## 2 Materials and Methods
### Boundary Conditions  
Figure 3 (right) shows the boundary conditions of the computational model. The values used for the boundary conditions are given in Table 3. Air-on and air-off streams are modelled in a closed-loop model. The velocity values are calculated by the fan flow rate and boundary length. The right boundary is defined as the open boundary with both inflow and outflow conditions supported. One of the most important tasks is to set an open boundary location in the horizontal distance to the display case. The distance significantly influences simulation results. Additional studies were conducted to set the location of the open boundary. Figure 4 shows the distance of the open boundary and the temperatures at the measuring points. The measuring points are marked in location 1 (Figure 4, temperature distribution in the middle plane after 10 s). It can be seen that the results are the same in the 2, 3, and 4 studies (Figure 4, locations 2, 3, and 4). Short distance produces worse results of the airflow temperature for the entire simulation time interval. Long distance produces worse results of the airflow temperature at the early air curtain formation time in that the initial model temperature is set to 10 \({}^{\circ}\)C. This value of the initial model temperature was chosen by measuring the temperature after the defrosting process of the refrigerated cabinet. The ceiling and floor are considered adiabatic walls. The air temperature is adopted at the one boundary of air-on. The air-on boundary is defined as the velocity inlet, and the air-off boundary is described as the velocity outlet. The products are defined as solid and non-slip boundary conditions. The thin-layer structure was used  
Figure 3: 2D mesh applied to the cabinet model (**left**); the computational domain of the 2D-CFD model for an open display cabinet and the locations of boundary conditions (**right**).  
Figure 2: Temperature profile obtained for points 1–5 using meshes M1–M4.  
to model the honeycomb to provide a more accurate flow direction. The wall shelves, the bottom shelf, the back panel, and other parts of the cabinet, were made from steel sheets, through which heat transfer occurs. The wall shelves and the bottom shelf were modelled as thin steel walls with a thickness of 1.4 mm. Other inner parts were modelled as thin steel walls with a thickness of 0.7 mm. The boundary condition of the back panel is defined as a porous jump, with other surfaces being walls. Lastly, there is strong natural convection between the refrigerator and the ambient air affected by the density of air at different temperatures. To simulate this natural convection, gravity was activated in the models and the density of the air was calculated based on the ideal gas formulas.  
Figure 4: Influence of the location of the open boundary on the air temperature in the middle plane.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Temperature, K** & **Velocity, m/s** & **Pressure** \\ \hline Air-on & 272.15 & 0.252 & \\ Air-off & & 0.95 & \\ Open boundary & 298.15 & & 0 \\ Model & 283.15 & & \\ \hline \hline
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