## 2 Materials and Methods
### Data Processing  
Aluminum silicate fiber wool is installed around the heating block to isolate the heating block from the external thermal environment, so the heat transfer from the side of the heating block can be ignored and the temperature change inside the heating block follows the one-dimensional thermal conductivity law. The heat flux at the surface of the simulated heat source can be obtained from [PERSON]'s one-dimensional thermal conductivity law as shown in Equation (1).  
\[q=-\lambda\frac{\Delta T}{\Delta y}, \tag{1}\]  
where \(q\) is the heat flux of the simulated heat source surface, W/cm\({}^{2}\), \(\lambda\) is the thermal conductivity of copper, W/(cm\(\cdot\)K), and \(\frac{\Delta T}{\Delta y}\) is the temperature distribution gradient in the axial direction of the heating block.  
Linear fitting of the temperature data from the four thermocouples yields the Equation (2)  
\[T(y)=a+by, \tag{2}\]  
The surface temperature of the heat source as shown in Equation (3).  
\[T_{\rm W}=T_{1}+by_{1}, \tag{3}\]  
where \(T_{\rm W}\) is the temperature at the surface of the simulated heat source, \({}^{\circ}\)C, \(T_{1}\) is the temperature measured by thermocouple K\({}_{1}\), \({}^{\circ}\)C, and \(y_{1}\) is the distance between thermocouple K\({}_{1}\) and the surface of the heat source, mm.  
Figure 2: Schematic diagram of the vertical arrangement of thermocouples.  
Figure 3 shows the linear fit analysis of one set of experimental data, and it can be seen that the data points are in good agreement with the fitted line, so the fitting results are reliable.  
The heat transfer coefficient on the simulated surface of the heat source is shown in Equation (4)  
\[h=\frac{q}{T_{W}-T_{in}}, \tag{4}\]  
where \(h\) is the surface heat transfer coefficient, W/(cm\({}^{2}\cdot\)K), \(T_{in}\) is the nozzle inlet temperature of the cooling medium, \({}^{\circ}\)C.  
A criterion-dependent correlation fit is performed at the spray impact point, and the temperature of the calculated fluid parameters depends on the average of the heated surface temperature and the medium temperature:  
\[T=\frac{T_{W}+T_{in}}{2}, \tag{5}\]  
The thermal conductivity of the mixed fluid is  
\[\lambda_{m}=\varphi_{1}\lambda_{1}+\varphi_{2}\lambda_{2}-(\lambda_{2}-\lambda _{1})(1-\varphi_{2}{}^{0.5})\varphi_{2}, \tag{6}\]  
where \(\varphi_{i}\) is the mass concentration of each component, \(\lambda_{i}\) is the thermal conductivity of each component, W/(m\(\cdot\)K).  
The dynamic viscosity of the mixed fluid is  
\[\mu_{m}=(\sum_{i=1}^{n}\varphi_{i}\mu_{i}{}^{3})^{3}, \tag{7}\]  
where \(\mu_{i}\) is the dynamic viscosity of each component, Pa\(\cdot\)s.  
The density of the mixed fluid is  
\[\rho_{m}=\rho_{1}\varphi_{1}+\rho_{2}\varphi_{2}, \tag{8}\]  
where \(\rho_{i}\) is the density of each component, kg/m\({}^{3}\).  
The specific heat at constant pressure of the mixed fluid is  
\[c_{pm}=\frac{c_{p1}\varphi_{1}\rho_{1}+c_{p2}\varphi_{2}\rho_{2}}{\rho_{m}}, \tag{9}\]  
where \(Cp_{i}\) is the constant pressure specific heat of each component, J/kg\(\cdot\)K.  
Re is calculated using the equation related to mass flux:  
\[\text{Re}=\frac{GD}{\mu}, \tag{10}\]  
Figure 3: Schematic of the linear fit of the longitudinal temperature.  
where \(D\) is the spray coverage diameter, m, \(\mu\) is the medium dynamic viscosity, Pa-s, \(G\) is the mass flux of cooling medium, kg/(s\(\cdot\)m\({}^{2}\)).  
The mass flux \(G\) is calculated by the equation:  
\[G=\frac{G_{m}}{A}, \tag{11}\]  
where \(G_{m}\) is the mass flow rate of the medium, kg/s, \(A\) is the area covered by the spray, m\({}^{2}\).  
Nusselt number is:  
\[Nu=\frac{hD}{\lambda}, \tag{12}\]  
where \(h\) is the surface heat transfer coefficient, W/(m\({}^{2}\cdot\)K), \(D\) is the spray coverage diameter, m, \(\lambda\) is the thermal conductivity, W/(m\(\cdot\)K).  
Prandtl number is:  
\[\Pr=\frac{\mu c_{p}}{\lambda}, \tag{13}\]  
where \(\mu\) is the medium dynamic viscosity, Pa-s, \(C_{Pi}\) is the constant pressure specific heat of each component, J/(kg\(\cdot\)K).