## 4 Results and Discussion
In addition, the heat transfer coefficient increases with distance from the minichannel and is reached to the maximum at the outlet. However, for higher mass flow rates, Figure 6c,d, higher coefficient values were obtained at the inlet compared to those collected at lower mass flow rates. Furthermore, the heat transfer coefficient decreases with increasing distance, at distances up to 3/4 minichannel length (starting from the inlet). The minimum values of the heat transfer coefficient are located near the middle of the minichannel. When the inlet area of the channel is analysed, with increasing fluid velocities, a decrease of the heat transfer coefficient is observed. Furthermore, at the outlet, similar coefficient values were obtained, comparing the results is illustrated in Figure 6a,b and Figure 6c,d. Figure 5: Heat flux versus fluid velocity \(v\) and mass flow rate \(Q_{m}\), data from all chosen experiments, corresponding to ONB points are marked on boiling curves, indicated by black arrows in Figure 4.  
In order to emphasize the comparison of the distributions of the heat transfer coefficient, the coefficient versus the coordinate \(x\) along the length of the minichannel is shown in Figure 7a,c,e. The graphs present the results determined from ADINA software (green curves), with the help of Trefftz functions (blue curves) and additionally according to the 1D mathematical method of calculations (red curves). The distributions of the heat transfer coefficient were captured for three selected mass flow rates (\(5\) [kg/h], \(30\) [kg/h] and \(55\) [kg/h]). Furthermore, in Figure 7b,d,f, the relative differences between the results of the heat transfer coefficient are highlighted. The relative difference between the heat transfer coefficients named \(\alpha_{1}\) and \(\alpha_{2}\) as the results of using two selected calculation methods (considering three methods described above) was estimated from the following formula:  
\[rd(x,t)=\frac{|\alpha_{1}(x,t)-\alpha_{2}(x,t)|}{\min\{\alpha_{1}(x,t),\alpha_ {2}(x,t)\}}\cdot 100\% \tag{19}\]  
Figure 4:0 The heat transfer coefficient versus coordinate \(x\) along the length of the minichannel determined using Trefftz functions and with the aid of ADINA software, the results obtained for several values of mass flow rate \(Q_{m}\): (**a,b**) \(5\) [kg/h], \(10\) [kg/h], \(15\) [kg/h], \(20\) [kg/h] and \(25\) [kg/h] and (**c,d**) \(30\) [kg/h], \(35\) [kg/h], \(40\) [kg/h], \(45\) [kg/h], \(50\) [kg/h] and \(55\) [kg/h]. The data corresponding to ONB points are indicated by black arrows in Figure 4:1  
The results presented in Figure 7 confirm the previous comments concerning the exposed dependencies. At lower mass fluxes, the heat transfer coefficient increased in the outlet part of the channel. Furthermore, the minimum values of the coefficient are recognizable in the middle part of the channel for the average mass flow rates. However: (i) at the highest flow rates, the highest heat transfer coefficient is detected at the inlet, (ii) at the medium flow rates, higher values of the transfer coefficient are observed in the middle part of the channel, and (iii) at the highest flow rates, the highest heat transfer coefficient is observed near the inlet and higher in the middle of the channel, compared to small and average \(Q_{m}\). In addition, for low mass flow rates, Figure 7a,b, greater discrepancies (up to 70%) are found when analysing the results compared to the results collected at higher mass flow rates, Figure 7c,d,e, for which differences reached a dozen or so per cent. The lowest values of relative differences are obtained for the highest \(Q_{m}\). Generally, for the lowest and the highest values of \(Q_{m}\), the lowest relative differences \(rd\) between the results for FEMT and FEMT are also observed.