# Interferometric Study of the Heat Transfer Phenomena Induced by Rapid Heating of Nickel Sheet
## 3 Results and Discussion
However, in order to observe visual outputs such as shock waves, it is necessary that the maximum temperature be reached within 0.015-0.023 s.  
The displacements of finite fringes are shown in Figure 5. Finite fringes were set perpendicularly on the upper part of the \(\delta=0.0075\) mm thick nickel sheet. The heating conditions were the same as in Figure 4. The heating phenomena were observed before 0.001-0.002 s for the heating conditions. At about 0.01 s, a cutting line that interrupted the finite fringes could be observed near the upper part of the nickel sheet, but it was extinguished immediately. This displacement was dependent on the surface temperature of the sheet, and it plays a leading part in understanding the characteristics of the heat transfer of the fluid near the metal sheet. Before 0.015 s, it was difficult to distinguish the critical point of the displacements. As time proceeded, however, the critical point could be observed. It could be distinguished with the naked eye that these local displacements varied according to the discharging energy. The displacement lines formed at the beginning of heating were disturbed at a certain time. The occurrence of these disturbance phenomena is considered as a critical point from which the natural convection originates, like in Figure 4.  
The local Nusselt number can be obtained in order to estimate the heat transfer characteristics in the heating wall by measuring local values of the interval between the order of interference (\(S_{w}\)) and the finite pattern, using the following equations:  
\[Nu_{H}=-\frac{H}{(T_{w}-T_{\infty})}\frac{1}{dn/dT}\frac{\lambda}{l_{z}}\frac{ \partial\Delta x}{\partial y}\bigg{)}_{w} \tag{1}\]  
\[\frac{dn}{dT}=-\frac{\lambda}{l_{z}}\cdot\frac{S_{w}}{(T_{w}-T_{\infty})} \tag{2}\]  
where \(H\) is the local height, and \(T_{w}\) and \(T_{\infty}\) are the wall temperature and the surround temperature, respectively. \(\lambda\) denotes the wavelength of the He-Ne laser source, which is 632.8 nm, and l\({}_{z}\) is the measured specimen length along the direction of light. The modified position and spacing of the patterns can be determined by measuring the pixel coordinates, as shown in Figure 6. The relevant values can be converted into actual dimensions or positions using Equation (3):  
\[h^{\prime}=\frac{y^{\prime}}{y}h \tag{3}\]  
The variations of the local Nusselt numbers for different nickel sheet thicknesses and heating energies are shown in Figures 7-9. As the thickness of the testing sheet increased, the total heat capacity increased accordingly. Therefore, a high charging voltage must be applied to ensure the temperature of the shock wave on the plate. The local Nusselt number distributions for the case of rapidly heated \(\delta=0.0125\) mm nickel sheet are shown in Figure 3:0 It was difficult to distinguish the exact deformed location in the finite patterns obtained until 0.015 s. This difficulty was caused by the natural convection generated due to buoyancy effects, which resulted from the relatively long time of 0.35 s to reach the maximum temperature, unlike with the initial expansion and compression and heat transfer by conduction. The local Nusselt number was decreased by increasing the charging voltage, indicating a dependence on the discharge energy. Figure 3:1 Temporal variations of interferogram with nickel sheet (finite fringe, \(\delta=0.0075\) mm). (**a**) 17 V, (**b**) 19 V, (**c**) 21 V.  
Figure 3:2 The methodology for the calculation of local position of fringe. (**a**) Reference, (**b**) Real state. Figure 3:3 Variation in local Nusselt numbers for different heating energies with nickel sheet (\(\delta\) = 0.0100 mm). Figure 3:4 Variations in local Nusselt numbers for different heating energies with nickel sheet (\(\delta\) = 0.0125 mm). Figure 3:5 Variation in local Nusselt numbers for different heating energies with nickel sheet (\(\delta\) = 0.0075 mm).