# A Validated Thermal Computational Fluid Dynamics Model of Wine Warming in a Glass
## 5 Results and Discussion
### Governing Physical Heating Mechanisms of the Warning Process  
Initially, the (sensible) heat of the glass is transferred to the wine by conduction. Buoyant flow starts to form. It is characterized by warmer wine with a lower density that rises in the wall area towards the surface. Accelerated fluid velocities lead to increased heat transfer from glass to wine, as cold wine is directed toward the glass. It should be noted that the convective heat transfer includes the conductive contribution, as the two cannot be subdivided at the boundary. The maximum velocity magnitude of the natural convective flow is \(2.4\times 10^{-3}\) m s\({}^{-1}\), which occurs within the first minute of the observation in the vicinity of the wall. The average velocity magnitude in wine peaks at \(8.23\times 10^{-4}\) m s\({}^{-1}\); see Figure 8(b). Warmer liquid rises in the wall area, passes by the surface towards the center, and then returns downwards to the stem wall along positions \(y_{1}\) to \(y_{3}\); see Figure 8(a). When the fluid reaches the lower part of the glass, one can observe a slight increase in velocities due to the narrowing of the glass; see \(t=120\) s in Figure 8(b), for example. The uptake of sensible heat from glass walls and initial natural convection result in the accelerated warming of wine within the first minute; see Figure 8(a). The magnitude of the velocities remains comparably moderate after the initial shocks within the first minute; see Figures 8(b) and 10. The Reynolds number in the liquid domain (\(H=127\) mm) is \(Re=\max(\|\mathbf{\psi}\|)\,H/\
u\approx 260\), where \(\
u\) is the kinematic viscosity. The maximum Grashof number is \(Gr=g_{1}\,\beta\,\left(T_{\mathrm{W}}-T_{0}\right)H^{3}/\
u\approx 4.38 \times 10^{6}\), where the index W denotes the glass wall temperature, and \(\beta\) is the thermal expansion coefficient. The Grashof number relates viscous forces to natural convective forces and helps to decide whether a turbulent buoyancy is to be expected. Turbulent boundary layers are present for \(Gr>4\times 10^{8}\)[38], which is two orders of magnitude higher than the maximum Grashof number within this work. The assumption of laminar flow in the liquid domain is, hence, valid. Investigating the natural convection closer, it does not seem to be able to equilibrate the temperature in wine. One can observe a stratification in temperatures from two minutes onwards; see Figure 11. This finding aligns with the findings from the model validation, where the exclusion of wine convection did not alter the simulation outcome considerably. As the wine starts to cool the wine glass, the latter engages in net radiative heat exchange with surrounding warmer walls of the air domain. The validation in Figure 7  
Figure 9: Decline of buoyant effects after one minute for temperatures and velocities. Probes at positions on the symmetry axis and volumetric averages. demonstrates the dominant influence of radiation. Moreover, the temperature difference enables sensible heat transfer from the air at room temperature into the glass; see Figure 11. Due to the higher density of cooler air, the air starts to fall past the glass and then hovers horizontally away on the table; see Figure 12. A natural convection cell forms in the air domain. The cooled air tumbles through the problem domain and regains room temperature before it may again pass by the glass. Figure 11 underlines that air continuously approaches the glass at room temperature. After one hour, the approaching air still has \(T_{\rm air}=22.997\,^{\circ}\)C, which confirms that the natural convection of air in a room can be modeled in a closed cavity with constant wall temperatures. The maximum velocity in the vicinity of the glass is \(1.4\times 10^{-1}\,\rm{m\,s^{-1}}\). The corresponding Reynolds number (\(H=225\,\rm{mm}\)) is \(Re\approx 2000\) and Grashof number is \(Gr\approx 2.44\times 10^{7}\). Hence, the initial assumption of dominantly laminar airflow seems valid for the scope of this work.