# Analysis of Shell Egg Pasteurization Using Computational Fluid Dynamics
## 2 Materials and Methods  
The thermal pasteurization of eggs was simulated using a multidimensional computational fluid dynamic model. The egg geometry was designed using 3D CAD (computer aided design) software (_Ansys DesignModeler, Release 22.1_, ANSYS, Inc., Canonsburg PA, USA) based on [PERSON]'s egg [19]. The model geometry was imported to _Ansys(r) Academic Research Mesh, Release 22.1_ (ANSYS, Inc., Canonsburg PA, USA) and discretized into an unstructured tetrahedral mesh. For the large-size egg (63-72 g), 314,029 cells were used for the discretization and the solution of the governing equations (Figure 1). The required values for the mesh used were obtained by taking into consideration the domain (fluid), the nature of the process, and the computational time required by means of mesh independence analysis. The software _Ansys(r) Academic Research Fluent, Release 22.1_ (ANSYS, Inc., Canonsburg PA, USA) was chosen to perform the required calculations. The calculation of heat transfer and fluid flow in the proposed domain due to natural convection required numerical solution of the generalized transport equations [20]. The external surface of the geometry representing the eggshell was defined as a wall. The internal volume of the egg, consisting of the yolk and the albumen without any air pocket, was defined as the fluid. A membrane around the yolk was used to not allow for mass exchange between the yolk and the albumen, and it was modeled as a wall with properties identical to yolk properties. All materials used were assumed to be homogenous and isotropic. Uniform initial conditions were used. A constant medium temperature and a given experimental heat transfer coefficient was applied to the external surface of the egg. External forces, moisture transfer, and viscous dissipation were neglected. The gravitational force was set to g = 9.81 m/s\({}^{2}\). A constant time step of 1 s was used to solve the transient process. The convergence criterion was set to be lower than 10\({}^{-6}\). Figure 1: Shape and dimensions of the large-size egg used for the simulations (**left**) and mesh imaging (**right**). For the design of egg geometry, fresh, large-size eggs, 63-72 g, were purchased from a local market (Athens, Greece). All eggs were examined macroscopically (ovoscopy), with the aid of a light source, for cracks and other shell defects and to determine the position of the yolk and the air pocket. At the same time, the shape of the eggs was evaluated in terms of their axial symmetry. Their weight (through a precision balance, MARK 2200, BEL Engineering(r), Monza, Italy), volume (through a 500 mL volumetric cylinder) and dimensions (width and height by means of a micrometer with 25-75 mm range) were determined prior to processing. These observations and the average values of the above measurements were used for the design of the large-size egg geometry, which was subsequently used for the CFD simulations and model validation (Figure 1). Specifically, following [PERSON]'s egg design, egg height was 0.05917 m, egg width was 0.04634 m, yolk diameter was 0.03135 m, yolk distance from the bottom of the egg was 0.03559 m, and egg volume was 6.4109 \(\times\) 10\({}^{-5}\) m\({}^{3}\). The terms \"large\" or \"large size\" egg are used throughout this paper when referring to the egg designed with the particular geometry and dimensions just presented. In order to study the effect of egg size, two additional egg sizes were designed: one corresponding to medium-size eggs (53-62 g) and one for extra-large-size eggs (>72 g), as defined by the European Regulation (EC) No 589/2008 marketing standards for eggs [21]. For the medium-size egg, egg height was 0.05500 m, egg width was 0.04594 m, yolk diameter was 0.03035 m, yolk distance from the bottom of the egg was 0.03559 m, and egg volume was 5.7009 \(\times\) 10\({}^{-5}\) m\({}^{3}\) (termed \"medium\" or \"medium size\" egg).