## 3 Analysis with Optimization Process  
In this paper, the optimization design for the LFHX for a small truck presented in [11] was re-executed through the optimal design process shown in Figure 4, and the current optimal design results obtained were compared and analyzed based on the performance calculated with the optimal design parameters presented in [11].  
Figure 4: Optimal design process for initial and final models.  
Initial Condition  
Prior to optimization, the physical properties and operating conditions of air and coolant in [11] were defined identically as shown in Tables 2 and 3, and the types and ranges of heat exchanger design parameters were revised as shown in Table 4. Furthermore, the number of optimization iterations was set to 1 million, and the number of populations was set to 250. The criteria for stopping genetic algorithms are when 98% of the population set has the same shape determinant and the objective function value becomes the same, or when the number of iterations reaches the number of iterations set by the user.  
Regarding optimization using GA, the result varies depending on the objective function setting, and the main performance indicators are set according to the designer's intention and are reflected in the objective function. In this paper, heat transfer rate (A), effectiveness (B), fin efficiency (C), and total weight (D) of the heat exchanger were set as main indicators, and the basic formula is as follows.  
\[Objective\ Function=\sqrt{k_{1}A^{2}+k_{2}B^{2}+k_{3}C^{2}+k_{4}D^{2}}\,\ k_{1}+k_{2}+k_{3}+k_{4}=1 \tag{27}\]  
In the above formula, k represents the weight of each term and, in this paper, it is set to 0.4, 0.3, 0.2, and 0.1 in order, respectively. Moreover, the optimization proceeds in the direction which minimizes the value of the objective function.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Design Parameters** & **Min.** & **Max.** \\ \hline \(R_{l}\) [mm] & 0.3 & 0.4 \\ \(T_{l}\) [mm] & 0.001 & 0.003 \\ \(T_{h}\) [mm] & 0.25 & 0.3 \\ \(T_{d}\) [mm] & 0.0156 & 0.0254 \\ \(N_{t}\) & 30 & 50 \\ \(F_{r}\) [mm] & 0.0005 & 0.002 \\ \(\text{rat}L_{l}\) & 0.8 & 0.95 \\ \(\text{rat}F_{d}\) & 0.9 & 1.1 \\ \(N_{f}\) & 150 & 300 \\ \(L_{h}\) [mm] & 0.0001 & 0.002 \\ \(L_{p}\) [mm] & 0.0001 & 0.002 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Dimension ranges for LFHX.  
\begin{table}
\begin{tabular}{c c} \hline \hline  & **Properties** & **Values** \\ \hline Air & Density (\(\rho_{a}\)) & 1.165 kg/m\({}^{3}\) \\  & Dynamic viscosity (\(\mu_{a}\)) & 18.63 \(\times\) 10\({}^{-6}\) Ns/m\({}^{2}\) \\  & Specific heat capacity (\(C_{pu}\)) & 1005 J/kg K \\  & Thermal conductivity (\(k_{a}\)) & 0.02675 W/m K \\ \hline Coolant & Density (\(\rho_{w}\)) & 980 kg/m\({}^{3}\) \\  & Dynamic viscosity (\(\mu_{w}\)) & 0.3344 \(\times\) 10\({}^{-3}\) Ns/m\({}^{2}\) \\  & Specific heat capacity (\(C_{pu}\)) & 4188 J/kg K \\  & Thermal conductivity (\(k_{w}\)) & 0.656 W/m K \\  & Prandtl number (\(Pr\)) & 2.85 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Air and coolant properties.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Values** \\ \hline Air Temperature (\(T_{a}\)) & 28 [\({}^{\circ}\)C] \\ Air Pressure (\(P_{a}\)) & 101.325 [kPa] \\ Air Velocity (\(V_{a}\)) & 14 [m/s] \\ Coolant Temperature (\(T_{w}\)) & 80 [\({}^{\circ}\)C] \\ Coolant Pressure (\(P_{w}\)) & 101.325 [kPa] \\ Coolant Mass flow rate (\(\dot{m}_{w}\)) & 0.1671 [kg/s] \\ \hline \hline \end{tabular}
\end{table}
Table 3: Operating conditions.