# Modeling and Experimental Verification of Induction Heating of Thin Molybdenum Sheets
## 3 Design of Electro-Thermal Simulation Model of Induction Heating  
The simulation model considering induction heating of Mo sheet is designed with the use of COMSOL software. It considers a 3D model offering the options for reconfiguration of various parameters that influence the heat distribution on the Mo sheet's surface. These parameters are:  
* the mutual position between the induction coil and the Mo sheet,
* the coil material properties as well as the coil geometry
* the frequency and intensity of the applied electromagnetic field. The model comprises the Mo sheet, a heating coil with a magnetic core (Figure 4). The molybdenum sheet is modeled as a block (domain) with a required width (sa), depth (sb), and thickness (sc). The coil's winding is designed as a square domain with a required thickness (ca) and the required size (cb). The coil's core is represented by the ferrite blocks whose parameters are also reconfigurable, i.e., ferrite height (fa) and ferrite thickness (fb). The variable parameter can also be the distance between the Mo sheet and heating element (cpd). The physics used in this model is \"Magnetic field (MF)\". The only feature of \"MF\" used is \"COIL\", which specifies the coil domain as a single conductor with current input surface and current output surface. All simulations are set as steady-state, frequency-domain simulations, so it is possible to determine the impact of investigated parameters \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Reference Point**} & **The Temperature at the** & **The Temperature at the** & **Relative Error** \\  & **Reference Point [\({}^{\circ}\)C]** & **Reference Point [\({}^{\circ}\)C]** & **[\%]** \\ \hline Sp1 & 38.9 & 39.88 & \(-2.52\) \\ Sp2 & 44.9 & 45.73 & \(-1.85\) \\ Sp3 & 54.9 & 55.59 & \(-1.26\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of the temperature within reference points. Figure 3: Temperature distribution and its evaluation for a designed thermal simulation model of induction heating. on the amplitude of electromagnetic losses (heat rate) within the molybdenum sheet [4,6]. The mentioned \"MF\" module of the COMSOL environment uses the standard Maxwell equations for modeling an electromagnetic field in the frequency domain. The material parameters and other model settings as final conditions settings of domains for the simulation analysis can be seen in Table 3.  
The definitions related to the boundary conditions of the simulation model are given by domain settings (Table 4) and by equations for heat transfer/source (1)-(4). These settings are relevant for the integrated simulation software definitions related to heat transfer and electrical currents physics. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Domain** & **Material** & **Domain Settings** & **Domain Equations** \\ \hline Environment & Air & Fluid, Initial Values [25 \({}^{\circ}\)C] & (1), (3) \\ Environment Boundary & Air & Fluid, Initial Values [25 \({}^{\circ}\)C], & (1), (3), (4) \\  & & Thermal Insulation & (1), (3), (4) \\ Molybdenum Plate & Molybdenum & Solid, Initial Values [25 \({}^{\circ}\)C] & (2), (3) \\ Heat Source in Molybdenum & Molybdenum & Solid, Initial Values [25 \({}^{\circ}\)C], & (2), (3), (5) \\ Plate & Molybdenum & Solid, Initial Values [25 \({}^{\circ}\)C] & (2), (3) \\ Coil & Copper & Solid, Initial Values [25 \({}^{\circ}\)C] & (2), (3) \\ Magnetics & Ferrite & Solid, Initial Values [25 \({}^{\circ}\)C] & (2), (3) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Boundary conditions of the induction heating model. Figure 4: The geometry description of the proposed induction heating model (**a**) and detailed geometry description of heating element—coil (**b**).