Computational Fluid Dynamics Simulation of Thermal Processes in Food Technology and Their Applications in the Food Industry

Abstract

In this review, the application of computational fluid dynamics (CFD) simulations in analyzing thermal processes within food technology is explored. The focus is on understanding heat transfer, fluid flow, and temperature distribution during various food processing methods, such as baking, frying, pasteurization, and cooling. Detailed insights that are often challenging to obtain through experimental methods alone are provided by CFD simulations, allowing for the optimization of process parameters to enhance product quality and safety. It is demonstrated that CFD can effectively model complex thermal phenomena, providing valuable data on temperature gradients and flow patterns. These simulations assist in the designing of more efficient processing equipment, improving energy consumption, and ensuring uniform heat treatment, which is crucial for maintaining the nutritional and sensory attributes of food products. Furthermore, the integration of CFD in the food industry leads to significant advancements in product development, reducing the time and cost associated with experimental trials. Future research should focus on refining these models for greater accuracy and exploring their application in emerging food processing technologies.

1. Introduction

Thermal processes play a critical role in food technology, profoundly impacting both the safety and quality of food products. Heat treatment is commonly employed to inactivate pathogens and damage microorganisms, extending shelf life and ensuring food safety. In addition, thermal processing contributes to the desired sensory properties, such as texture, colour, and flavour, which are essential for consumer acceptance [1]. Furthermore, heating promotes various chemical reactions, including the Maillard reaction and caramelization, which enhance flavour and aroma. However, the improper control of these processes can lead to nutrient loss, degradation of quality, or even the formation of harmful compounds, such as acrylamide. For this reason, it is essential to optimize thermal conditions, balancing microbial safety with nutritional and sensory quality [2,3]. Advances in food technology have led to the development of novel thermal methods, such as ohmic heating and microwave processing, which offer faster and more energy-efficient alternatives to traditional methods. These innovations not only improve processing efficiency but also minimize thermal damage, helping to retain essential nutrients. Consequently, understanding and controlling thermal processes are vital to meeting industry standards and consumer expectations [4,5,6]. Computational fluid dynamics (CFD) simulations have become an invaluable tool in the food industry, providing detailed insights into the complex transport phenomena that occur during food processing. Through CFD, engineers and researchers can model fluid flow, heat transfer, and mass transfer with high precision, enabling the optimization of processes such as pasteurization, drying, and refrigeration. These simulations aid in predicting temperature distribution and flow patterns, which are crucial for ensuring product quality and safety [7,8]. In addition, CFD allows for the virtual testing of equipment design, which can significantly reduce costs and development time by minimizing the need for physical prototypes. By simulating various scenarios, food engineers can identify optimal processing conditions, enhancing energy efficiency and resource use. However, despite its numerous advantages, CFD still faces challenges, particularly in accurately modelling food products with complex structures and variable properties [9,10]. Despite the difficulties, recent advances in CFD software have made it possible to simulate multiphase flows and reactions, expanding its applications in areas such as fermentation and emulsification. As the food industry increasingly embraces digital solutions, the role of CFD in process optimization, equipment design, and quality control continues to grow, offering a powerful approach to meeting modern production standards and consumer demands [11,12,13].

This literature review aims to provide a comprehensive overview of the current applications and developments in CFD simulations related to thermal processes within the food industry. Specifically, it examines how CFD contributes to optimizing processing conditions, enhancing food safety, and improving product quality. In addition, the review addresses both the capabilities and limitations of CFD methods, identifying key areas for future research. By synthesizing recent advancements, this work seeks to highlight CFD’s growing role in meeting industry and consumer demands efficiently and sustainably.

2. Theoretical Foundations of CFD

2.1. Principles, Mathematical Models, and Numerical Methods in CFD

CFD is a powerful numerical tool that facilitates the simulation of fluid flow, heat transfer, and other related phenomena through the solution of governing differential equations. These include the Navier–Stokes equations, continuity equation, and energy equation, which are fundamental to describing the conservation of mass, momentum, and energy in fluid systems. The Navier–Stokes equation (Equation (1)), for instance, is expressed as follows:

$${\displaystyle \frac{\partial v}{\partial t}}+\left(v\times \nabla \right)v=-{\displaystyle \frac{1}{\rho }}\nabla p+v{\nabla }^{2}v+f$$

(1)

where v represents the velocity vector field, ρ is the density, p is the pressure, v is the kinematic viscosity, and f accounts for external body forces [14]. The solution of these equations provides detailed insights into fluid flow behavior under various boundary conditions and geometries. Similarly, the energy equation governs the transfer of thermal energy (Equation (2)) as follows:

$$\rho C_p\left({\displaystyle \frac{\partial T}{\partial t}}+v\times \nabla T\right)=\nabla \cdot \left(k\nabla T\right)+\dot{Q}$$

(2)

where C_p is the specific heat capacity at constant pressure, T is the temperature, k is the thermal conductivity, and Q represents the heat generation term, which may arise due to chemical reactions or other sources [14].

To solve these continuous equations in a computational environment, CFD employs discretization techniques such as the finite volume method (FVM), finite element method (FEM), and finite difference method (FDM). These methods convert the governing partial differential equations into algebraic equations, allowing their numerical solution. FVM, for example, is widely used due to its ability to conserve quantities such as mass, momentum, and energy across control volumes. The domain is divided into small discrete cells (volumes), and the integral form of the conservation equations is applied to each cell [15,16,17].

CFD methods are widely used for modelling and optimizing thermal processes in food engineering. Specifically, they are applied to simulate heat transfer, turbulent flows, and multiphase phenomena, enabling improvements in process efficiency. Various CFD methods, such as the finite difference method (FDM), Reynolds-averaged Navier–Stokes (RANS), large eddy simulation (LES), and direct numerical simulation (DNS), have specific applications depending on the problem characteristics. FDM is mainly used for simulating simple heat transfer processes where the model geometry is homogeneous and boundary conditions are well defined. For example, it is applied to model bread baking, analyzing heat conduction in homogeneous dough, and predicting temperature distribution during the pasteurization or cooking of homogeneous food products, such as cheesecakes or chocolate masses. Its advantages include straightforward implementation and low computational requirements, though it is limited to simple geometries and less complex processes [18]. The RANS method is particularly popular for analyzing turbulent flows in industrial systems. It is used, for instance, to simulate the air flow in industrial ovens, optimizing the temperature and turbulence distribution to improve baking uniformity. RANS is also applied in freezing chambers to analyze turbulent air flows, which are crucial for ensuring the uniform cooling of products. The main advantage of this method is its low computational requirements, though it may not always capture detailed turbulent structures [19]. LES allows for the more detailed modeling of turbulent structures by directly resolving large eddies and modeling smaller scales using subgrid models. This method is applied in dynamic processes, such as multiphase mixing in homogenization or emulsification, and in industrial drying, where modeling turbulent flows improves process uniformity. While LES offers greater precision than RANS, it requires significantly higher computational resources [20,21]. DNS provides the highest modeling accuracy by solving all turbulence scales without approximations. As a result, it is mainly used in fundamental research, such as modeling bubble dynamics in frying processes or predicting liquid behavior in microflows. Its advantage lies in the lack of simplifications, making it the most precise method, though its enormous computational demands limit its industrial applications [22].

