## 2 CFD Methodology and Numerical Modeling
### Model Validation  
In this study, the experimental data from [PERSON] et al. on non-isothermal mixed convection in a square-type ventilated box were employed for model validation [54]. An experiment was conducted in a cavity with dimensions of 1040 \(\times\) 1040 \(\times\) 700 mm\({}^{3}\) (D \(\times\) H \(\times\) W), where an air inlet with a height of 18 mm was set on the wall on the width side and an outlet with a height of 24 mm was set at the bottom of the wall opposite to the inlet. The entire cavity was divided into three smaller cavities, including the measuring cavity in the center and the protective cavities on both sides, which are separated by transparent double glazing. The cavities on both sides were used to eliminate the influence of the surrounding thermal environment on the flow in the center measurement cavity. Moreover, the surrounding walls were maintained at a constant uniform wall temperature (15 \({}^{\circ}\)C) using a temperature-controlled water system, while the bottom wall was heated to 35.5 \({}^{\circ}\)C and maintained at a constant level. The inlet air temperature was controlled at 15 \({}^{\circ}\)C in the experiment, the inlet velocity was set to 0.57 m/s, and the turbulence intensity at the inlet was 6%. Time-averaged velocity and temperature measurements were performed when the experimental conditions reached a statistical steady state. The measurements from this experiment provide validation support for numerical calculations of the non-isothermal mixed flow and heat transfer of indoor air [55; 56].  
In order to validate the accuracy of the numerical model in predicting the experimental results, this study validates the turbulence model for non-isothermal convective airflow conditions using the experiments conducted by [PERSON] et al. (1992) [54]. In this numerical model, the computational domain was specifically designed and meshed to focus on the central cavity where the measurements were performed in the experiment. The outer two cavities were not included in the model. The two side walls without inlets and outlets were designated as adiabatic walls to emulate the impact generated by the two side cavities, thereby circumventing the influence of the external environment on the flow pattern within the central cavity (Figure 4). In the model construction, a tetrahedral mesh was employed to discretize the computational domain. To enhance the accuracy of predicting velocity gradients and convective heat transfer, a finer mesh was employed on the surfaces of the inlet, outlet, and the bottom hot wall within the computational domain. The distributions of vertical velocity components (V) and horizontal velocity components (U) along the horizontal center line (\(y\)/\(L\) = 0.5) and vertical center line (\(x\)/\(L\) = 0.5), as well as the air temperature, are compared between the numerical model and the experimental measurements conducted by [PERSON] et al. [54]. From Figure 5, it is evident that the numerical model accurately predicted both the velocity and temperature distributions. This indicated that the existing numerical model was reliable and could ensure the accuracy of subsequent simulation studies.  
Figure 4: Geometry models for validation.