## 4 Results and Discussion
Moreover, when the part of the boiling curves that corresponds to saturated boiling (Section C-D) is taken into consideration, it is noticed that line C-D is almost parallelly shifted in the \(X\) axis (in such a manner that heat fluxes correspond to lower temperature differences with increasing distance from the inlet). It should also be added that similar courses of part of the boiling curves correspond to a single convection process (Section A-ONB). The local heat transfer coefficients on the heated wall-fluid contact were calculated from the following formula:  
\[\alpha_{2D}(x,t)=\frac{-\lambda_{H}\frac{\partial T_{H}(x,\delta_{H},t)}{ \partial y}}{T_{H}(x,\delta_{H},t)-T_{F,ref}(x,t)} \tag{16}\]  
where the temperature distributions at the fluid and foil domains were taken from the results of the numerical calculations (using Trefftz functions or ADINA software). Temperature \(T_{F,ref}(x,t)=T_{F}\Big{(}x,y_{ref},t\Big{)}\) is a reference temperature, i.e., temperature in the fluid domain at fixed line \(y=y_{ref}\). This line was selected with the assumption that temperature does not change much in the direction perpendicular to the length of the minichannel and is approximately equal to the temperature at the inlet of the minichannel. It was assumed that \(y_{ref}/L=0.25\), as in [24]. In addition, to verify the results obtained from the numerical methods, the local heat transfer coefficients in the heated wall-fluid contact were also calculated from a simple formula, based only on experimental measurements, as in [20]:  
\[\alpha_{1D}(x,t)=\frac{I(t)\Delta U(t)}{A\cdot(T_{H,IR}(x,\delta_{H},t)-T_{F, bulk}(x,t))} \tag{17}\]  
where \(A,I(t),\ \Delta U(t)\) and \(T_{H,IR}(x,\delta_{H},t)\) were defined in Section 3. Temperature distribution \(T_{F,bulk}(x,t)\) is assumed as follow:  
\[T_{F,bulk}(x,t)=\frac{x}{L}(T_{F,out}(t)-T_{F,in}(t))+T_{F,in}(t) \tag{18}\]  
Figure 5 shows the dependence between the heat flux \(q\) and the fluid velocity \(v\) (corresponding to the mass flow rate \(Q_{m}\)). Data from experimental measurements regarding the onset of boiling were taken into consideration. When analysing the relationships shown in Figure 5, with increasing mass flow rate (flow velocity), the heat flux corresponding to the boiling incipience increases. This dependence is particularly recognizable for \(Q_{m}<30\) [kg/h]. For higher values of \(Q_{m}\), this relationship runs slightly. The heat transfer coefficient versus the coordinate \(x\) along the length of the minichannel is illustrated in Figure 6. The results are based on the data from experiments performed at several values of the mass flow rate. The curves shown in Figure 6a,c present the results of FEM calculations using Trefftz functions, while Figure 6b,d are the results from numerical computation with the aid of ADINA software. It should be explained that the results illustrated in Figure 6 correspond to the selected heat flux, corresponding to the onset of boiling (the point marked ONB, indicated by the black arrows on the boiling curves shown in Figure 4). After a comparable analysis of the results presented in Figure 6, similar values and coefficient distributions were obtained from two calculation methods. When analysing the results collected at \(Q_{m}=5\)-\(25\) kg/h, the local heat transfer coefficients determined with the help of the ADINA program turned out to be higher compared to the results of the heat transfer coefficient obtained from FEMT (except the channel outlet region). It should be noted that the results gained at \(Q_{m}=10\) kg/h differ slightly compared to the results found at other mass flow values. The maximum value of the heat transfer coefficient for this mass flow rate value is reached closer to the minichannel inlet part. Furthermore, when the results are analysed at the channel inlet, it can be indicated that, for lower fluid velocities, lower values of the heat transfer coefficient were obtained, Figure 6a,b.