A critical challenge in CFD simulations is turbulence modelling, as most industrial applications involve turbulent flows. Turbulence models are necessary to approximate the effects of unsteady and chaotic fluid motion, as the direct resolution of turbulence on a fine scale is computationally prohibitive. The most commonly used turbulence models are as follows:

• Reynolds-averaged Navier–Stokes (RANS): This approach averages the Navier–Stokes equations to model the flow in steady-state or near-steady conditions. The RANS equations include additional terms to account for the effects of turbulence, often represented by eddy-viscosity models. The k − ε and k − ω models are widely adopted, where k represents the turbulent kinetic energy and ε (or ω) represents the dissipation rate of turbulent energy. These models offer a balance between accuracy and computational efficiency [23].
• Large eddy simulation (LES): LES resolves large-scale turbulent structures (large eddies) while modelling the smaller, more chaotic eddies through subgrid-scale models. This approach is computationally more expensive but provides more detailed information, and is especially useful in cases requiring high accuracy for transient or unsteady flows [24].
• Direct numerical simulation (DNS): DNS solves the Navier–Stokes equations without any turbulence modelling, directly resolving all scales of motion. This method is the most accurate but extremely demanding in terms of computational resources, limiting its application primarily to fundamental research rather than industrial processes [24].

CFD simulations in the food industry frequently involve multiphase flow models, as many food processing operations (for example, mixing, emulsification, or phase separation) involve interactions between multiple phases, such as solid–liquid, liquid–gas, or immiscible fluids. Common approaches for modeling multiphase flow include the following:

• Volume of fluid (VOF): This method tracks the interface between immiscible phases, such as oil and water, by solving a transport equation for a phase fraction. VOF is commonly used to simulate processes like emulsion formation, phase separation, or boiling [25].
• Eulerian–Eulerian Model: This method is used for modeling continuous phases where both phases are treated as interpenetrating fluids. This model is often applied in situations where the interaction between multiple fluids (for example, liquid and gas) is important [26].
• Eulerian–Lagrangian Model: This approach models one phase (typically discrete particles or droplets) using Lagrangian tracking, while the continuous phase is modeled using the Eulerian method. It is useful for simulating phenomena like slurry flows, solid–liquid suspensions, or droplet dynamics in spray drying [27].

Furthermore, heat transfer models are essential for accurately simulating thermal processes in food engineering. In many thermal food processing operations, such as baking, frying, or pasteurization, the interaction between heat conduction, convection, and radiation governs the efficiency and uniformity of heat transfer. Conjugate heat transfer (CHT) models allow for the coupled simulation of heat transfer between solids and fluids. In these models, the heat transfer in the solid phase (for example, food material) and the surrounding fluid phase (for example, air or oil) is solved simultaneously, ensuring that the boundary conditions are consistent across both phases [28]. 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. Mathematical models and numerical algorithms used in CFD for thermal processes in the food industry.

Model/Algorithm	Description	Applications in CFD for the Food Industry	Advantages	Limitations	References
Heat Conduction Model (Fourier)	Describes heat transfer in solid materials based on Fourier’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]
Convection Model (Navier–Stokes)	Describes heat transfer in fluids due to turbulent or laminar flow, accounting for external and internal forces, as well as interactions with solid surfaces.	Processes such as frying, baking, cooking in liquids, pasteurization.	Accounts for fluid dynamics and turbulence, enabling modeling of complex airflow patterns.	High computational demands, difficulties in reproducing non-uniform flows.	[38,39,40]
Thermal Radiation Model (RTE)	Solves the RTE, modeling emission, absorption, and scattering of radiation within a medium, essential for high-temperature processes.	Baking, grilling, drying. Processes where heat exchange through radiation plays a significant role.	Accurately models heat exchange in high-temperature processes.	High computational costs, difficulties in modeling geometry and radiation properties.	[37,41,42,43]
Chemical Reaction Modeling	Accounts for chemical reactions during thermal processes, such as Maillard reaction, protein denaturation, and changes in flavour and texture due to temperature.	Frying, baking, cooking. Modeling temperature impact on chemical reactions.	Enables simulation of flavour, texture, and colour changes in food products.	Challenges in accurately reproducing reactions under real conditions.	[9,44,45]
Heat Conduction in Porous Materials Model	Extends the heat conduction model to porous materials, accounting for fluid flow through pores and material density effects.	Processes involving porous products, such as baking bread or drying vegetables.	Enables accurate modeling of processes in porous materials.	Difficulties in obtaining accurate parameters for porous materials.	[46,47,48,49]
Heat and Mass Transfer Modeling	Solves heat and mass transport equations, accounting for gas flow and interactions with material surfaces.	Drying, evaporation, smoking, cooking in liquids.	Simultaneously models heat and mass transfer.	High demands for input data and computational resources.	[41,50,51]
Phase Change Models	Simulate phase transitions (e.g., ice melting, water boiling) by incorporating latent heat and phase boundaries into heat transfer equations.	Freezing, boiling, thawing. Modeling processes with phase transitions.	Accurately represents phase changes and their effects on heat transfer.	Requires detailed thermophysical property data and complex numerical schemes.	[52,53]
Multicomponent Reaction Models	Account for interactions between multiple chemical species undergoing simultaneous reactions during thermal processing.	Frying, baking. Modeling flavour, texture, and nutritional changes in food.	Captures complex reaction kinetics, improving accuracy of quality predictions.	High computational complexity and input data requirements.	[54,55,56]
Numerical Methods: FEM	Solves PDEs by dividing space into elements for numerical solutions, effective for complex geometries.	Practically all thermal processes requiring precise spatial modeling.	Highly flexible, widely used, allows modeling of complex geometries.	High computational requirements, need for a detailed mesh.	[57,58]
Numerical Methods: FVM	A numerical method dividing space into small volume cells, used for solving heat and mass transport equations in the volume, considering diverse boundary and internal conditions.	Baking, frying, drying. Used in processes where heat and mass transfer in various phases is crucial.	Excellent for simulating flow and transport in diverse materials, high accuracy in solutions.	Challenges in obtaining stable solutions in complex geometries, issues with computational time.	[59,60]
Numerical Methods: FDM	Approximates differential equations using finite difference approximations over a grid of points.	Processes with simple geometries or 1D/2D models, such as heat diffusion.	Simple and computationally efficient for structured grids.	Less flexible for complex geometries, may require finer grids for accuracy.	[61,62]

presents the mathematical models and numerical algorithms used in the computational fluid dynamics analysis of thermal processes in the food industry.

2.2. Typical Stages of CFD Simulation: Pre-Processing, Solving, Post-Processing

CFD simulations typically encompass three fundamental stages: pre-processing, solving, and post-processing, each of which plays a critical role in the overall success and accuracy of the simulation [63]. The pre-processing stage involves several crucial tasks, beginning with the definition of the computational domain and the creation of the geometry that represents the physical system under investigation. This is followed by mesh generation, where the domain is divided into discrete elements or cells, a process that significantly influences the accuracy and computational efficiency of the simulation. A finer mesh can yield more accurate results, particularly in regions of high gradient, such as near solid boundaries. In addition, the boundary and initial conditions must be specified, detailing the physical parameters, such as velocity, temperature, and pressure, that define the system’s behavior. The careful consideration of these conditions is essential, as inaccuracies can lead to misleading results [43]. The solving stage involves the application of numerical algorithms to solve the discretized governing equations. This process may include iterative methods that converge to a solution over multiple time steps. During this phase, the choice of solver, as well as the turbulence and heat transfer models, are critical. Various solvers can be employed depending on the flow regime—steady or unsteady—and the complexity of the model. However, achieving convergence can sometimes be challenging, requiring adjustments to the mesh, solver settings, or relaxation factors to ensure numerical stability [64]. Post-processing is the final stage, where the raw simulation data are transformed into meaningful visualizations and analyses. This typically includes the generation of contour plots, vector fields, and surface renderings to illustrate the velocity, temperature distributions, and pressure fields within the domain. In addition, a quantitative analysis, such as extracting specific data points or calculating flow rates and heat transfer coefficients, is performed to evaluate performance metrics and validate the results against experimental or theoretical benchmarks. By interpreting the outcomes of the simulation, engineers can gain critical insights into the fluid dynamics and thermal processes, guiding further optimization and design efforts in food technology applications [65].

