# Design of a Solenoid Actuator for a Cylinder Valve in a Fuel Cell Vehicle
## 4 Analysis of Solenoid Actuator  
### Thermal Analysis  
For more accurate prediction of the saturation temperature of the solenoid actuator, steady-state heat transfer analysis was conducted using ANSYS WORKBENCH (V15, ANSYS Inc., Canonsburg, PA, USA). Internal heat generation conditions were applied to the actuator coil, and 5.53 W of power was applied at the saturation temperature. Convection conditions were applied to the plane where the actuator comes in contact with air and convection occurs due to temperature differences. The convection heat transfer coefficient was assumed to be \(5\,W/\mathrm{m}^{2.\circ}\mathrm{C}\). Heat conduction was assumed between actuator components due to contact [16; 17]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbols** & **Values** \\ \hline Height of coil bobbin & \(h\) & 30 mm \\ Width of coil bobbin & \(w\) & 4.4 mm \\ Bare copper wire diameter & \(N_{d}\) & 0.45 mm \\ Enameled wire diameter & \(C_{d}\) & 0.52 mm \\ Enameled wire resistance per unit length & \(\rho\) & 109.2 \(\Omega/\mathrm{km}\) \\ Saturation temperature & \(T_{s}\) & 97 \({}^{\circ}\mathrm{C}\) \\ Number of turns in a coil & \(N\) & 456 \\ Coil resistance at 20 \({}^{\circ}\mathrm{C}\) & \(R_{20}\) & 3.2 \(\Omega\) \\ Coil resistance at saturation temperature & \(R_{s}\) & 4.17 \(\Omega\) \\ Attraction force at saturation temperature & \(F_{A}\) & 23.1 N \\ Power consumption at saturation temperature & \(P_{s}\) & 5.53 W \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimization results. Figure 7: Procedure of optimal design. Radiation conditions were applied to the plane where convective heat transfers from the outermost surface to the atmosphere, and the air temperature was designated as 25 \({}^{\circ}\)C. Figure 8 shows the convection and radiation conditions applied to the actuator. Table 3 shows the density, specific heat capacity, and thermal conductivity coefficient of the solenoid actuator component material used in the heat transfer analysis, as well as the emissivity used in the radiation conditions. The heat transfer analysis was conducted using tetrahedron elements, and 558,984 nodes and 362,091 elements were generated. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Properties** & **Values** \\ \hline \multirow{4}{*}{Copper} & Density (kg/m\({}^{3}\)) & 8930 \\  & Specific heat capacity (J/kg.\({}^{\circ}\)C) & 385 \\  & Reference temperature (\({}^{\circ}\)C) & 20 \\  & Thermal conductivity (W/m.\({}^{\circ}\)C) & 401 \\ \hline \multirow{4}{*}{STS430 FR} & Density (kg/m\({}^{3}\)) & 7610 \\  & Specific heat capacity (J/kg.\({}^{\circ}\)C) & 460 \\  & Reference temperature (\({}^{\circ}\)C) & 20 \\  & Thermal conductivity (W/m.\({}^{\circ}\)C) & 24.9 \\ \hline \multirow{4}{*}{STS316L} & Density (kg/m\({}^{3}\)) & 8000 \\  & Specific heat capacity (J/kg.\({}^{\circ}\)C) & 500 \\  & Reference temperature (\({}^{\circ}\)C) & 20 \\  & Thermal conductivity (W/m.\({}^{\circ}\)C) & 14.0 \\  & Emissivity & 0.28 \\ \hline \multirow{4}{*}{SUM24L} & Density (kg/m\({}^{3}\)) & 7700 \\  & Specific heat capacity (J/kg.\({}^{\circ}\)C) & 472 \\  & Reference temperature (\({}^{\circ}\)C) & 20 \\  & Thermal conductivity (W/m.\({}^{\circ}\)C) & 51.9 \\  & Emissivity & 0.75 \\ \hline \multirow{4}{*}{PA66+G35\%} & Density (kg/m\({}^{3}\)) & 1410 \\  & Specific heat capacity (J/kg.\({}^{\circ}\)C) & 1500 \\ \cline{1-1}  & Reference temperature (\({}^{\circ}\)C) & 20 \\ \cline{1-1}  & Thermal conductivity (W/m.\({}^{\circ}\)C) & 0.35 \\ \cline{1-1}  & Emissivity & 0.95 \\ \hline \multirow{4}{*}{PEEK1000} & Density (kg/m\({}^{3}\)) & 1310 \\ \cline{1-1}  & Specific heat capacity (J/kg.\({}^{\circ}\)C) & 320 \\ \cline{1-1}  & Reference temperature (\({}^{\circ}\)C) & 20 \\ \cline{1-1}  & Thermal conductivity (W/m.\({}^{\circ}\)C) & 0.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Thermal properties of materials. Figure 8: Conditions for thermal analysis. Figure 9 shows the results of the actuator heat transfer analysis.