## 4 Modeling of Physicochemical Parameters and Their Impact on Thermal Processes
### Models and Algorithms Incorporating Real-Time Property Changes  
To accurately simulate thermal processes in food technology, it is crucial to account for the dynamic variation in food properties during thermal treatment. Traditional models often rely on static parameters, which fail to adequately represent the time-dependent changes induced by temperature fluctuations, phase transitions, and compositional alterations. In many food processing operations, food materials exhibit non-Newtonian behavior, which significantly influences fluid flow and heat transfer. Examples of such materials include pastes, emulsions, doughs, and fluids with a high solid content. In the CFD literature, non-Newtonian models, such as pseudoplastic fluid models (e.g., Herschel-Bulkley or Carreau models), are widely applied to account for viscosity variations as a function of shear rate [133; 134]. These models enable more accurate representations of real-world conditions during processes such as mixing, pasteurization, and drying. Furthermore, the thermal properties of food materials, such as thermal conductivity and specific heat capacity, often change with temperature, moisture content, and chemical composition. CFD simulations that incorporate these variable thermal properties allow for more precise predictions of temperature distributions and thermal phenomena during processing. Specifically, the use of conjugate heat transfer (CHT) models and interface-tracking methods, such as the volume of fluid (VOF) approach, facilitates the realistic modeling of phase changes and dynamic variations in material properties [28]. Recent advancements in CFD have led to the development of highly sophisticated models and numerical algorithms that dynamically integrate these real-time property variations, significantly enhancing the predictive accuracy of thermal simulations [1]. These advanced CFD models employ a combination of adaptive mesh refinement techniques and time-dependent governing equations to capture the evolving physicochemical properties of food during thermal processing. For example, as the temperature increases, food properties such as viscosity, thermal conductivity, specific heat capacity, and density exhibit significant temperature dependence. Such property changes are often modeled using temperature-dependent functions, such as the Arrhenius equation. The temperature-dependent viscosity \(\mu(T)\), for instance, can be expressed as (Equation (16)) [135]:  
\[\mu(T)=\mu_{0}exp\left(\frac{E_{a}}{RT}\right) \tag{16}\]  
where \(\mu_{0}\) is the pre-exponential factor, \(E_{a}\) is the activation energy, \(R\) is the universal gas constant, and \(T\) is the absolute temperature. This equation highlights how the viscosity of the material exponentially decays with increasing temperature, providing a clear mathematical framework for integrating thermal dependence into the CFD simulations. Similarly, thermal conductivity and specific heat capacity can be modeled as functions of temperature, often incorporating polynomial fits or empirical relationships derived from experimental data [136]. Additionally, CFD simulations utilize the energy conservation equation, incorporating both convective and conductive heat transfer mechanisms, typically described by (Equation (17)):  
\[\rho C_{p}\frac{\partial T}{\partial t}+\
abla\cdot\left(\rho v(T-T_{\infty}) \right)=\
abla\cdot\left(\kappa\
abla T\right) \tag{17}\]  
where \(\rho\) is the density, \(C_{p}\) is the specific heat capacity, \(v\) is the velocity vector, \(\kappa\) is the thermal conductivity, and \(T_{\infty}\) is the temperature of the surrounding environment. This equation is solved numerically using the finite volume method or FEM to simulate the temperature distribution and its evolution within the food matrix during heating [137]. The integration of machine learning (ML) models with CFD simulations represents a cutting-edge approach to optimizing thermal processing in food technology.