## 3 Experimental Methodology
Since tin solder has a different thermal conductivity than the copper material of the heat exchanger, a compensation for this effect was necessary. The adjusted temperature difference (\(\Delta T_{s}\)) that the sensor could measure was calculated according to Equation (6). In this equation, (\(K_{s}\)) represents the thermal conductivity of the tin solder, (\(L_{s}\)) denotes the thickness of the tin solder, (\(A\)) is the area, and (\(Q\)) is the heat transfer. Although the effect of this discrepancy was minimal, it was nonetheless compensated for in our measurements. \[\Delta T_{s}=\frac{Q}{A}\times\frac{L_{s}}{K_{s}} \tag{6}\]  
The \(G_{TR}\) was determined by subtracting the fluid temperature from the highest temperature of the mini heat exchanger, which is the outer wall temperature (\(T_{1}\)) and then dividing the result by the heat (\(Q\)), which is equal to (\(HER\)) [10; 36] as shown in Equation (7). \[G_{TR}=\frac{T_{1}-T_{\infty}}{Q} \tag{7}\]  
The thermal circuit is used to calculate \(G_{TR}\), which is determined using Equation (8). This equation accounts for the resulting global thermal resistance from both the solid copper wall of the heat exchanger and the resistance of the fluid. As expected, the result obtained was consistent with the outcome from Equation (7). \[G_{TR}=\frac{T_{1}-T_{s}}{Q}+\frac{1}{A\cdot h} \tag{8}\]  
The hydraulic diameter (\(D_{h}\)) is determined by first calculating the cross-sectional area (\(A_{S}\)), multiplying that area by 4, and dividing the result by the wetted perimeter (\(P\)). This process is expressed in Equation (9) and illustrated in \[K\frac{\partial^{2}T}{\partial^{2}y}=0 \tag{1}\]0 The hydraulic diameter is the characteristic length of the geometry [38], which is essential for calculating the Reynolds number. This calculation helps to identify whether the fluid flow regime is laminar with a Reynolds number below 2100, as is the case in this study, transient with a Reynolds number above 2100 and below 4000, or turbulent with a Reynolds number above 4000. The hydraulic diameter was determinate based on Equation 9, as found in the literature [28; 39]. \[K\frac{\partial^{2}T}{\partial^{2}y}=0 \tag{1}\]1To facilitate the study of minichannel heat exchangers and assess the scale effect, [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) developed criteria for categorizing minichannels based on their hydraulic diameter (\(D_{h}\)). The classifications are as follows:  
* Transitional channel: 0.1 \(\upmu\)m \(<D_{h}\) \(<\) 10 \(\upmu\)m;
* Microchannel: 10 \(\upmu\)m \(<D_{h}\) \(<\) 200 \(\upmu\)m;
* Minichannel: 200 \(\upmu\)m \(<D_{h}\) \(<\) 3 mm;
* Conventional channel: \(D_{h}\) \(>\) 3 mm. The heat exchanger examined in this study falls into the minichannel category, with a hydraulic diameter of 832 \(\upmu\)m.  
In Figure 6, a cross-section of the heat exchanger is illustrated. The blue area represents the cross-sectional area through which the fluid flows, denoted as \(A_{S}\), and is used to calculate the hydraulic diameter. The solid copper section of the heat exchanger is depicted in orange. The fluid in blue is enclosed by the remainder of the heat exchanger, which is constructed from acrylic. The portion of the cross-sectional area where the fluid comes into contact is referred to as the wetted perimeter (\(P\)). The Reynolds number is calculated by multiplying the density of the fluid (\(\rho\)), velocity (\(V\)), and characteristic length of the geometry (\(D_{h}\)), in this case, the hydraulic diameter. This product is then divided by dynamic viscosity (\(\mu\)), as shown in Equation (10). \[K\frac{\partial^{2}T}{\partial^{2}y}=0 \tag{1}\]2  
In the experiment, the velocity used to calculate the Reynolds number was derived from the volumetric flow rate and the cross-sectional area. The dynamic viscosity applied in the calculations was determined based on the average temperature and pressure of the fluid, whereas the density was dependent on the average temperature of the fluid.