## 2 Materials and Methods
### The Heat Treatment Process Using CDF Simulation
#### 2.3.2 Numerical Model  
The Analyzed Space  
The model consisted of three separate regions. The first area covered the fluid surrounding the sleeve-shaped rotor, which rotated at a predetermined speed. This setup allowed for the simulation of the rotor's movement within the chamber, with the blades depicted as surfaces. The second region represented the chamber space where air circulation was generated by the rotating rotor. Finally, the third section comprised two solid elements: the sample insert and the supporting plate. Mesh  
A Hex structural mesh was applied to the rotor space, incorporating surface compaction for the rotor blades to enhance flow representation. For the chamber, a Tetra/Prism mesh was used, with prismatic elements strategically placed, such as along the meat and plate walls, for heat transfer analysis. Hexa mesh was chosen for the goose breast sample and plate. The model specifications were as follows: rotor space--152,880 hexes and 177,702 nodes; chamber--339,867 tetras, 100,385 prisms, and 120,714 nodes; meat and plate--54,528 hexes and 62,148 nodes. Materials  
In the computations, the materials used included a blend of air and water vapor, goose breast meat as the used material, and stainless steel (AISI 304). The initial temperature of the solids was set at 25 \({}^{\circ}\)C.  
Material data:  
Goose breast meat:  
The determination of the conduction coefficient (\(\lambda\)) relied on Equation (1) following the description by [PERSON] and [PERSON], considering the essential composition of the sample [35]. \[\lambda=0.205x_{c}+0.20x_{p}+0.175x_{f}+0.135x_{a}+0.61x_{w} \tag{1}\]  
where:  
\(x\)--mass fraction of the food ingredient,  
indexes:  
\(c\)--carbohydrates,  
\(p\)--proteins,  
\(f\)--fat,  
\(a\)--ash,  
\(w\)--water. The computation of specific heat (\(C_{p}\)) was derived from Equation (2) following the explanation provided by [PERSON] and [PERSON], considering the fundamental composition of the samples [36]. \[C_{p}=1.424x_{c}+1.549x_{p}+1.675x_{f}+0.837x_{a}+4.187x_{w} \tag{2}\]  
where:  
\(x\)--mass fraction of the food ingredient,  
indexes:  
\(c\)--carbohydrates,  
\(p\)--proteins,  
\(f\)--fat,  
\(a\)--ash,  
\(w\)--water. Stainless Steel (AISI 304--properties at 300 K) [37]  
Conduction coefficient (\(\lambda\))--14.9 W/m\(\cdot\)K  
Specific heat (\(C_{p}\))--477 J/kgK. Air--Air Ideal Gas:  
The ideal gas equation of state can be applied for the computation of different gas properties according to Equation (3). \[pV=nRT \tag{3}\]  
where:  
\(p\)--the absolute pressure of the gas,  
\(V\)--the volume of the gas,  
\(n\)--the amount of substance of gas (also known as number of moles),  
\(R\)--the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant,  
\(T\)--the absolute temperature of the gas. Water vapor--Redlich-Kwong Dry Steam:  
Properties were determined using the Redlich-Kwong equation, as denoted by Equation (4) [38]. \[p=\frac{RT}{V_{m}-b}-\frac{a}{\sqrt{T}V_{m}(V_{m}+b)} \tag{4}\]  
where:\(p\)--gas pressure,  
\(R\)--gas constant,  
\(T\)--temperature,  
\(V_{m}\)--molar volume (V/n),  
\(a\)--constant that corrects for attractive potential of molecules,  
\(b\)--constant that corrects for volume. The measurement used a gas mixture comprising steam and air, with the composition of the blend determined by the mass fractions of its constituent components. Humidity  
The Goff-Gatch equation (Equation (5)) [39] was applied to convert humidity into mass fractions of steam and air at a particular temperature. \[ \begin{split}\log e^{*}=-7.90298\Big{(}\frac{T_{st}}{T}-1\Big{)}+ 5.02808\log\Big{(}\frac{T_{st}}{T}\Big{)}-1.3816\times 10^{-7}\Big{(}10^{11.344(1- \frac{T}{T_{st}})}-1\Big{)}\\ +8.1328\times 10^{-3}\Big{(}10^{-3.49149}(\frac{T_{st}}{T})-1 \Big{)}+\log e^{*}_{st}\end{split}