## 3 Results
### The Impact of Increased Water Flow Rate on Heat Output and Exergy Use  
It is important to further evaluate the validity of using high water flow rates in heating systems. Therefore, the focus in this section is to evaluate the impact of increased water flow rate on heat output and exergy use of the considered heating systems, in other words, to rate the efficiency of natural resources utilization when using high water flow rates in heating systems.  
Figure 7 illustrates the variation of the relative heat output with change of relative water flow for the analyzed space heaters. It shows that floor heating benefits most from increased water flow rate, followed by baseboard radiators, while conventional radiator benefitted the least from this increase. By increasing the water flow from 0.01 to 0.035 kg/s the heat output from the considered floor, baseboard and conventional radiator heating systems increased by 38, 28 and 25%, respectively. Figure 7 also reveals that a 50% decrease of the initial water flow rate (=0.01 kg/s) would reduce the heat output from the considered space heaters by 22 to 30%. This clearly shows that the heat output from a high-flow system is largely affected by the operational water flow. Therefore, it is very important to fine-tune high-flow systems carefully in order to maximize their thermal performance.  
Figure 8 shows the variation of exergy use per unit mass of water with temperature dropped across the considered conventional radiator. Figure 8 reveals two things. First, the largest contributor of exergy use in a radiator system is the thermostatic valves. Second, a large temperature drop over the radiator requires a high exergy use. It shows that a radiator system with a temperature drop of  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Heat Emission** & **Pipe Length** & **Supply** & **Return** & **Water Flow** & **Pump Power Need** & **COP** \\ \hline \(P_{\text{heat}}/A_{\text{hour}}\) & \(\text{l}_{\text{pipe}}/A_{\text{hour}}\) & 0\({}_{\text{empty}}\) & 0\({}_{\text{min}}\) & \(\text{m}_{\text{water}}/\text{circuit}\) & \(\text{(m}_{\text{water}}/A_{\text{hour}})\) & \(\text{P}_{\text{pump}}/\text{m}_{\text{water}}\) & \(\text{(P}_{\text{pump}}/\text{P}_{\text{heat}})\) \(\times\) & \(\text{P}_{\text{cond}}/\text{P}_{\text{pump}}\) \\  & & & & & \(\times\) 3600 & & 100 & \(\text{P}_{\text{heat}}/\text{m}^{2}\) & \(\text{W}/\text{(kg/s)}\) & \(\text{W}/\text{W}\) & \(\text{W}/\text{W}\) \\ \hline \(W/\text{m}^{2}\) & \(\text{m}/\text{m}^{2}\) & \({}^{\circ}\)C & \({}^{\circ}\)C & kg/s & \(\text{(kg/s)}/\text{m}^{2}\) & \(\text{W}/\text{(kg/s)}\) & \(\text{W}/\text{W}\) & \(\text{W}/\text{W}\) \\ \hline
29 & 3.5 & 41.0 & 27.5 & 0.01 & 1.8 & 3.2 & 5.5 x 10\({}^{3}\) & 4.1 \\
29 & 3.5 & 35.1 & 31.1 & 0.035 & 6.3 & 28 & 0.17 & 4.8 \\
29 & 3.5 & 34.8 & 32.0 & 0.05 & 9.0 & 54 & 0.47 & 4.9 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The heat emission, pump power need and heat pump efficiency (COP) of a floor heated room of 20 m\({}^{2}\) floor area. Pipe length of heating circuit was set to 70 m and pipe diameter to 13 mm. Energy need for DHW is not considered.  
Figure 7: The variation of relative heat output with change in relative water flow rate for floor, baseboard and conventional radiator heating systems. The water flows are normalized by \(\text{m}_{\text{water, ref.}}=0.01\) kg/s, and the heat outputs by corresponding output, \(\text{P}_{\text{heat, ref.}}\), at 0.01 kg/s.  
20 \({}^{\circ}\)C (low-flow system, 0.0074 kg/s per radiator) would use about 4.1 times more exergy per unit mass of water than it would use when operated with a temperature drop of 5 \({}^{\circ}\)C (high-flow system, 0.0283 kg/s per radiator). This suggests that high-flow/low-temperature systems are more exergy efficient than low-flow/high-temperature systems.