3. Simulation of Thermal Processes in the Food Industry Using CFD

3.1. Conduction, Convection, and Thermal Radiation in CFD Context

In CFD simulations for food processing applications, the accurate modeling of heat transfer mechanisms—namely conduction, convection, and thermal radiation—is essential to predict thermal behavior and ensure the quality, safety, and efficiency of food processing. Each mechanism requires specific mathematical formulations to capture its unique contribution to overall heat transfer.

Conduction refers to the transfer of thermal energy through solid materials, governed by molecular interactions where kinetic energy is exchanged among particles. In CFD, conduction is typically modeled using Fourier’s Law (Equation (3)) [66,67]:

$$q=-k\nabla T$$

(3)

where q is the heat flux, k represents the thermal conductivity of the material, and ∇T denotes the temperature gradient. The accurate CFD modeling of conduction requires precise values for k, which can vary anisotropically within food products due to heterogeneous compositions, including variations in fat, water, and fibre. The thermal properties of food matrices often exhibit temperature-dependent behaviors, adding complexity to the model and requiring empirical data or experimental validation.

Convection involves heat transfer between a solid surface and an adjacent fluid in motion and is categorized as natural convection (buoyancy-driven) or forced convection (induced by external sources like pumps or fans). In CFD simulations, convective heat transfer is governed by solving the Navier–Stokes equations coupled with the energy equation, which accounts for both fluid flow and temperature distribution (Equation (1)) Convection modeling in food systems may be complicated by the non-Newtonian nature of some food fluids, necessitating custom viscosity models [67].

Thermal radiation becomes particularly relevant at high temperatures or in low-pressure (vacuum) environments, where it can be a dominant mode of heat transfer. Radiation is governed by the Stefan–Boltzmann Law (Equation (4)):

$$q=\mathrm{ϵ}\mathsf{\sigma }{T}^4$$

(4)

where ϵ is the emissivity of the surface, σ is the Stefan–Boltzmann constant, and T is the absolute temperature [68]. In CFD, modeling thermal radiation is complex, especially in media where participation effects (absorption, emission, scattering) occur. In these cases, the RTE is employed, which requires iterative solution methods or approximations, like the discrete ordinates method (DOM) or the P1 approximation, to simplify calculations while accounting for radiation interactions in semi-transparent food layers [69,70,71].

By integrating these three mechanisms, CFD allows for high-resolution simulations of temperature distribution and thermal gradients within food products (Figure 1). This level of modeling supports the optimization of thermal processes by predicting potential hot and cold spots within food matrices, ensuring uniform heating and improved energy efficiency.

3.2. Examples of Thermal Processes Modeled Using CFD

3.2.1. Baking, Frying, and Grilling Processes

Baking, frying, and grilling are key thermal processes in the food industry, each characterized by complex heat transfer mechanisms that can be accurately simulated using CFD. These processes involve intricate interactions between heat transfer, fluid dynamics, and mass transfer, making CFD an essential tool for optimizing product quality, energy efficiency, and process design. Through the application of advanced mathematical models, CFD simulations can provide detailed insights into thermal behavior, enabling more precise control over manufacturing conditions.

Baking Process

In the baking process, heat transfer occurs predominantly via conduction and convection. Thermal energy is transferred from the oven surfaces to the dough through conduction, while convective heat transfer occurs as hot air circulates within the baking chamber. The CFD models employed for baking simulations typically integrate the Navier–Stokes equations (Equation (1)) for fluid flow, Fourier’s law of heat conduction (Equation (6)), and equations governing moisture migration and phase change phenomena. These models enable the prediction of temperature distributions, moisture content profiles, and crust formation dynamics with high spatial resolution [72,73]. To accurately model airflow patterns within the oven, turbulence models such as k-ε or k-ω are commonly employed. These models allow for the prediction of turbulent eddy viscosities and the characterization of the interaction between turbulent eddies and heat transfer. For instance, studies have demonstrated that adjusting airflow configurations in the oven can significantly improve heat transfer uniformity, reduce baking times, and enhance product consistency [26]. Additionally, CFD simulations can account for the moisture diffusion and vaporization processes occurring in the dough, employing models for phase change, such as the Clausius–Clapeyron relation and the Fick’s law of diffusion. These considerations are critical for controlling the final texture and moisture content of the product [74].

Frying Process

The frying process is primarily driven by convective heat transfer between the hot oil and the food product. The temperature of the frying medium plays a pivotal role in determining the final texture, flavour, and nutritional properties of the food. CFD simulations of frying incorporate models such as the VOF method, which is used to track the interface between the oil and the food (Equation (5)) [25]. The VOF method captures the oil–food interface dynamics, which is crucial for accurately modeling oil absorption and frying efficiency. Additionally, empirical correlations for the convective heat transfer coefficient in the oil phase can be integrated to improve the precision of the heat transfer predictions [75]. Furthermore, CFD allows for the analysis of bubble dynamics during frying, which can significantly impact heat transfer and oil degradation. The dynamics of gas bubbles, such as their rise velocity and coalescence, influence both the thermal conductivity of the oil and the mass transfer between the oil and the food. The incorporation of chemical kinetics into CFD models enables the simulation of oil oxidation and degradation reactions, which are critical for understanding the shelf life and safety of fried products [75,76].

Grilling Process

Grilling is characterized by both conduction (from the grill surface to the food) and convection (through the surrounding hot air). The application of CFD in grilling involves solving heat conduction equations for the grill surface and convective heat transfer equations for the surrounding air, typically using the Boussinesq approximation for buoyancy effects in the air flow (Equation (2)) [20,77]. For enhanced accuracy in predicting airflow patterns and heat transfer in grilling, LES models are often employed to capture the fine-scale turbulence structures and their interaction with the grill surface. LES resolves the large turbulent eddies directly while modeling the smaller scales using subgrid-scale models, providing a more precise description of the airflow and heat transfer around the food.

CFD also facilitates the investigation of surface interactions such as Maillard browning and fat rendering. These processes are crucial for flavour development and product quality. To model these, CFD simulations incorporate reaction kinetics for the Maillard reaction and other thermal degradation processes, such as lipid oxidation [34,78]. The temperature-dependent Arrhenius equation for reaction rates can be used (Equation (5)):

$$k=Aexp\left({\displaystyle \frac{-E_a}{RT}}\right)$$

(5)

where k is the reaction rate, A is the pre-exponential factor, E_a is the activation energy, R is the gas constant, and T is the absolute temperature [79].

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)):

$${\displaystyle \frac{\partial \left(\rho \right)}{\partial t}}+\nabla \cdot \left(\rho v\right)=0$$

(6)

where ρ represents the fluid density and v is the velocity vector field.

The Navier–Stokes equations are given by (Equation (7)):

$${\displaystyle \frac{\partial \rho v}{\partial t}}+\nabla \cdot \left(\rho v\otimes v\right)=-\nabla p+\mu {\nabla }^{2}v+\rho g$$

(7)

where ρ denotes fluid density, v is the velocity vector, p is the pressure, μ 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-ε or k-ω 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 (ε or ω), 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]:

$${\displaystyle \frac{\partial H}{\partial t}}+\nabla \cdot \left(Hv\right)=\nabla \cdot \left(k\nabla T\right)+S$$

(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

3.2.3. Pasteurization and Sterilization Processes

Pasteurization and sterilization are critical thermal processes in the food industry, aimed at eliminating pathogenic microorganisms and extending product shelf life. The modeling of these processes using CFD facilitates a comprehensive understanding of heat transfer and microbial inactivation dynamics, thereby enhancing process efficiency and ensuring product safety.

Pasteurization Process

Pasteurization is a thermal process where food is subjected to controlled heating to a specified temperature for a defined time, followed by rapid cooling. The effectiveness of pasteurization hinges on the precise regulation of temperature and exposure time, parameters that can be rigorously optimized using CFD simulations. In these simulations, both heat conduction within the material and convective heat transfer at the fluid boundaries are critical for accurately capturing the thermal profile of the product [84].

