## 5 CFD in Extrusion Processes
### Prediction of Pressure, Temperature, and Shear Profiles  
Accurate prediction of pressure, temperature, and shear stress profiles along the extrusion barrel and die is essential for understanding the thermomechanical environment that shapes the final structure and properties of extruded food products. These physical parameters govern critical aspects of the process, including material flow, energy input, product expansion, moisture reduction, and textural development. CFD provides a robust and non-invasive means to simulate and visualize these fields with high spatial and temporal resolution, supporting process design, control, and optimization [74]. Pressure profiles along the extrusion screw are particularly important, as they determine the extent of material compaction, melting, and the force required to push the mass through the die. In CFD simulations, pressure gradients are obtained from the momentum conservation equations and are influenced by the screw geometry and configuration (including compression zones and kneading elements), the viscosity and flow resistance of the processed matrix, and the backpressure created by the die. Typically, pressure is low in the feeding zone, gradually increases through the compression and melting sections, and reaches a maximum at the die entry--often in the range of 5 to 20 MPa, depending on the product type and moisture content. CFD allows for virtual testing of different screw designs and die geometries, enabling optimization of pressure buildup and prevention of issues such as overpressurization, incomplete melting, or throughput fluctuations [57]. Temperature distribution within the extruder also plays a pivotal role, as many physicochemical changes--such as starch gelatinization, protein denaturation, and moisture vaporization--are thermally activated. CFD solves the energy balance equation to simulate temperature fields, accounting for external barrel heating, viscous and frictional heat generation, thermal conduction through the matrix, and latent heat associated with phase transitions. These simulations provide temperature maps across both axial and radial sections of the barrel, which help identify hot spots that may degrade nutrients or induce color changes, and cold zones where incomplete cooking or phase transitions can occur. Accurate modeling of thermal gradients is particularly relevant for maintaining product homogeneity and ensuring efficient expansion. CFD-based temperature profiles also support thermal validation and safety assessments, such as estimating lethality in pasteurized extrudates [97]. Shear stress and shear rate distributions are equally critical in extrusion processes, as mechanical deformation influences microstructural alignment, mixing efficiency, and energy dissipation. Shear stress (\(\tau\)) is computed in CFD from local velocity gradients and the apparent viscosity of the food matrix using the following relationship:  
\[\tau=\mu(\gamma)\cdot\gamma\]  
where \(\mu(\gamma)\) represents the shear-rate-dependent viscosity and \(\gamma\) denotes the local shear rate. This relationship is especially important for modeling non-Newtonian materials such as doughs, meat analogues, or protein-rich formulations, which exhibit shear-thinning, viscoplastic, or viscoelastic behavior. CFD simulations allow identification of high-shear regions--typically near barrel walls, screw surfaces, or narrow die channels--where energy input is concentrated. These zones play a key role in dispersive and distributive mixing, as well as in the alignment of fibrous structures in plant-based extrudates. However, excessive shear may lead to overprocessing or mechanical degradation of sensitive compounds, underscoring the importance of accurate shear modeling for texture control [98]. Figure 2 shows how nozzle diameter affects the shear rate distribution in syringe-based extrusion of rice paste, highlighting the influence of die geometry on flow behavior and material deformation during food 3D printing.