## 2 Experimental Methods
### Data Reduction and Uncertainty Analysis  
Figure 8a illustrates the test section setup and a representative temperature profile within the solid copper base. Figure 8b shows a schematic indicating the placement of sheathed K-type thermocouples (labeled \(T_{1}\), \(T_{1}^{\prime}\), \(T_{2}\), \(T_{3}\), and \(T_{4}\)) embedded along the central axis at different depths within the copper block to measure the temperature gradient during the pool-boiling experiments. Figure 8: Test section view: (**a**) locations where the thermocouples were inserted, (**b**) representative plot of the temperature profile along the block height. Heat flux calculation: The heat flux (\(q\)) passing through the copper block and into the test surface was calculated using Fourier's Law of heat conduction, based on the measured temperature gradient within the solid copper base, as in Equation (1). \[q=-k_{\text{Cu}}\frac{dT}{dx} \tag{3}\]  
where \(k_{\text{{C}U}}\) is the thermal conductivity of copper, and \(dT/dx\) is the temperature gradient in the direction of heat flow (axial). Temperature gradient determination: The temperature gradient along the primary heat conduction path was established by measuring temperatures at four distinct K-type thermocouple locations (\(T_{1}\), \(T_{2}\), \(T_{3}\), and \(T_{4}\)) at corresponding depths (x\({}_{1}\), x\({}_{2}\), x\({}_{3}\), and x\({}_{4}\)) (Figure 8b). A linear regression approach was used to derive the temperature gradient. The linear relationship is expressed as:  
\[T(x)=mx+b \tag{4}\]  
where \(T\) is the temperature (K), \(m\) is the temperature gradient dT/dx(K/m), \(x\) is the axial position (m), and \(b\) is the intercept. This method assumes one-dimensional, steady-state conduction, which is reasonable due to the central placement of thermocouples, minimizing the lateral conduction effects. It is worth noting that, even though we have five measurement locations, we only use four thermocouples for our calculations. The fifth point, x\({}_{1}\)', is positioned off-center. Its sole purpose is to verify that the temperature is uniform across the entire heat transfer surface. Uncertainty analysis of heat flux: An uncertainty analysis was conducted to evaluate the reliability of the calculated heat flux (q) values. The primary source of uncertainty in the heat flux calculations is directly attributed to the uncertainty in the temperature gradient \(\frac{dT}{dx}\), as \(k\) is a material property. The residuals, \(T_{i}-(ax_{i}+b)\), were then used to compute the residual sum of squares (RSS), from which the variance \(\sigma^{2}\) of the fit was obtained. The uncertainty in the slope, representing the standard error \(u_{a}\), was then calculated using the formula:  
\[u_{a}=\sqrt{\frac{\sum\left(T_{i}-(ax_{i}+b)\right)^{2}}{n-2}\frac{1}{\sum \left(x_{i}-\overline{x}_{i}\right)^{2}}} \tag{5}\]  
The uncertainty in the calculated heat flux primarily arises from the uncertainty in the slope of the temperature profile, which stems from uncertainties in the measured temperatures, the precision of thermocouple placement, and the defined distances. The associated standard uncertainty in the heat flux, \(u_{q}\), is computed as the product of the copper thermal conductivity and the standard uncertainty of the slope. \[u_{q}=k\cdot u_{a} \tag{6}\]  
Wall superheat determination: The temperature at the heating surface (\(T_{wall}\)) was determined by extrapolating the linear temperature profile measured by the embedded thermocouples to the position of the boiling surface (\(x=0\)) to the position of the boiling surface (\(x=0\)). The wall superheat (\(\Delta T\)) was then calculated as the difference between the extrapolated wall temperature and the measured saturation temperature of the fluid, as shown in Equation (4):  
\[\Delta T=T_{wall}-T_{Sat} \tag{7}\]  
The saturation temperature corresponds to the temperature at which the saturation pressure is measured using a pressure gauge.