## 2 Materials and Methods
### Numerical Procedure and Boundary Conditions  
The 2D (two-dimensional) time-dependent CFD model was constructed to analyze airflows inside the OTRDC (Figure 1) and their effects on the temperature inside the cabinet. The objective of numerical research is to study the capability of the two-dimensional \(k\)-\(\varepsilon\) model to estimate the formation speed of the air curtains and temperatures of the products within the OTRDC. In the numerical simulations, the following assumptions were used in order to simplify the procedure and preserve the fundamental properties of the process:  
* The moisture transfer process is not taken into account;
* The thermal properties of the fluid in the air-on section are in a steady state, with fixed velocities and temperatures of both airflows;
* The mass transfer from the load into the air (mass loss) is not taken into account;
* Fans and the evaporator are replaced by an air-on stream with a fixed temperature and flow velocity.  
The mathematical model of heat transfer at the fluid interface, the turbulence kinetic energy equation, and the equation of turbulence dissipation rate are presented in [9].  
Heat transfer between products and air, as well as the airflows inside the OTRDC, were simulated using Comsol Multiphysics software. In this study, the numerical solving was conducted using the finite element method (FEM). Three different meshes (number of elements: 4415, 8648, and 16,010) were used to assess simulation precision. Figure 2 shows the temperatures at the same locations inside the OTRDC calculated using different mesh sizes. Significantly finer meshes were used, particularly in areas near the DAG (Figure 1), the RAG, and the fluid/solid interfaces. Mesh sets exhibit relative errors below 0.5%. The mesh with 8648 elements was proven satisfactory, as the calculation results did not change with decreasing mesh size (Figure 2). The 8648-element mesh shown in Figure 3 Left, was used in all numerical simulations. Numerical studies were performed on a computer (64-bit operation system) with an Intel(R) Core(TM) i7-7700K processor (Intel Corporation, Santa Clara, CA, USA) running at 4.20 GHz and 32 GB RAM.  
Figure 2: Temperatures (**left**) obtained for points 1–5 (**right**) using meshes 4415; 8648; and 16,010.  
The computational domain with positions of boundary conditions is presented in Figure 3 Right; values are listed in Table 2. Air-off and air-on streams are simulated in a closed-loop model. Air velocity values are computed on the basis of the length of the boundaries and the fan flow rate. The right boundary is described as the open boundary with supported outflow and inflow conditions. In different cases, the air temperature is assumed to be at the one or two air-on boundaries. The air-off boundary is described as the velocity outlet, and the air-on boundary is defined as the velocity inlet. Products are described as non-slip and solid boundary conditions. A thin-walled structure was adopted for the DAG honeycomb modeling to ensure a more precise flow direction. The PBP, shelves, and other parts of the OTRDC were assumed to be made of sheer steel through which heat exchange takes place. The bottom shelf and wall shelves were simulated as 1.4 mm thick steel walls. Other inner sheet parts were adopted as 0.7 mm thick steel walls. The boundary condition of the PBP was described as a porous jump, while conditions of other surfaces are defined as walls. Finally, a strong natural convection exists between the OTRDC and the surrounding air, which is influenced by the density of the air at different temperatures. In order to simulate natural convection, gravity was switched on in the model, and the air density was calculated from the ideal gas formulas.