## 2 Theoretical Foundations of CFD
### Principles, Mathematical Models, and Numerical Methods in CFD
The accuracy of CFD simulations in food technology depends heavily on several factors, such as the mesh quality, boundary conditions, and the thermophysical properties of the materials being modeled. These properties, including thermal conductivity, specific heat, and density, can exhibit significant spatial and temporal variability, particularly in biological materials like meat, vegetables, or dairy products. Therefore, accurate experimental data or well-defined correlations are crucial for the proper calibration of CFD models. Additionally, reactive flow models have become increasingly important in food processing simulations, as many thermal processes involve complex chemical reactions, such as the Maillard reaction, caramelization, or protein denaturation. CFD can incorporate these reactions using detailed reaction kinetics models to simulate the formation of flavour compounds, colour changes, and texture alterations during processing. These models often involve solving additional transport equations for the concentration of chemical species, coupled with solving the energy equation to account for the heat generated or consumed during the reactions [29]. Turbulence modelling is a critical aspect of CFD simulations in food technology, where flow regimes are frequently turbulent. The RANS approach, which decomposes the flow field into mean and fluctuating components, introduces models to provide closure relations for the turbulent viscosity. While these models are computationally efficient, they may fail to capture the full complexity of turbulence. More advanced methods, such as LES, resolve larger eddies explicitly while modeling smaller scales, providing improved accuracy at the expense of higher computational costs. DNS, which resolves all turbulence scales, offers the highest level of accuracy but is generally computationally impractical for industrial applications [9, 30, 31]. In addition to turbulence, heat transfer models are integral to predicting temperature distributions during thermal food processing. CHT models, which simultaneously solve heat conduction in solids and convection in fluids, are essential in applications such as pasteurization, sterilization, and baking. These models require precise material properties, which can vary considerably due to the heterogeneous nature of food matrices, such as variations in moisture content, fat composition, and structure [32, 33]. Reactive flow models are also increasingly incorporated into CFD simulations to model chemical reactions occurring during food processing, such as the Maillard reaction. These models integrate reaction kinetics into the CFD framework, providing valuable insights into both the physical and chemical transformations that occur during thermal treatment. Such simulations can be crucial for process optimization, ensuring food quality, and understanding complex reaction pathways in food systems [34]. Table 1 presents the mathematical models and numerical algorithms used in the computational fluid dynamics analysis of thermal processes in the food industry. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model/Algorithm** & **Description** & \begin{tabular}{c} **Applications in CFD** \\ **for the** \\ **Food Industry** \\ \end{tabular}  & **Advantages** & **Limitations** & **References** \\ \hline \multirow{4}{*}{\ \begin{tabular}{c} Heat Conduction \\ Model (Fourier) \\ \end{tabular}  } & Describes heat transfer in solid materials based on [PERSON]’s law, assuming material homogeneity and no internal heat sources. & Frying, baking, freezing, cooking, smoking. Modeling heat exchange in solid materials. & Simple to implement, well understood, widely used in many standard simulations. & Limited in modeling materials with irregular structures, such as foods with porous structures. & [35, 36, 37] \\ \hline \multirow{4}{*}{ \begin{tabular}{c} Convection Model \\ (Navier-Stokes) \\ \end{tabular}