## 4 Results and Discussion
Furthermore, the distribution of the relative differences between the heat transfer coefficient, determined according to two  
Figure 4:7 The distribution of the heater temperature versus coordinate \(x\) and time, based on infrared thermography measurement, performed on the outer foil surface, mass flow rate: (**a**) \(Q_{m}=5\)\(\left[\text{kg}/\text{h}\right]\); (**b**) \(Q_{m}=10\)\(\left[\text{kg}/\text{h}\right]\); (**c**) \(Q_{m}=15\)\(\left[\text{kg}/\text{h}\right]\); (**d**) \(Q_{m}=20\)\(\left[\text{kg}/\text{h}\right]\); (**e**) \(Q_{m}=25\)\(\left[\text{kg}/\text{h}\right]\); (**f**) \(Q_{m}=30\)\(\left[\text{kg}/\text{h}\right]\); (**g**) \(Q_{m}=40\)\(\left[\text{kg}/\text{h}\right]\); (**i**) \(Q_{m}=45\)\(\left[\text{kg}/\text{h}\right]\); (**j**) \(Q_{m}=50\)\(\left[\text{kg}/\text{h}\right]\); (**k**) \(Q_{m}=55\)\(\left[\text{kg}/\text{h}\right]\), \(\text{INA}\) software. calculation methods (ADINA and FEMT) for the selected mass flow rate (\(Q_{m}=55\) [kg/h]), is presented in Figure 10h. When analysing the dependence of the heat transfer coefficient versus coordinate \(x\) and time presented in Figure 10, it can be seen that after about 60 s there was a sudden increase in heat flux (see Figure 4l), which corresponds to a stepwise increase in the heat transfer coefficient. Generally, similar distributions of the local heat transfer coefficient were achieved. Furthermore, there is good agreement between the heat transfer coefficients, determined with the help of ADINA software, and based on the FEMT calculation using Trefftz functions, Figure 10c,f,i. It can also be noticed that a high level of relative differences is reached between the results of the numerical calculations in small regions of the \(t\) and \(x\) variation domain, but in the rest of this domain, the relative differences are low. Therefore, even though there is a high maximum of relative differences, their average values appeared to be low. For the lowest mass flow rate, significantly higher relative differences were  
Figure 4:8 The distribution of the heat transfer coefficient versus coordinate \(x\) and time \(t\) obtained using ADINA software (**a,d,g**) and FEMT with applying Trefftz functions (**b,e,f**); the relative differences between local heat transfer coefficients as the results of calculations according to these two methods (ADINA and FEMT). The calculations performed on the basis of the results of experiments were performed at three values of mass flow rate: (**a–c**) \(Q_{m}=5\) [kg/h]; (**d–f**) \(Q_{m}=30\) [kg/h]; (**g–i**) \(Q_{m}=55\) [kg/h]. achieved up to 80%, Figure 10c, compared to the results obtained for higher mass flow rates, Figure 10f,i. It can be emphasized that, during experiments, the heat flux increases over time (the experimental methodology is described in Section 'Experimental background'), while the example dependence of the heat flux, as a function of time for the entire experiment, is given in Figure 4l, for \(Q_{m}=55\ [\mathrm{kg/h}]\). It can be observed that maximum relative differences between heat transfer coefficients, according to both calculation methods, occur when there is a sharp increase in the heat flux. In Figure 11 are shown the average values of relative differences of the heat transfer coefficient, obtained from calculations performed using different calculation methods (ADINA software, FEMT using Trefftz functions and the 1D approach), as a function of the mass flow rate. When analysing the graph, it can be found that, with an increase in mass flow rate, the mean relative differences decrease. It should be underlined that for \(Q_{m}>15\ [\mathrm{kg/h}]\), the relative differences are below 10%. The highest relative differences occurred for the lowest mass flow rate, especially \(Q_{m}=10\ [\mathrm{kg/h}]\) and when FEMT versus 1D method or ADINA versus FEMT were considered (value of relative differences greater than 40%).