## 2 Materials and Methods
### Numerical and Experimental Studies  
In this study, the freezing of ice cream inside molds was investigated. First, the proposed specific heat correlation was validated by comparing experimental results with numerical simulation results. After validating the numerical studies, a parametric analysis \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Food Item** & \begin{tabular}{c} **Water** \\ \(\mathbf{X_{nro}}\) \\ \end{tabular} & \begin{tabular}{c} **Protein** \\ \(\mathbf{X_{p}}\) \\ \end{tabular} & \begin{tabular}{c} **Fat** \\ \(\mathbf{X_{f}}\) \\ \end{tabular} & \
\begin{tabular}{c} **Carbohydrate** \\ \(\mathbf{X_{c}}\) \\ \end{tabular} &
\begin{tabular}{c} **Ash** \\ \(\mathbf{X_{a}}\) \\ \end{tabular} \\ \hline \hline \multicolumn{1}{c}{Chocolate ice cream} & 55.7 & 3.8 & 11 & 29.4 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Chocolate ice cream’s physical properties. Figure 1: Specific heat calculations according to literature data. of freezing conditions was conducted. The effects of the glycol-water mixture temperature, the initial ice cream temperature, and the air volume within the ice cream were compared in the numerical studies. During the experimental studies, the mold was placed in the glycol-water mixture, and the temperature of the glycol-water mixture was adjusted to \(-34\)\({}^{\circ}\)C. The temperature of the ice cream was collected only from one point, located at the center point of the ice cream, which was measured by a PT100 probe with 0.05 \({}^{\circ}\)C accuracy, and temperature data were collected every second. A schematic experimental setup visual can be found in Figure 2.  
Real experimental setup and equipment visuals can be found in Figure 3.  
Figure 3: Experimental setup: 1 corresponds to the glycol–water mixture, 3 represents the mold, 4 denotes the PT100 probe, and 5 signifies the data logger equipment. Figure 2: Schematic visualization of the experimental setup. To simulate real production conditions during experimental studies, the ice cream mixture was aerated to 30% of its volume using cooling mixer equipment. This basic equipment is a type of scraped surface heat exchanger, which we used to cool down the ice cream mixture. Since it was exposed to the environment, it was observed that the ice cream mixture became aerated by 30% during the beating process. The aerated ice cream mixture was then poured into the mold at 4 \({}^{\circ}\)C, and the temperature at the center of the ice cream was measured for 10 min, with data collected every second. As mentioned before, numerical modelling was also developed using commercial software, Academic Ansys Thermal Transient Tool. The thermal properties of ice cream were uploaded according to the temperature points in the software. Before starting simulations, a mesh independence study was conducted to compare numerical results using 12,576, 63,210, and 123,845 elements. It was found that there was no difference between elapsed time until the ice cream center temperature reached \(-18\)\({}^{\circ}\)C using 63,210 and 123,845 elements, indicating that exceeding 63,210 elements is unnecessary for this numerical analysis and would unnecessarily lead to a longer solution time and heavier computer performance load. A mesh independence study can be found in Figure 4.  
The tetrahedron mesh type was used, and the 63,210 elements were created to solve the problem. The average skewness was 0.25, which is considered to be good quality for meshing in general applications. Boundary layer inflation is placed between the ice cream and mold to simulate heat transfer better between the two boundary layers. Mesh elements and boundary layer meshing visuals can be found in Figure 5.  
The Ansys Transient Thermal Tool solves the three-dimensional time-dependent heat transfer equation in an explicit form. Three-dimensional time-dependent heat transfer formulation can be found in Equation (25).