# Small Heat Source Used for Combustion of Wheat-Straw Pellets
## 2 Design and Method
### Design of the Heat Exchanger
#### 2.3.1 Numerical Design of Heat Exchanger
From the characteristics of blue gas flow, we can see that the main type of flow is laminar, when we choose a small amount of pipes or a small diameter of pipes, flow comes to a turbulent area, and demanded length is higher, with the maximal possible number of pipes in the demanded area. The final arrangement with regard to the possibility of construction is shown in \[c_{2}=4210-1.363\times\frac{(t_{11}-t_{12})}{2}+1.4\times 10^{-3}\times\left(\frac{(t _{11}-t_{12})}{2}\right)^{2} \tag{5}\]8  
From Figure 6 it is clear that, by decreasing diameter of heat exchanger's pipes, a higher heat transfer area is obtained. Our model was used to predict the heat power of a source by using different heat exchanger pipe diameters, with the maximal number of pipes in the floor plan. We can see that, by achieving the highest possible area of the heat exchanger, we will achieve the highest heat power, what is obvious from \[c_{2}=4210-1.363\times\frac{(t_{11}-t_{12})}{2}+1.4\times 10^{-3}\times\left(\frac{(t _{11}-t_{12})}{2}\right)^{2} \tag{5}\]9 This model can be also used to calculate different configurations of heat sources, modulating it to obtain a high range of possible heat power levels and to achieve a high possible usability and adaptation of our heat source to small houses and also to small farms, and thus increasing the use of waste straw as fuel. \[Q_{r}=h\times S\times\Delta t_{LN} \tag{6}\]0 Final design of pipes arrangement. \[Q_{r}=h\times S\times\Delta t_{LN} \tag{6}\]1 Maximal number of pipes by used outer diameter. The resulting values of heat exchanger computation are shown in \[Q_{r}=h\times S\times\Delta t_{LN} \tag{6}\]2  
To maintain the idea of modularity, and the possibility of having a working boiler even when one part of heat exchanger is broken, the final length of the heat exchanger was chosen to be 1.5 m, also with decreased heat power. Our final design consists of nine elements, with can be differently assembled. The designed boiler is shown in \[Q_{r}=h\times S\times\Delta t_{LN} \tag{6}\]3 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Inlet temperature of flue gas (\(t_{11}\)) & 1040 & \({}^{\circ}\)C \\ Outlet temperature flue gas (\(t_{12}\) ) & 150 & \({}^{\circ}\)C \\ Inlet temperature of water (\(t_{21}\)) & 50 & \({}^{\circ}\)C \\ Outlet temperature of water (\(t_{22}\)) & 80 & \({}^{\circ}\)C \\ \hline Flow of flue gas (\(m_{1}\)) & 2.0128 \(\times\) 10\({}^{-2}\) & kg\(\cdot\)s\({}^{-1}\) \\ Flow of water (\(m_{2}\)) & 1.5968 \(\times\) 10\({}^{-1}\) & kg\(\cdot\)s\({}^{-1}\) \\ Demanded heat power (\(Q\)) & 20 & kW \\ Depth of heat exchanger (\(a\)) & 4 \(\times\) 10\({}^{-1}\) & m \\ Width of heat exchanger (\(b\)) & 4 \(\times\) 10\({}^{-1}\) & m \\ Number of pipes in rows (\(n_{1}\)) & 6 & - \\ Number of pipes in columns (\(n_{2}\)) & 6 & - \\ Inner diameter (\(d_{1}\)) & 3.2 \(\times\) 10\({}^{-2}\) & m \\ Outer diameter (\(d_{2}\) ) & 4. \(\times\) 10\({}^{-2}\) & m \\ \hline
**Calculated parameters** & **Value** & **Units** \\ \hline Reynolds number of flue gas flow (\(Re_{1}\)) & 492.24 & - \\ Nusselt number of flue gas flow (\(Nu_{1}\)) & 4.49 & - \\ Flue gas side heat transfer coefficient (\(h_{1}\)) & 8.13 & W\(\cdot\)m\({}^{-1}\)\(\cdot\)K\({}^{-1}\) \\ Reynolds number of water flow (\(Re_{2}\)) & 14742 & - \\ Nusselt number of water flow (\(Nu_{2}\)) & 53.96 & - \\ Water side heat transfer (\(l_{2}\)) & 915.37 & W\(\cdot\)m\({}^{-1}\)\(\cdot\)K\({}^{-1}\) \\ Overall heat transfer coefficient (\(k\)) & 8.05 & W\(\cdot\)m\({}^{-1}\)\(\cdot\)K\({}^{-1}\) \\ Proposed length (\(l_{rp}\)) & 1.62 & m \\ Chosen length (\(L_{ch}\)) & 1.5 & m \\ Real heat power of heat exchanger (\(Q_{r}\)) & 18.703 & kW \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Heat exchanger final design. Figure 7: Maximal heat power of one-meter-long heat exchanger with different pipe diameters.