# Heat Transfer Performance and Flow Characteristics of Helical Baffle-Corrugated Tube Heat Exchanger
## 3 Results and Discussion
### Optimization of Helical Baffle-Corrugated Tube Heat Exchanger
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **A** & **B** & **C** \\ \hline
1 & Triangle & 37.07 & 18.10 \\
2 & Triangle & 53.09 & 35.33 \\
3 & Triangle & 67.69 & 51.07 \\
4 & Rectangle & 37.07 & 35.33 \\
5 & Rectangle & 53.09 & 51.07 \\
6 & Rectangle & 67.69 & 18.10 \\
7 & Semicircle & 37.07 & 51.07 \\
8 & Semicircle & 53.09 & 18.10 \\
9 & Semicircle & 67.69 & 35.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Orthogonal experiment scheme L\({}_{9}\) (\(3^{3}\)). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{4}{c}{**Total Heat Transfer Coefficient (W/(K\(\cdot\)m\({}^{2}\)))**} & \multicolumn{4}{c}{**Pressure Drop (Pa)**} \\ \cline{2-10}  & **I** & **II** & **III** & **IV** & **V** & **I** & **II** & **III** & **IV** & **V** \\ \hline
1 & 1924.21 & 2004.43 & 2065.96 & 2029.77 & 2133.15 & 2412.93 & 2587.97 & 2825.65 & 4792.44 & 8035.30 \\
2 & 1925.21 & 1804.46 & 1840.36 & 1847.35 & 1904.45 & 650.89 & 774.80 & 930.55 & 1185.08 & 1887.77 \\
3 & 1657.01 & 1720.70 & 1750.51 & 1761.90 & 1829.52 & 319.22 & 407.42 & 520.10 & 552.27 & 856.89 \\
4 & 2267.64 & 2451.92 & 2498.81 & 2424.29 & 2532.09 & 668.93 & 855.98 & 1101.73 & 1171.77 & 1855.14 \\
5 & 2095.01 & 2283.82 & 2393.30 & 2257.31 & 2357.66 & 345.79 & 472.91 & 638.03 & 579.89 & 883.67 \\
6 & 1855.67 & 1975.78 & 2053.03 & 1952.99 & 2038.76 & 2349.20 & 2436.36 & 2541.85 & 4743.77 & 7990.80 \\
7 & 2138.51 & 2285.93 & 2378.58 & 2325.26 & 2431.43 & 363.79 & 513.18 & 708.61 & 598.04 & 901.49 \\
8 & 2412.39 & 2633.87 & 2759.83 & 2538.50 & 2639.94 & 2354.99 & 2462.44 & 2600.67 & 4698.94 & 8009.70 \\
9 & 1855.86 & 2422.98 & 2532.53 & 2383.01 & 2476.16 & 674.00 & 664.67 & 770.72 & 1084.96 & 1774.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Numerical simulation results of the 9 programs under 5 conditions. The analysis results for the total heat transfer coefficient and pressure drop are shown in Table 6 and Figure 9. As seen from Table 6, the factor influence of the total heat transfer coefficient decreases in the order **A** > **B** > **C** according to the \(R\) values; the pressure drop decreases in the order **C** > **B** > **A**. Figure 9 indicates that the semicircle cross-section helical groove has a significant advantage over other shapes for enhancing the heat transfer coefficient. Moreover, the best program of the optimized total heat transfer coefficient is **A3**, **B1**, and **C1** for the low tube flow rate, low shell flow rate condition (Condition I). With the increase in the tube flow rate and shell flow rate (Conditions II, IV, and V), the best optimization scheme of the total heat transfer coefficient is **A3**, **B1**, and **C2**. It should be noted that when the tube flow rate is much higher than the shell flow rate (Case III), the best optimized solutions for the total heat transfer coefficient are **A3**, **B2**, and **C1**. Figure 9 also shows that it is always impossible to achieve the optimal flow resistance characteristic optimization at the same time as the optimal heat transfer performance optimization. Therefore, in this paper, the effectiveness evaluation parameter _EEC_ proposed by [PERSON] et al. [28] for the complex flow of heat exchangers is used for the evaluation, and the calculation method is shown in Equation (9):  
\[EEC=\frac{Q/Q_{0}}{(q_{v}\cdot\Delta P)/(q_{v0}\cdot\Delta P_{0})} \tag{9}\]  
where \(Q\) is the heat transfer, \((q_{v}\cdot\Delta P)\) is the pump power, and \(q_{v}\) is the volume flow rate. The numerator represents the heat transfer benefit; the denominator represents the pump power loss. Equation (9) directly represents the ratio of heat transfer gain to flow cost. The analysis results for the _EEC_ are shown in Table 7 and Figure 10. As seen from Table 7, the factor influence of the _EEC_ decreases in the order **C** > **A** > **B** according to the \(R\) values.