CFD simulations of pasteurization leverage the principles of fluid mechanics and thermodynamics, beginning with the fundamental energy and mass conservation equations. For these systems, the energy equation is typically expressed as Equation (2). This equation is often coupled with the Navier–Stokes equations governing fluid motion (Equation (1)).

To simulate pasteurization accurately, CFD models often incorporate the Boussinesq approximation for natural convection, which accounts for buoyancy effects due to temperature-induced density variations. This approach enhances the realism of the model by simulating thermal gradients that cause fluid movement, thereby improving the accuracy of predictions for temperature distribution within the food matrix [14,85]. In CFD applications in food pasteurization, the FVM is commonly used to discretize the governing equations, transforming partial differential equations into a set of algebraic equations that can be solved iteratively. The FVM’s control volume approach conserves fluxes across each cell interface, making it particularly suitable for modeling complex fluid flows and heat transfer in food products with irregular geometries. Advanced meshing techniques are applied to create fine grids around regions of high thermal gradients, which ensures numerical accuracy in capturing rapid temperature changes at fluid–solid interfaces, such as the container wall [42]. These simulations generate detailed temperature profiles throughout the product, allowing engineers to evaluate thermal lethality by calculating the cumulative microbial reduction using the concept of FF-values (F-value equivalents), which measure the time–temperature effectiveness against microbial populations. The FF-value is defined as the equivalent time (in minutes) at a reference temperature, typically 60 °C, that would result in the same level of microbial inactivation as a given thermal treatment at varying temperatures. By adjusting parameters such as the inlet flow rate, heating time, and target temperature, engineers can optimize pasteurization processes to achieve microbial inactivation while preserving the sensory and nutritional qualities of the food.

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]:

$$D\left(T\right)=D_0\times e^{{\displaystyle \frac{E_a}{R}}\times \left({\displaystyle \frac{1}{T}}-{\displaystyle \frac{1}{T_0}}\right)}$$

(9)

where D₀ is the reference D-value at temperature T₀, E_a 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.

3.2.4. Food Drying Processes

Food drying is a critical thermal process aimed at reducing the moisture content in food products to inhibit microbial growth and extend shelf life. The modeling of drying processes using CFD provides valuable insights into the complex interactions between heat transfer and mass transfer, enabling the optimization of drying parameters [89]. The fundamental equations used in CFD simulations for food drying include the Navier–Stokes equations for fluid flow, the energy equation for heat transfer, and Fick’s laws of diffusion for mass transfer. To effectively model convective heat transfer and the diffusion of moisture within the food matrix, numerical methods such as the FVM are employed. This approach allows for the efficient discretization of the governing equations in space. Additionally, turbulence models, such as k-ε or k-ω, are often used to improve the prediction of airflow distribution, thereby enhancing the accuracy of temperature and moisture profiles within the drying environment [90]. During the drying process, heat is transferred from the surrounding medium—usually air—to the food product, leading to moisture evaporation. The heat transfer equations are linked to the energy balance equation, which includes both convective and conductive heat transfer, as well as enthalpy changes associated with the moisture evaporation process. Moreover, the analysis of temperature gradients, moisture distribution, and airflow patterns helps in identifying the optimal operating conditions, such as temperature, relative humidity, and air velocity, which significantly influence the drying efficiency and product quality [27]. CFD also facilitates the exploration of various drying techniques, such as hot air drying, freeze-drying, and microwave drying. Each method presents unique challenges and advantages. For instance, hot air drying typically operates at higher temperatures, which may negatively affect the sensory quality of the product, while freeze-drying preserves texture and flavour but is more energy-intensive. CFD allows for the quantification of the impact of each technique on drying kinetics by modeling the heat and mass transfer coefficients specific to each method, as well as the corresponding drying rate equations [91]. In particular, the incorporation of phase change phenomena, such as the transition from liquid to vapor, poses a significant challenge in CFD modeling, as it requires the accurate representation of moisture content dynamics and enthalpy changes during the drying process. Despite these complexities, CFD remains a powerful tool for optimizing food drying processes, allowing for precise control over operational conditions and leading to improved product quality, enhanced energy efficiency, and extended shelf life. By utilizing CFD, food technologists can optimize drying processes, reduce energy consumption, and better preserve the sensory attributes of dried products [92].

3.2.5. Extraction and Evaporation Processes

Extraction and evaporation processes are fundamental to the food industry, particularly in the concentration of flavours, aromas, and bioactive compounds. These processes are often modeled through CFD, which offers significant insights into the complex interplay of heat and mass transfer phenomena critical for optimizing efficiency and ensuring product quality [50].

Extraction Process

The extraction process involves the transfer of soluble compounds from solid food matrices into a solvent, such as water or alcohol. Modeling this process using CFD requires the incorporation of various physical phenomena, including fluid flow dynamics, diffusion, and thermal effects. The primary mathematical models used in these simulations include the Navier–Stokes equations, which govern the motion of the solvent within the food matrix, and Fick’s laws of diffusion, which describe the mass transfer of solutes. Additionally, the energy balance equation is employed to model heat transfer during the extraction process [93]. The generalized form of the energy equation is expressed as Equation (2).

The diffusion term in the mass transfer equation is typically modeled using Fick’s law (Equation (10)):

$$J=-D\nabla C$$

(10)

where J is the diffusion flux, D is the diffusion coefficient, and ∇C is the concentration gradient of the solute [94].

CFD simulations of extraction processes must resolve concentration gradients and solute diffusion rates within heterogeneous food matrices, where the distribution of solvents and solutes is influenced by both convection and molecular diffusion. By utilizing numerical techniques such as the FEM or FVM, these coupled equations can be discretized and solved iteratively to predict the optimal extraction parameters, including temperature, pressure, and solvent-to-solid ratios. Furthermore, empirical models like the Freundlich or Langmuir isotherms can be incorporated to better predict the solute–solvent interactions and adsorption behaviors within the food matrix during extraction [95]. Optimizing these parameters is crucial to maximizing the yield of target compounds while minimizing the degradation of heat-sensitive molecules, such as volatile flavours, antioxidants, and other bioactive components [96].

Evaporation Processes

Evaporation plays a vital role in concentrating liquid food products by removing moisture, which in turn improves shelf life and intensifies flavour. CFD simulations of the evaporation process model both the heat and mass transfer mechanisms involved, including convection, conduction, and latent heat transfer. The governing equations typically involve the energy balance equation for latent heat flux and the mass transfer equation that describes the rate of evaporation [97].

The energy balance equation in the context of evaporation can be expressed as (Equation (11)):

$$\rho C_p\left({\displaystyle \frac{\partial T}{\partial t}}+\overrightarrow{v}\times \nabla T\right)=\nabla \times \left(k\nabla T\right)+L{\displaystyle \frac{\partial Y}{\partial t}}$$

(11)

where L is the latent heat of vaporization, and Y is the mass fraction of vapor.

The mass transfer equation governing the rate of evaporation is given by (Equation (12)):

$${\displaystyle \frac{\partial C}{\partial t}}+\overrightarrow{v}\times \nabla C=\nabla \times \left(D\nabla C\right)$$

(12)

where C represents the concentration of the evaporating substance, and D is the mass diffusion coefficient.

