by a stagnation of the natural convective airflow in the opening of the glass; see Figure 12. Consequently, a pronounced thermal boundary layer can build up; see Figure 11. The reduced air temperature trapped in the glass leads to a reduced driving temperature difference for heat conduction at the surface. At the glass-air interface, heat fluxes start to form with continuously decreasing glass temperatures, as, initially, the glass and air both are at \(T_{\rm R}\). Radiative and convective heat fluxes at the air-glass interface do not add up to the total heat flux that enters the wine; see Figure 13b. The difference results from the sensible heat of the glass, which is transferred predominantly within the first minutes of the simulation. The magnitude of heat intake at the glass-wine interface is up to two orders larger than at the air-wine interface. Radiation, again, slightly dominates the heat intake into the glass, which is also reflected in the model validation; see Figure 7. All in all, the main heat stems from the outside convection of air and the radiative heat exchange of the glass with surrounding walls and the table. The maximum conductive heat flux from the table is \(1.2\times 10^{-2}\) W and, hence, can be neglected. Both radiative and convective heat transfers govern the second warming period for \(t>2\) min, when the sensible heat exchange of the glass diminishes. Radiative and convective fluxes reach their maximum after approximately ten minutes. Afterwards, the mechanisms again gradually attenuate as the driving temperature difference between glass and room temperature decreases.  
To analyze the local effects of heat transfer, the heat flux at the wine-glass interface (W m\({}^{-2}\)) is integrated over horizontal lines of equal heights, such that one can evaluate the integrated heat flux (W m\({}^{-1}\)) at variable \(y\)-positions. Figure 14a illustrates these height-dependent heat fluxes at the interface at discrete points in time. Although a dominant heat flux from the stem could be expected, this is not the case. Dominant heating comes from the thin parts of the glass at elevated heights. The heat flux attenuates by one order of magnitude within the first two minutes, where the exchange of sensible heat of the glass dominates the heating. The heat flux from air to the outer wine glass surface at \(t=10\) min is analyzed in Figure 14b. The dominant convective heat flux appears in a small vertical zone of the glass \(y\in[125,150]\) mm, where the glass diameter is large. Below this area, the airflow slightly detaches from the glass, which leads to decreased convective heat  
Figure 12: Velocity distribution in the air and wine for \(T_{0}=12\,^{\circ}\)C and \(T_{\rm R}=23\,^{\circ}\)C in the symmetry plane.  
flux. In the stem and foot area, the cold air regains heat from the glass. On the contrary, the radiative heat exchange can occur within the full range of heights where wine is located on the other side of the wall.  
Overall, one can differentiate between two heating periods. Within the first minutes, accelerated heating takes place. The driving mechanisms are the transfer of sensible heat from the glass to the wine and subsequent natural convection. The second period is characterized by the radiative and convective heating of the wine glass that occurs at the outer surface of the glass.