## 3 Simulation of Thermal Processes in the Food Industry Using CFD
### Sterilization Process  
Sterilization processes, such as those used in food technology for canning, require higher temperatures and longer processing times to achieve complete microbial destruction. CFD simulations provide significant advantages in modeling these closed systems, where complex interactions between heat transfer, fluid flow, and pressure changes must be accounted for. By simulating the thermal behavior of food products within sterilization systems, engineers can identify areas with excessive or insufficient temperatures--known as \"hotspots\" and \"coldspots\"--that could result in inadequate processing, thereby ensuring that all parts of the product receive sufficient thermal treatment. The mathematical models used in CFD simulations for sterilization processes are based on solving the Navier-Stokes equations, which describe fluid flow under the influence of resistance forces and changing thermal conditions. In combination with the energy balance equation, which accounts for heat transfer through convection, conduction, and radiation, these models provide an accurate representation of the sterilization process within a system. Additionally, incorporating equations of state for gases (for example, the ideal gas law for steam) is critical, especially in processes involving dynamic phase changes. An important aspect of CFD simulations in sterilization is the modeling of phase change phenomena, which play a significant role in heat transfer, particularly in high-temperature processes where steam dynamics influence heat exchange efficiency. One method to capture these effects is the enthalpy-porosity approach, which allows for the simulation of condensation and evaporation in the presence of steam. This approach enables the accurate modeling of the influence of changing the gas phase volume on heat transfer and the temperature distribution within the product being processed. Furthermore, to evaluate the effectiveness of microbial inactivation under varying thermal conditions, empirical correlations such as the D-value (decimal reduction time) can be integrated into CFD models. The D-value is commonly used to assess the efficiency of thermal processes in pathogen inactivation [86]. The D-value is temperature-dependent, and its relationship is typically described by the Arrhenius equation, which allows for the calculation of microbial inactivation rates under different thermal conditions (Equation (9)) [87]:  
\[D(T)=D_{0}\times e^{\frac{E_{R}}{T}\times\left<\frac{1}{T}-\frac{1}{T_{0}}\right>} \tag{9}\]  
where \(D_{0}\) is the reference \(D\)-value at temperature \(T_{0}\), \(E_{R}\) is the activation energy, \(R\) is the universal gas constant, and \(T\) is the temperature in Kelvin. Integrating such relationships with CFD simulations enables a more accurate assessment of sterilization efficiency and the optimization of processing conditions [88].  
CFD simulations in sterilization and pasteurization processes contribute to the optimization of equipment design and operational conditions, ultimately enhancing energy efficiency and product quality. By leveraging advanced mathematical models and computational techniques, food technologists can better understand thermal processes, effectively select processing parameters, and ensure microbiological safety and product quality.