Understanding the interactions between the evaporating liquid and the surrounding environment is essential, as variations in temperature, pressure, and airflow significantly influence evaporation rates and, consequently, the concentration of flavours and bioactive compounds in the product. CFD simulations frequently incorporate turbulence models, such as RANS, to predict the effects of air velocity and turbulence on the mass transfer process, which directly impacts the efficiency of the evaporation and the final product characteristics [98]. Despite the complexity of food structures and the nonlinear behavior of fluid systems, the application of CFD in modeling extraction and evaporation processes offers substantial advantages. CFD provides a detailed framework for visualizing flow patterns, temperature distributions, and concentration profiles within the food product. This level of detail enables the identification of optimal processing conditions, resulting in enhanced product quality, reduced energy consumption, and the minimized loss of valuable compounds. Moreover, CFD simulations allow for multi-scale modeling, accounting for the microscale (for example, solvent diffusion in the food matrix) as well as macroscale effects (for example, overall fluid flow and temperature distribution in the extraction or evaporation chamber). The ability to simulate these processes at various scales significantly improves the predictive capabilities of CFD models, providing a comprehensive understanding of the underlying mechanisms. The applications of CFD for the analysis of foods thermal processes have been presented in

Table 2. Thermal processes in the food industry and their CFD applications.

Thermal Process	Description	CFD Modeling Focus	Key Computational Parameters	Applications in Food Industry	Key Benefits of CFD in Modeling	Challenges and Limitations	Key Findings from Literature	References
Baking	Process of cooking food by dry heat, typically in an oven. It involves complex heat and moisture transfer.	Heat conduction in solid food, convection in ovens, moisture evaporation, temperature gradients in the dough.	Temperature distribution, moisture content, surface and interior heat flux, air circulation in ovens.	Bread, cakes, pastries, pizza. Optimization of temperature and humidity for better texture, flavour, and uniformity.	Optimization of baking parameters (time, temperature), prediction of texture, and flavour changes.	High computational cost due to complex geometry and phase changes in porous materials.	Uniform heat transfer in porous food, optimized energy usage, reduced baking time.	[10,41,99,100,101,102,103,104,105]
Frying	Cooking food by immersing it in hot oil, involving convective and conductive heat transfer.	Convection in oil, heat conduction in food, oil temperature distribution, interactions between food surface and hot oil.	Oil temperature distribution, heat flux in food, oil absorption, food surface temperature.	Frying of potatoes, meat, fish, doughnuts. Optimization of oil temperature to reduce oil absorption.	Accurate prediction of oil temperature, surface heat flux, minimization of oil absorption.	Modeling the variable thermal conductivity of food, impact of oil temperature on food texture.	Oil temperature distribution, modeling heat flow in non-uniform food shapes.	[106,107,108,109,110,111]
Grilling	Cooking food with direct heat, usually from below, involving both radiation and convection.	Radiation heat transfer, convection from grill surface, temperature gradients and interactions between heat and food surface.	Radiative heat flux, air flow dynamics, temperature distribution, heat loss due to convection.	Grilling of meats, vegetables, fish, burgers, sausages. Optimization of heat intensity and cooking time.	Real-time control of cooking parameters, prediction of grill marks and surface texture.	Radiative heat transfer in non-uniform grill designs, heat penetration in thick food cuts.	Radiative heat flux modeling, understanding of temperature gradients in large food cuts.	[17,112]
Cooling and Freezing	Processes involving the reduction in temperature in food, often aiming to preserve it by slowing down microbial growth.	Modeling of heat transfer during cooling/freezing, phase change modeling, air and fluid flow in freezing chambers.	Freezing point, phase transition modeling (ice crystallization), heat flux distribution, air circulation.	Freezing of fruits, vegetables, ready meals, meat. Preservation of nutrients and texture in frozen foods.	Optimization of freezing rates, reduction in ice crystal formation in delicate foods.	Modeling phase change and non-uniform freezing rates, computational cost of modeling ice formation.	Control of freezing time, maintaining food quality (texture, appearance), prevention of large ice crystals.	[51,81,82,113,114,115]
Pasteurization	Heat treatment process to destroy harmful microorganisms without significantly affecting food quality.	Convection and conduction during heating, temperature profiles, microbial inactivation rates.	Temperature profiles over time, heat retention, microbial kinetics, energy consumption.	Pasteurization of juices, milk, sauces, soups. Optimization of temperature–time curves to preserve flavour.	Optimization of heating time and temperature to improve food safety and quality.	Modeling microbial inactivation, ensuring uniform temperature distribution.	Optimization of pasteurization time, reduction in thermal degradation of nutrients.	[15,22,85,116,117,118]
Sterilization	Similar to pasteurization, but at higher temperatures, often used for canned or jarred food.	Modeling of heat transfer at higher temperatures, pressure dynamics in sterilization chambers.	Pressure and temperature profiles, heat penetration rates, sterilization time, energy consumption.	Sterilization of canned vegetables, meats, soups, sauces. Minimization of energy consumption while maintaining safety.	Enhanced process control, minimisation of overcooking, consistent product quality.	High pressure conditions, uniform heating in different food product types.	Modeling of sterilization cycles, uniformity of thermal treatments in complex geometries.	[14,119,120,121]
Drying	Removal of moisture from food, often via heat, to extend shelf life and prevent microbial growth.	Heat and mass transfer, moisture migration, airflow, and drying kinetics. Detailed modeling of fluid–particle interactions.	Moisture content, heat flux, airflow pattern, product shrinkage, drying rate.	Drying of fruits, vegetables, grains, herbs, meat. Minimization of energy use while preserving quality.	Maximization of drying efficiency, minimization of product shrinkage and nutrient loss.	Complex moisture migration dynamics and air distribution in large drying chambers.	Modeling of drying uniformity, minimization of nutrient loss, energy optimization.	[89,91,122,123,124]
Evaporation and Extraction	Removal of volatile components from food through heat and mass transfer, often used in flavour extraction.	Modeling of vapour phase and heat transfer dynamics, solvent evaporation in food matrices, temperature gradients.	Vapour flow dynamics, heat transfer, solvent concentration, efficiency of extraction.	Extraction of essential oils, flavour compounds, drying of high-value food products. Improved flavour concentration.	Optimization of extraction time, energy usage, reduction in solvent waste.	Modeling solvent dynamics, controlling the loss of volatile compounds during evaporation.	Modeling of extraction efficiency, control of volatile compound preservation.	[50,93,97,122,125]

.

4. Modeling of Physicochemical Parameters and Their Impact on Thermal Processes

4.1. Influence of Food Structure and Physical Properties on Heat Transfer

The heat transfer mechanisms within food systems are critically influenced by the physicochemical properties of the food matrix, including its structural characteristics and intrinsic physical properties. The primary modes of heat transfer—conduction, convection, and radiation—are intricately affected by the spatial arrangement and interactions of food components at both the microscopic and macroscopic levels. In particular, heterogeneous distributions of temperature are observed due to the complex phase transitions and material heterogeneity present within food structures. For instance, the presence of fats, water, and air pockets significantly alters thermal conductivity, leading to complex temperature gradients that must be accurately modeled to understand the overall heat transfer efficiency during food processing [56,126]. The thermal conductivity of food materials exhibits a high degree of variability, often depending on the composition and moisture content of the matrix. Proteins, typically exhibiting thermal conductivities in the range of 0.2 W/m·K, display markedly lower heat transfer rates compared to fats, which can have thermal conductivities as high as 0.5 W/m·K. This disparity directly impacts the rate of heat penetration during thermal treatments such as baking, frying, and pasteurization [11]. The variability in these thermal properties underscores the need to account for specific heat capacities, thermal diffusivities, and the phase transitions (for example, water to vapor, fat melting) that occur within the food matrix during processing [127]. The food microstructure, encompassing properties such as porosity, bulk density, and the organization of fibre networks, is a critical determinant of heat transfer behavior. For instance, an increase in porosity can facilitate convective heat transfer by providing pathways for air or fluid movement within the food product. Air pockets, in particular, have been shown to enhance heat transfer by reducing thermal resistance. In contrast, denser matrices with lower porosity—common in meat and some vegetables—tend to impede thermal penetration, resulting in temperature gradients and non-uniform cooking or processing. Additionally, factors such as water activity and phase changes (for example, the melting of fats and evaporation of water) exert significant influence over the effective thermal properties of food, directly impacting the heat transfer efficiency during different processing stages [56].

