## 3 Experimental Methodology  
The mini heat exchanger and the temperature and pressure measuring sockets were effectively thermally insulated using ceramic fiber, elastomeric rubber, and aluminum foil. This thermal insulation ensured that heat Q flowed in a unidirectional manner from the electrical resistance to the heat exchanger. Figure 5 shows the setup for unidirectional heat transfer [34; 35; 36]. To model heat transfer in the mini heat exchanger, several assumptions were made [34; 35; 36]:  
* Energy balance based on the first law of thermodynamics;
* One-dimensional heat conduction;
* Constant properties, such as thermal conductivity;
* Negligible thermal radiation;
* Negligible heat loss; \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Value** \\ \hline The Uncertainty in the Electrical Resistance Power at 30 W & \(\pm\)0.42 W \\ \hline The Uncertainty in the Electrical Resistance Power at 65 W & \(\pm\)0.75 W \\ \hline Global Thermal Resistance Uncertainty [\({}^{\circ}\)C\(\cdot\)W\({}^{-1}\)] & \(\pm\) 3.00\% \\ \hline Uncertainty of the Coefficient Heat Transfer [W\(\cdot\)m\({}^{-2}\)\({}^{\circ}\)C\({}^{-1}\)] & \(\pm\)5.00\% \\ \hline Flow Rate Uncertainty [L/min] & \(\pm\)5.00\% \\ \hline Ambient Temperature Uncertainty & \(\pm\)0.50 \({}^{\circ}\)C \\ \hline Pressure Uncertainty & \(\pm\)3.50 kPa \\ \hline Water Temperature Uncertainty & \(\pm\)0.20 \({}^{\circ}\)C \\ \hline Uncertainty in the Temperature of the Heat Exchanger Wall & \(\pm\)0.50 \({}^{\circ}\)C \\ \hline Uncertainty in Relative Humidity & \(\pm\)2.00\% \\ \hline Reynolds number uncertainty & \(\pm\)9.00\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental uncertainties. * No internal heat generation;
* A uniform convection coefficient;
* Steady-state conditions;
* Fluid incompressible and Newtonian;
* No-slip condition. These factors simplify the analysis of the heat exchanger's performance. Fourier's Law has been applied to assess heat transfer through conduction in the electrical resistance that is in contact with the copper surface of the mini heat exchanger. In one dimension, [PERSON] et al. [28] describe the heat transfer scenario using Equation (1) considering the simplifications that have been assumed:  
\[K\frac{\partial^{2}T}{\partial^{2}y}=0 \tag{1}\]  
According to the first law of thermodynamics and the simplification of the heat equation [20,22], the heat transferred by electrical resistance (\(HER\)) is described by Equation (2), which is conducted to the heat exchanger. This heat then passes through the wall and exits via convection, as explained in Equation (3), inside the mini heat exchanger, which is cooled with water. The fluid in contact with the wall has zero velocity, and heat transfers through conduction before exiting the heat exchanger via convection. The heat transferred by the electrical resistance equaled the electrical power supplied [35], which was monitored every second by the DPS 5020 power supply; however, data were only used from the steady state. \[HER=-KA\left.\frac{dT}{dy}\right|_{y=0} \tag{2}\]  
\[-KA\left.\frac{dT}{dy}\right|_{y=0}=hA(T_{S}-T_{\infty}) \tag{3}\]  
Figure 5: Thermally insulated mini heat exchanger. By applying the conservation of energy and rearranging Equation (3), the average convective heat transfer coefficient (\(h\)) can be determined using Equation (4) [28; 36; 37]. \[h=\frac{-K\frac{dT}{dy}\Big{|}_{y=0}}{(T_{S}-T_{\infty})} \tag{4}\]  
For internal flow, the fluid temperature is determined by averaging the inlet and outlet temperatures. Since the difference between these temperatures is small, this average temperature was used to calculate properties such as specific heat, viscosity, density, and thermal conductivity. The water temperature (\(T_{\infty}\)) for these calculations is provided by Equation (5). \[T_{\infty}=\frac{T_{in}+T_{out}}{2} \tag{5}\]  
The inner wall temperature (\(T_{s}\)) in contact with the water was measured using type-K thermocouples, which were fixed in place with tin solder.