## 3 Simulation of Thermal Processes in the Food Industry Using CFD
### Examples of Thermal Processes Modeled Using CFD
#### 3.2.2 Cooling and Freezing of Food Products  
Cooling and freezing are critical thermal processes in food preservation, both of which substantially impact product shelf life, quality, and safety. Modeling these processes with CFD enables a detailed analysis of heat and mass transfer mechanisms, thereby facilitating optimization in food manufacturing and preservation.  
During cooling, heat is extracted from food products primarily through convective heat transfer between the product's surface and the surrounding medium, typically air or water. CFD models of this process employ the Navier-Stokes equations to describe fluid flow, the energy equation to capture heat transfer, and the continuity equation to ensure mass conservation.  
The continuity equation is expressed as (Equation (6)):  
\[\frac{\partial(\rho)}{\partial t}+\
abla\cdot(\rho v)=0 \tag{6}\]  
where \(\rho\) represents the fluid density and \(v\) is the velocity vector field.  
The Navier-Stokes equations are given by (Equation (7)):  
\[\frac{\partial\rho v}{\partial t}+\
abla\cdot(\rho v\otimes v)=-\
abla p+\mu \
abla^{2}v+\rho g \tag{7}\]  
where \(\rho\) denotes fluid density, \(v\) is the velocity vector, \(p\) is the pressure, \(\mu\) is the dynamic viscosity, and \(g\) represents gravitational acceleration [80]. These equations are foundational for simulating fluid dynamics around food surfaces [78]. CFD simulations apply turbulence models, such as the \(k\)-\(\varepsilon\) or \(k\)-\(\omega\) models, to account for the chaotic nature of fluid flow in industrial settings. These models solve additional transport equations to represent the kinetic energy of turbulence (\(k\)) and its dissipation rate (\(\varepsilon\) or \(\omega\)), which are crucial for capturing detailed temperature distribution and flow patterns in cooling processes. This approach is particularly valuable in scenarios like blast chilling, where rapid and uniform cooling is essential to inhibit microbial growth and maintain food safety [81].  
For freezing, the process becomes more complex due to the phase transition of water within food matrices, which transforms into ice as temperature decreases. This phase change is typically modeled using the enthalpy-porosity technique, which involves tracking the latent heat associated with the freezing process. The energy equation for freezing is expressed as Equation (8) [82]:  
\[\frac{\partial H}{\partial t}+\
abla\cdot(Hv)=\
abla\cdot(k\
abla T)+S \tag{8}\]  
where \(H\) is the enthalpy, \(T\) is temperature, \(k\) is thermal conductivity, and \(S\) represents the source term related to phase change. By introducing an effective heat capacity that accounts for the latent heat of freezing, the model can simulate how temperature and phase distribution evolve over time within the food product. Moving boundary techniques are also utilized to track the solid-liquid interface, which is particularly important in high-precision applications where freezing fronts move non-uniformly due to complex geometries and variations in thermal properties across the food matrix [83].  
Additionally, CFD models incorporate moisture migration and thermal conductivity variations associated with the freezing medium, whether air, liquid nitrogen, or brine, by defining boundary conditions that reflect real-world freezing environments. The food product's geometry, initial temperature, and specific heat capacity are key factors influencing freezing behavior, and these are integrated into simulations to predict freezing rates and ensure optimal parameter settings. For example, modeling the nucleation and growth of ice crystals--a process governed by classical nucleation theory--can help control crystal size, as large ice crystals tend to disrupt cellular structures, resulting in texture degradation after thawing. By predicting conditions that encourage the formation of smaller, uniformly distributed crystals, CFD simulations enable the preservation of texture and quality in the final product