Mathematically, the modeling of heat transfer within food systems is grounded in the application of Fourier’s law of heat conduction, expressed as (Equation (13)) [34,128]:

$$q=-k\nabla T$$

(13)

where q is the heat flux (W/m²), k is the thermal conductivity (W/m·K), and ∇T is the temperature gradient (K/m). In the case of convection, the convective heat transfer rate is described by Newton’s law of cooling (Equation (14)) [72,81]:

$$q=hA\left(T_s-T_{\infty }\right)$$

(14)

where h is the convective heat transfer coefficient (W/m²·K), A is the heat transfer area (m²), T_s is the surface temperature, and T_∞ is the ambient temperature of the surrounding medium. Additionally, radiation heat transfer is often modeled using the Stefan–Boltzmann law (Equation (15)):

$$q=\sigma ϵA\left(T^4-T_{env}^4\right)$$

(15)

where σ is the Stefan–Boltzmann constant, ϵ is the emissivity of the surface, A is the surface area, and T and T_env are the temperatures of the object and surrounding environment, respectively [34].

CFD provides an advanced framework for the integrated modeling of these complex heat transfer phenomena, allowing for the simulation of fluid flow and heat conduction within food matrices. CFD simulations typically solve the Navier–Stokes equations for fluid flow, coupled with the energy equation for heat transfer [129]. In the context of food processing, these equations must also account for the complex interactions between different phases (solid, liquid, gas) and the material properties that evolve with temperature and phase transitions. For example, changes in the state of water from liquid to vapor (evaporation) or the melting of fats involve latent heat exchange, which can significantly alter the thermal behavior of the system [130,131]. The use of CFD simulation in food technology enables precise predictions of temperature distributions and heat fluxes within food products. These models are invaluable for optimizing thermal processes, such as pasteurization, sterilization, drying, and cooking, as they allow for the prediction of thermal profiles and the identification of regions with potential temperature anomalies. By integrating the detailed physicochemical properties of food materials into the simulation, it is possible to enhance product quality, ensure uniform processing, and minimize energy consumption, ultimately improving food safety and efficiency in the food industry [96,132].

4.2. 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 μ(T), for instance, can be expressed as (Equation (16)) [135]:

$$\mu \left(T\right)={\mu }_{0}exp\left({\displaystyle \frac{E_a}{RT}}\right)$$

(16)

where μ₀ 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)):

$$\rho C_p{\displaystyle \frac{\partial T}{\partial t}}+\nabla \cdot \left(\rho v\left(T-T_{\infty }\right)\right)=\nabla \cdot \left(\kappa \nabla T\right)$$

(17)

where ρ is the density, C_p is the specific heat capacity, v is the velocity vector, κ is the thermal conductivity, and T_∞ 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. By using sensor data (for example, temperature, moisture content, or texture properties) in conjunction with CFD, ML algorithms can predict real-time variations in food properties and adjust processing parameters accordingly. This combination allows for the continuous and adaptive control of thermal treatments, optimizing conditions for consistent product quality, energy efficiency, and food safety [138].

4.3. Accounting for Chemical Reactions During Thermal Processes

Thermal processing in the food industry extends beyond mere heat transfer, involving complex chemical reactions that influence both the sensory properties and the safety of food products. A key example is the Maillard reaction, a non-enzymatic browning process that occurs between reducing sugars and amino acids. This reaction is highly temperature-dependent and follows intricate pathways that are sensitive to both time and temperature conditions [139]. The Maillard reaction contributes to the development of characteristic flavours, aromas, and the desirable brown colour in cooked foods. To model this reaction accurately within thermal processes, it is essential to incorporate detailed kinetic models that account for the thermally activated nature of the reaction [29].

The reaction rate can be expressed using an Arrhenius-type equation (Equation (18)):

$$k=A\times e^{-{\displaystyle \frac{E_a}{RT}}}$$

(18)

where k is the rate constant, A 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 reflects the temperature dependence of the Maillard reaction rate, with k increasing exponentially as the temperature rises, thereby affecting the quality and safety of the final product [34]. In parallel, protein denaturation is another crucial chemical process occurring during thermal treatment. As the temperature increases, protein molecules undergo conformational changes that result in the loss of tertiary structures, leading to altered solubility and emulsifying properties. These transformations significantly affect food texture, water retention, and other functional characteristics. The kinetics of protein denaturation can also be described using an Arrhenius model, where the rate of denaturation is similarly dependent on temperature [140,141]. To accurately simulate these chemical transformations, CFD is coupled with reaction kinetics models, enabling the prediction of heat transfer, mass transfer, and the evolution of chemical reactions under different thermal conditions. The CFD simulations solve the governing equations of fluid flow, energy conservation, and species transport. These include the Navier–Stokes equations for momentum conservation, the energy equation for heat transfer, and species conservation equations for chemical reaction modeling. By incorporating reaction rates into these simulations, it is possible to simulate the concurrent effects of thermal processes and chemical reactions on food quality [74,142].

5. Industrial Applications of CFD Simulations in Food Technology

5.1. Optimization of Production Processes Using CFD

CFD simulations offer a significant advantage in optimizing thermal processes in food production. The application of CFD in food technology is often centered around the enhancement of heat and mass transfer, which are critical in processes such as baking, frying, pasteurization, and sterilization. By utilizing CFD, engineers can simulate and analyze the temperature distribution, airflow patterns, and moisture content within the processing environment, allowing for a deeper understanding of how these factors influence product quality and production efficiency [143].

In the optimization of production processes, CFD can be employed in several key ways to achieve improvements in performance. The process typically begins with the creation of detailed simulations that represent the physical conditions of the production environment, including the geometry of the equipment, boundary conditions (such as temperature, pressure, and velocity), and material properties. This allows for a thorough investigation of various operational parameters and their impact on the process.

The optimization can be achieved by focusing on the following key areas:

Heat and Mass Transfer Enhancement: By adjusting the design parameters of equipment (such as heat exchangers, ovens, or fryers), CFD can help to optimize the heat transfer rates and mass flow characteristics. This is especially important for achieving uniformity in temperature distribution, which affects the quality and safety of food products. For example, in baking processes, CFD can help determine the optimal air velocity and temperature distribution inside the oven to ensure an even bake, reducing the risk of over- or undercooking.

Energy Efficiency: One of the significant advantages of CFD is its ability to simulate different configurations of equipment and processing conditions to identify the most energy-efficient setup. By predicting temperature and airflow patterns, CFD can help minimize energy consumption in processes like pasteurization and sterilization, where controlling the temperature precisely is crucial. This can lead to reduced operational costs and a smaller environmental footprint.

Process Design Optimization: CFD simulations can also assist in designing or redesigning production lines for optimal performance. For example, simulating air circulation in a cooling tunnel can help design a system that maximizes heat dissipation while minimizing energy use. Moreover, CFD can be used to determine the optimal size and placement of fans, heat exchangers, or evaporators, thus improving overall system efficiency.

Quality Control and Product Consistency: By predicting the thermal profiles and moisture content distribution within food products, CFD enables manufacturers to control product quality more precisely. This is particularly valuable in processes such as drying or frying, where achieving the right moisture content and texture is essential. CFD can be used to test different operational parameters, ensuring that the desired product quality is consistently achieved.

Mathematically, CFD relies on solving the Navier–Stokes equations for fluid flow, coupled with the energy equation for heat transfer, and species transport equations for mass transfer [144]. These equations are expressed as the following:

Continuity Equation (Equation (19)):

$$\nabla \cdot v=0$$

(19)

where v is the velocity vector, ensures the conservation of mass.

