# Heat and Flow Study of the Internally Finned Tubes with Different Fin Geometries
## 3 Results and Discussion
### Parametric Analysis for the Reference Case  
The first part of the results section regards the presentation of the results about the reference cases which correspond to the empty tube without internal fins. The results are given for different combinations of the fluid inlet temperature from 290 K up to 360 K, and of mass flow rates from 0.20 kg/s up to 0.35 kg/s. Figure 7 shows the variation of the Nusselt number for the different examined scenarios. Higher fluid temperature and higher mass flow rate lead to higher values of the Nusselt number. The Nusselt number ranges from 112 to 251 for all the studied cases. Moreover, Figure 8 indicates that the fluid heat transfer coefficient has similar behavior to the Nusselt number. More specifically, the heat transfer coefficient increases with the increase of both inlet fluid temperature and mass flow rate. Moreover, the heat convection coefficient ranges from 3761 to 8471 W/m\({}^{2}\)K for all the studied scenarios. The next part of the investigation rewards the fluid energy loss during the movements in the tube. Figure 9 shows the variation of the friction factor with the variation of the independent parameters. It is obvious that the increase in the fluid temperature and the mass flow rate leads to a lower friction factor. However, the reduction of the friction factor is not high and generally, the friction factor takes values in the range from 0.019 to 0.027. Figure 10 illustrates the pressure drop for the different cases. Interestingly, the pressure drop increases with the increase of the mass flow rate, while it reduces with the increase of the fluid temperature. It was found that the pressure drop ranges from 445 to 1455 Pa, so there is an important variation in the pressure drop among the examined cases. Figure 7: Nusselt number variation for the different operating scenarios in the reference case of the empty tube. Figure 8: Heat transfer coefficient variation for the different operating scenarios in the reference case of the empty tube. Figure 9: Friction factor variation for the different operating scenarios in the reference case of the empty tube. Figure 11 depicts the pumping work demand which takes generally low values compared to the heat input of 6281 W. The pumping work ranges from 0.09 W to 0.51 W. The pumping work demand is directly associated with the pressure drop, and thus it takes lower values when the temperature increases. Figure 11: Pumping work demands variation for the different operating scenarios in the reference case of the empty tube. Figure 10: Pressure drop variation for the different operating scenarios in the reference case of the empty tube. The Bejan number is an important index, which is depicted in Figure 12. This criterion is defined as the ratio of the generated entropy due to the fluid temperature increase to the total generated entropy. It has to be said that the total generated entropy includes the entropy generation due to both temperature increase and pressure drop. According to Figure 12, the Bejan number takes high values (over 99%), which indicates that the main reason for the entropy generation is the fluid temperature increase. Therefore, the application of thermal enhancement methods, such as the use of internal fins, is needed in order to enhance the heat transfer conditions and reduce the total entropy generation. It is notable to state that the Bejan number reduces a bit with the increase of the mass flow rate due to the higher pressure drop in these cases. Moreover, it has a very small decrease with the increase in the fluid's temperature. This criterion is an important one in order to evaluate the impact of the pressure drop on heat transfer problems. The mean wall temperature is an important parameter which is depicted in Figure 13. This temperature level increases approximately linearly with the increase of the inlet fluid temperature. Moreover, it takes higher values when the fluid moves with a lower velocity, which means a lower mass flow rate.