# Modeling and Experimental Verification of Induction Heating of Thin Molybdenum Sheets
## 3 Design of Electro-Thermal Simulation Model of Induction Heating
### Heat Distribution and Heat Performance for Optimal Parameter Settings of Induction Heating  
The simulation experiments previously realized uses results to determine the dependency between the parameters settings and volumetric power losses within the molybdenum. Those optimal settings have been adapted here, and the only change during parametric simulation will be the value of the coil's current.  
* The current flowing through the coil is 50:50:500 A.
* The thickness of the ferrite core is 7 mm.
* The operating frequency of the applied field is 40 kHz.
* Distance (gap) between sheet and heating element is 3 mm.  
Figure 10: Distribution of the volumetric loss density within the molybdenum sheet at selected values of the operating frequency.  
Figures 11 and 12 show that with the increase of the coil's current, the sheet's volumetric losses and the generated power of the coil rises. The limitation within this experiment was given on the current value, which cannot exceed 500 A due to the electrical parameters of the heating element's conductor.  
This behavior is based on the basic laws of the accumulation of energy within the inductor. Figure 11 shows that the energy has exponential character; thus, it is confirmed here that energy is proportional to the value of inductance and square of the current flowing through the inductor.  
Figure 13 shows the distribution of the volumetric losses within the molybdenum sheet for selected values of the coil's current. The purpose of this research was to identify the amount of volumetric loss. Simultaneously, these values will consequently serve within the thermal simulation of the induction heating, where the input boundary condition for the heating is identified values of molybdenum sheet losses.  
Figure 11: The dependency of maximal electromagnetic losses within the molybdenum sheet on the value of the coil’s current.  
Figure 12: The dependency of coil power on the value of the coil’s current.  
After getting relevant information for the optimal operational parameters setting, the experiment defined by all optimal measures was realized. Figure 15 represents the situation as mentioned above, while it is seen that the temperature distribution refers to the results achieved during the simulation result (Figure 14--right). There is a slight difference at the maximum temperature achieved at the Mo sheet hotspot (626 \({}^{\circ}\)C) instead of the simulation (607 \({}^{\circ}\)C). Even there is a difference, it is evident that the research of the optimal parameter settings of the induction heating through a simulation approach gives satisfying results. The model shall serve for any optimization purposes needed for the induction heating.  
Experimental results of the induction heating supported by the optimal settings received from simulations have been compared to the different heating processes, i.e., contact resistive heating (Figure 16). This comparison demonstrates that induction heating provides a more uniform temperature distribution than alternative heating techniques [24; 25; 26]. The maximal difference (diff\({}_{\text{T}}\)) between the area with the lowest and the highest temperature for induction heating is lower than resistive heating (diff\({}_{\text{Tind}}\) = 150 \({}^{\circ}\)C, diff\({}_{\text{Pres}}\) = 225 \({}^{\circ}\)C). Based on the obtained results, it is expected that with consequent utilization of the translation move during optimal induction heating setting, the thermal distribution within Mo sheet will satisfy the required forming performance.  
Figure 16: Comparison of the temperature distribution in the direction of the cut at the surface of the investigated molybdenum plate considering contact heating and induction heating.  
Figure 15: Experimental measurement for the optimal settings of parameters of induction heating of Mo sheet.