Momentum Equation (Navier–Stokes equation) (Equation (20)):

$$\rho \left({\displaystyle \frac{\partial v}{\partial t}}+v\cdot \nabla v\right)=-\nabla p+\mu {\nabla }^{2}v+f$$

(20)

where ρ is fluid density, p is pressure, μ is dynamic viscosity, and f represents body forces.

Energy Equation (Equation (21)):

$$\rho C_p\left({\displaystyle \frac{\partial T}{\partial t}}+v\cdot \nabla T\right)=\nabla \cdot \left(k\nabla T\right)+Q$$

(21)

where C_p is specific heat, T is temperature, k is thermal conductivity, and Q represents internal heat generation.

By solving these equations, CFD models allow for the prediction of temperature and velocity profiles, identifying areas with undesirable thermal gradients or airflow inefficiencies. These data can then be used to guide the optimization of production processes, improving design and operation in various ways. For example, by simulating different scenarios, engineers can identify the best operational conditions, such as flow rates, heating profiles, or equipment configurations, that result in reduced energy consumption, improved product uniformity, and minimized waste.

In conclusion, CFD serves as a powerful tool in the optimization of food production processes, offering both a detailed understanding of thermal dynamics and a platform for testing various process configurations before implementation. By applying CFD, food manufacturers can not only improve the efficiency of their processes but also enhance the quality and consistency of their products, ensuring better resource utilization and lower operational costs [14,145].

5.2. Application of CFD in Equipment Design and Development for the Food Industry (For Example, Ovens, Dryers, Freezers)

CFD simulations are integral in the design and optimization of food processing equipment, such as ovens, dryers, and freezers, where thermal processes play a pivotal role in product quality. In ovens, for example, CFD can be employed to simulate the heat distribution within the cooking chamber. This is crucial for ensuring uniform baking, preventing overcooking or undercooking, and optimizing energy consumption. Similarly, in dryers, CFD helps in modeling the airflow and moisture removal rate, which can be adjusted to achieve the desired texture and preservation of nutrients in food products [96]. For thermal treatment equipment, such as pasteurizers and sterilizers, CFD is often used to model the convective heat transfer between hot water or steam and the food product. By resolving the fluid flow and thermal fields, engineers can fine-tune the temperature distribution to ensure that the product undergoes sufficient heat treatment while maintaining its quality and safety [146]. To capture these phenomena, models for forced convection (when air or fluids are actively circulated), natural convection (driven by temperature gradients), and heat conduction within solids are employed. In addition, phase change models (for drying or freezing processes) are crucial, as they account for the latent heat during phase transitions, such as water evaporation or ice crystallization [147].

5.3. Quality Control and Monitoring in Thermal Processes Through CFD Simulations

CFD simulations offer a comprehensive approach for real-time quality control and the monitoring of thermal processes in food production. By simulating the entire thermal cycle—from preheating to cooling—it is possible to not only predict but also actively monitor the temperature distribution throughout the product. This is crucial for ensuring consistent product quality, particularly in processes where precise temperature control is essential, such as pasteurization or sterilization. CFD provides insights into the temperature fluctuations within the food product and its environment, allowing for a deeper understanding of how thermal profiles affect microbiological safety and product quality [117]. To enhance the monitoring and control of thermal processes, CFD simulations can be integrated with sensors, real-time feedback systems, and control algorithms. This integration enables dynamic adjustments to the thermal process based on live data, ensuring that any deviation from the desired conditions can be promptly corrected. For example, by comparing real-time temperature measurements with the CFD predictions, operators can identify discrepancies in heat transfer or flow patterns and adjust parameters, such as heating times, temperatures, or fluid flow rates, in real-time. This adaptive approach is essential for maintaining product consistency, optimizing energy usage, and reducing waste during production. Moreover, CFD simulations allow for the early detection of potential deviations from optimal thermal conditions, facilitating preventive actions before the product reaches the consumer. By continuously monitoring and adjusting the process in response to simulation outcomes, manufacturers can ensure that the thermal process remains within the optimal range, reducing the risk of quality issues, such as underpasteurization or overcooking [14,148].

5.4. Case Studies and Examples of CFD Implementation in Food Companies

Several case studies demonstrate the practical applications of CFD in the food industry. One notable example is the optimization of air distribution in commercial ovens, where CFD was used to simulate airflow and thermal profiles to ensure a uniform heat distribution across various baking trays. This simulation helped reduce energy consumption by 15% while improving the consistency of baked goods [89,149]. In another example, CFD simulations were applied in the development of a high-efficiency freeze-drying process. By simulating the airflow, temperature, and pressure variations in the freeze dryer, the company was able to minimize energy use and maximize the moisture removal efficiency. This not only reduced operational costs but also improved the preservation of sensitive nutrients and flavours in the final product [140,150]. Additionally, CFD has been successfully applied to simulate heat transfer in continuous sterilization systems, helping food manufacturers optimize processing times and temperature profiles to enhance product shelf life while maintaining nutritional quality [14].

6. Benefits, Challenges, and Limitations of CFD in the Food Industry

6.1. Economic and Technological Benefits

The implementation of CFD in the food industry is often constrained by significant cost and hardware requirements. High-performance computing (HPC) systems are necessary for simulating complex food processes, especially when dealing with large 3D models or transient phenomena. The computational power required for these simulations translates to increased costs in terms of software licensing, the maintenance of hardware infrastructure, and energy consumption [151]. Additionally, advanced CFD software often requires expertise in both food science and computational modeling, necessitating specialized training and technical support. For smaller food manufacturers, these costs may present a barrier to entry, limiting the widespread adoption of CFD tools in the industry [112,152].

6.2. Challenges Related to Accuracy and Computational Time

Despite its advantages, CFD simulations in food technology face significant challenges regarding its accuracy and computational time. The accuracy of results depends heavily on the quality of input data, such as the physical properties (for example, thermal conductivity, specific heat and viscosity) of food materials, which often exhibit complex and variable behavior under different conditions. In particular, food systems are non-homogeneous and exhibit temperature-dependent phase changes (such as freezing, melting, and drying), which are difficult to model accurately [142]. Additionally, turbulence, laminar flow regimes, and heat transfer in porous media (typical in food systems) require advanced models, such as the RANS equations or Large Eddy Simulations. The computational time required for high-resolution simulations, particularly in 3D models or real-time simulations, can be prohibitive. This makes the application of CFD less accessible for time-sensitive processes or small-scale operations, despite the advancements in parallel computing and cloud-based solutions [55,153].

6.3. Limitations Associated with Physical Modeling of Complex Food Structures

The physical modeling of food structures in CFD presents unique limitations due to the heterogeneous nature of food materials. Foods consist of complex geometries, including porous structures, heterogeneous phases (solid, liquid, gas), and varying thermal properties across different components, which complicate the modeling process. For instance, in simulations of heat transfer during cooking or drying, food matrices such as meat, dough, or fruit often exhibit multiphase behavior, making it challenging to model phase transitions like evaporation, melting, or crystallization [53]. Furthermore, the interaction between food structure and fluid dynamics, such as how liquids flow through porous solids or how bubbles behave in frying oil, requires specialized models, such as the VOF or Lattice Boltzmann methods, which can be computationally intensive [14]. Additionally, the difficulty in acquiring accurate, high-resolution 3D scans of food microstructures limits the ability to fully capture these complex interactions [95]. These challenges underscore the need for further research and development in multi-scale modeling approaches to more accurately simulate the diverse physical phenomena in food processing [154,155].

6.4. Cost and Hardware Requirements

The implementation of CFD in the food industry is often constrained by significant cost and hardware requirements. High-performance computing systems are necessary for simulating complex food processes, especially when dealing with large 3D models or transient phenomena. The computational power required for these simulations translates to increased costs in terms of software licensing, the maintenance of hardware infrastructure, and energy consumption [151,156].

