## 3 Results
### Effect of the Cooling Water Temperature
Figure 10: Distribution of the Nu\({}_{\rm t}\) in the heat exchanger at Re\({}_{\rm in}\approx\) 9500 and at different cooling water inlet temperatures. The temperature distribution results for higher \(\rm Re_{in}\) numbers are presented in Figure 12. The results (Figure 12a) are similar to the already discussed earlier (Figure 5b). The only difference is a little higher tube wall and cooling water temperatures for a higher inlet flue gas temperature as compared to a lower cooling water inlet temperature (Figure 5b). Some changes along the tube were determined in the \(\rm Nu_{t}\) (Figure 13). When the cooling water inlet temperature was lower, the \(\rm Nu_{t}\) remained almost constant along the tube, while at a higher water inlet temperature at the beginning of the tube, the \(\rm Nu_{t}\) was smaller (\(\rm Nu_{t}\approx 175\)). But it was constantly increasing until \(\rm x/d\approx 90\), where in the \(\rm x/d\) range \(\approx\)90-130 it reached almost the same value as at a lower cooling water inlet temperature. Then, a slight decrease in \(\rm Nu_{t}\) was noticed for both cases. However, at a lower water inlet temperature, the \(\rm Nu_{t}\) stabilized, while at a higher temperature, the \(\rm Nu_{t}\) was decreasing constantly. The distribution of the \(\rm Nu_{t}\) at higher water inlet temperatures indicates that the condensation process is not even along the tube, yet it has expressed minimums and maximums. The condensation efficiencies determined in the analyzed case were similar: 42% and 39%. Higher efficiency was obtained at a lower cooling water inlet temperature. Figure 12: Temperature distribution in heat exchanger at \(\rm Re_{in}\approx\) 21,000, flue gas temperatures (a) \(\rm t_{in}\approx 102~{}^{\circ}C\), (b) \(\rm t_{in}\approx 132~{}^{\circ}C\), and similar cooling water inlet temperatures: (1) center of the tube, (2) the inner wall of the tube, (3) cooling water, (4) the dew point temperature. Figure 13: Distribution of the \(\rm Nu_{t}\) in the heat exchanger at \(\rm Re_{in}\approx\) 21,000, the same flue gas inlet temperature, cooling water flow rate, and cooling water inlet temperatures. The temperature distribution results presented in Figure 12b are also typical: the blue gas temperature decreases constantly, the water temperature increases, the characteristics of the tube wall and cooling water temperatures are similar (c.f. Figure 5d). Temperature differences between the flue gas, tube wall, and cooling water are slightly smaller at a higher cooling water inlet temperature (Figure 12b). Smaller temperature differences have a certain impact on heat transfer and therefore change the distribution of the \(\mathrm{Nu_{t}}\) along the tube (Figure 14). The comparison of the \(\mathrm{Nu_{t}}\) for different water inlet temperatures shows that in the initial part of the tube, at the water inlet temperature of \(\approx\)8 \({}^{\circ}\)C, the \(\mathrm{Nu_{t}}\) is larger than at \(\mathrm{t_{\text{cw-in}}}\approx 15\)\({}^{\circ}\)C. When \(\mathrm{t_{\text{cw-in}}}\approx 8\)\({}^{\circ}\)C, \(\mathrm{Nu_{t}}\) increases slightly along the tube up to \(\mathrm{x/d}\approx 110\), where it reaches a maximum value of \(\approx\)220 and then starts decreasing. For the case of the cooling water inlet temperature of \(\approx\)15 \({}^{\circ}\)C, the variation of the \(\mathrm{Nu_{t}}\) along the tube is more expressed. From the inlet, the \(\mathrm{Nu_{t}}\) increases intensively up to \(\mathrm{x/d}\approx 100\)-110, where the \(\mathrm{Nu_{t}}\) is \(\approx\)260. After that, the \(\mathrm{Nu_{t}}\) starts decreasing with even greater intensity until the end of the tube and reaches almost the same value as in the beginning of the tube (\(\mathrm{Nu_{t}}\approx 115\)). The difference between the condensation efficiencies in this case was about 9%, i.e., \(\approx\)42% and \(\approx\)31% for the lower and higher cooling water inlet temperatures, respectively.