# Interferometric Study of the Heat Transfer Phenomena Induced by Rapid Heating of Nickel Sheet
## 3 Results and Discussion  
Experiments were performed to confirm the generation and propagation of the thermo-acoustic waves from a nickel sheet in an R-C rapid heating circuit. Figure 3 shows the trial process to find the testing sheet temperature and thickness of it, generating the Mach number (\(Ma\)) with various charging voltages. This confirmed that the Mach number had the value of 0.99, which comes close to the value of 1, as in the case of \(\mathrm{E_{c}=19}\) V [31]. We performed the experimental works to confirm the effects of charging voltages based on the value of charging voltage at 19 V. Figure 3a shows the thickness effects of the specimen with various values of temperature, as in the case of continuously discharging energy by a 68,000 \(\upmu\)F capacitor with a charging voltage of \(\mathrm{E_{c}=21}\) V. For the specimen thicknesses of \(\mathrm{\delta=0.0125\ mm}\) and \(\mathrm{\delta=0.01\ mm}\), the maximum temperature values were obtained as 142 \({}^{\circ}\)C and 185 \({}^{\circ}\)C, with acquisition times of 0.35 s and 0.065 s, respectively. The effects of the discharging energy on the temperature distribution of the specimen with \(\delta\) = 0.0075 mm thickness are shown in Figure 3b. The maximum temperature values were found to be about 257 \({}^{\circ}\)C, 362 \({}^{\circ}\)C, and 475 \({}^{\circ}\)C when the discharging voltages of the capacitor were E\({}_{\text{d}}\) = 16 V, 19 V, and 21 V, respectively [31]. Infinite fringes of the interference phenomena in the upper part of a heating surface of the nickel sheet are shown in Figure 4. A Mach-Zehnder interferometer and high-speed digital camera were used to visualize the interference phenomena. In order to elucidate the effects of charging energies, the charging voltages of the capacity were set to E\({}_{\text{c}}\) = 17 V, 19 V, and 21 V, in order to check the interference phenomena with various charging energies based on the value of \(Ma\) = 1. The maximum temperatures of 296 \({}^{\circ}\)C, 378 \({}^{\circ}\)C, and 480 \({}^{\circ}\)C, corresponding to each discharging voltage, respectively, were reached in about 0.05 s.  
Figure 3: Temperature variation of nickel sheet with C = 68,000 \(\upmu\)F [31]. (**a**) Thickness effect with 21 V, (**b**) Voltage effect with \(\delta\) = 0.0075 mm. At the beginning of heating, conduction or radiation heat transfer were expected from the rapid heating and cooling of fluid, which makes contact with the heated wall. It was verified from the results that the distance between the isothermal line and the nickel sheet was shorter than 0.5 mm. Then, the distance between them gradually increased because of the expansion of the fluid. The cutting line of the infinite fringes appeared at 0.01 s and then disappeared after about 0.001 s. This is because the thermo-acoustic wave generated by the fluid heating source dissipated. Therefore, the heating energy and time required to reach the maximum temperature are important factors in the generation of thermally powerful acoustic waves. For generating the thermo-acoustic waves, rapid heating  
Figure 4: Temporal variations of interferogram with nickel sheet (infinite fringe, \(\delta=0.0075\) mm). (a) 17 V, (b) 19 V, (c) 21 V.  
should be supplied within 0.01-0.03 s, and sufficient energy is needed to grow and propagate the thermo-acoustic waves. The isothermal lines that occurred at the beginning of heating are disturbed at a certain time. Figure 4c shows that the largest heating energy occurs at about 0.008 s. In Figure 4a,b, the largest heating energy occurs at about 0.12-0.14 s and 0.1 s, respectively. The occurrence of these disturbance phenomena is considered a critical point from which the natural convection originates. The critical point of the nickel sheet is shortened by about two times relative to that of a stainless steel sheet, despite having a five to eight times lower heating energy.