6.5. Promoting Interdisciplinary Cooperation for Advancing CFD Applications in the Food Industry

The application of CFD in the food industry has gained significant traction, offering insights into complex thermal and fluid dynamics that enhance process optimization and product quality. However, the successful deployment of CFD technologies in this domain often hinges on robust interdisciplinary collaboration. Effective interdisciplinary cooperation begins with creating platforms where professionals from diverse fields can interact. These platforms, which can take the form of joint workshops, seminars, and conferences focused on the integration of CFD in food technology, provide opportunities for sharing advancements in CFD tools and their applicability to food processes, identifying gaps in knowledge and challenges in specific applications, and building networks among researchers, technologists, and industry practitioners. To bridge the knowledge gap between disciplines, it is crucial to offer cross-disciplinary education and training programs. Workshops and certification courses can train food technologists in the basics of CFD and familiarize CFD experts with the unique challenges of food materials and processes. Universities can introduce specialized courses or modules combining CFD fundamentals with food science and engineering applications. Additionally, online learning platforms can provide flexibility for professionals to acquire interdisciplinary skills [157]. Interdisciplinary research and development (R&D) projects can drive innovation by pooling expertise from different domains. Joint research grants, funded by agencies prioritizing collaboration between CFD researchers and food engineers, can play a significant role. Industry-academic partnerships, where industries provide practical problems and the academia develops CFD-driven solutions, can be equally impactful. Moreover, providing access to shared computational resources, such as high-performance computing facilities, can support joint simulations and data analysis [158]. One of the barriers to the widespread application of CFD in food technology is the lack of standardized models tailored to food processes. Collaborative efforts can address this by developing benchmark datasets and simulation protocols for common food processing scenarios, creating open-source CFD models validated for food-specific challenges, such as non-Newtonian fluid behaviors and complex heat transfer mechanisms, and forming working groups within international organizations to establish the best practices [159]. Integrating CFD with Artificial Intelligence (AI) and Machine Learning (ML) can significantly enhance its applicability by reducing computation time and improving prediction accuracy. Collaborative efforts in this area could focus on developing AI-driven tools for automated mesh generation and parameter optimization, utilizing ML algorithms to analyze large datasets generated from CFD simulations and experimental results, and building interdisciplinary teams to design hybrid AI-CFD models tailored to food processes [136,153]. Demonstrating the tangible benefits of interdisciplinary collaboration through real-world case studies can inspire the further adoption of CFD in the food industry. Pilot projects implementing CFD-based process optimization in food manufacturing facilities can showcase improvements in efficiency and product quality. Publishing detailed case studies highlighting the collaboration between CFD specialists and food engineers, and organizing interactive demonstrations such as live simulations or virtual reality-based walkthroughs of CFD models applied to food processes, can also play a crucial role [9]. Policymakers and industry leaders have a critical role in fostering interdisciplinary collaboration. Offering tax benefits or subsidies to companies investing in CFD-integrated food processing technologies, streamlining regulatory approval processes for innovations developed through interdisciplinary efforts, and establishing long-term roadmaps that highlight the role of CFD in addressing food industry challenges are key actions that can support this goal [72]. Interdisciplinary cooperation is essential to unlocking the full potential of CFD in the food industry. By fostering collaboration between CFD experts, food technologists, and engineers, the industry can develop innovative solutions to optimize processes, enhance product quality, and meet sustainability goals. Strategic initiatives, such as joint education programs, collaborative R&D, and policy advocacy, can serve as catalysts for this integration, ensuring that CFD continues to transform the landscape of food technology [96].

7. Future Directions for CFD Research and Development in Food Technology

7.1. Development of Hybrid Modeling Methods

Hybrid modeling methods in CFD hold significant promise for the food industry, as they combine multiple modeling approaches to achieve more accurate and versatile simulations. By integrating mechanistic models, which describe physical and chemical phenomena, with data-driven models, such as empirical or statistical models, hybrid methods can offer improved precision in simulating complex food processing environments. This is particularly valuable for systems with varying thermal, physical, and chemical properties, such as those encountered in fermentation, pasteurization, or drying processes. Hybrid models allow researchers to capture both micro- and macroscopic dynamics, bridging gaps that standalone models often fail to address. Moreover, these approaches enable simulations to account for real-time variations and nonlinear behaviors, thus enhancing process optimization and control. The development of such hybrid techniques is a growing area in CFD, with the potential to improve predictive accuracy, streamline testing protocols, and reduce the time needed for developing new food processing methods [156].

7.2. Potential of Large-Scale Simulations

Large-scale simulations represent a promising frontier for CFD in the food industry, offering insights into comprehensive systems with multiple interacting components, such as entire production lines or complex thermal processing units. Advances in computational power and cloud-based resources have made it feasible to run high-resolution simulations that account for various scales of phenomena—from molecular interactions to macroscopic flows—within a single model. This level of simulation can enable food technologists to explore the cumulative effects of different processing stages, helping to optimize entire workflows rather than individual steps. For example, large-scale CFD simulations can be used to model the airflow, temperature distribution, and moisture content in large drying chambers, helping to ensure a uniform quality across large batches. By understanding the interdependencies within these systems, large-scale CFD simulations offer the potential to streamline production, enhance energy efficiency, and reduce waste. The growing accessibility of computational resources continues to expand the potential applications of large-scale simulations in industrial food processes [160].

7.3. Prospects for Advancements in CFD Software and Hardware

The continuous development of CFD software and hardware is critical for expanding the applications and accuracy of simulations in food technology. Emerging software tools are incorporating more intuitive interfaces, advanced solver algorithms, and expanded libraries of food-specific material properties, making CFD more accessible to food engineers without specialized CFD expertise. In parallel, advancements in hardware, such as high-performance computing clusters and GPUs, enable the processing of highly detailed simulations in significantly reduced times [138]. Cloud computing platforms are also becoming increasingly relevant, providing scalable resources that reduce the need for costly on-site infrastructure. These advancements will allow researchers and industry professionals to conduct rapid prototyping, real-time simulations, and multi-scale modeling, which can support more efficient and sustainable production practices [161]. As software and hardware continue to evolve, CFD’s role in the food industry is likely to grow, facilitating faster innovation cycles and more robust modeling capabilities across a wider range of food processing scenarios [162,163,164].

8. Conclusions

The application of CFD in food technology has significantly enhanced the understanding and control of thermal processes, such as pasteurization, drying, and cooking. Key findings from this research indicate that CFD allows for the precise simulation of fluid flows, heat transfer, and temperature distribution in complex food systems. CFD has proven especially useful in optimizing process parameters, reducing energy consumption, and ensuring food safety and quality. The simulations conducted demonstrate that CFD can accurately predict the behavior of food products under various processing conditions, offering a reliable, cost-effective, and efficient tool for innovation in the food industry. CFD holds considerable promise for the food industry as it addresses critical challenges in process optimization and product quality control. Its capability to simulate and optimize processes before scaling up to industrial production helps reduce experimental costs and product development time. As the food industry continues to adopt digitalization and Industry 4.0 principles, CFD will become an integral part of digital twins and smart manufacturing systems. The future of CFD in this field will likely see more advanced simulations incorporating biochemical changes and texture transformations, contributing to safer, more sustainable, and higher-quality food production methods. To fully leverage CFD in the food industry, professionals should integrate it with real-time monitoring and control systems to enable dynamic process adjustments. Further research should focus on refining CFD models to include multiphase and multi-component flows, as well as biochemical transformations that occur during processing. Additionally, the interdisciplinary collaboration between CFD specialists, food technologists, and engineers will be essential to develop customized, industry-specific models. Expanding the use of CFD to smaller food businesses could democratize access to these tools, leading to broader innovations across the sector.