# Thermal Optimization Design for a Small Flat-Panel Synthetic Aperture Radar Satellite
## 4 Thermal Analysis  
The satellite orbit is at an altitude of 515 km, with an inclination angle of 97.42\({}^{\circ}\) and a local time of 6:00 AM at the descending node. The beta angle of the orbit varies between 59\({}^{\circ}\) and 87\({}^{\circ}\) annually. This implies that most of orbital cycles are in full sunlight, with a small number experiencing brief periods of ground shadow (Figure 5). This enables the solar array to harvest sufficient energy even when the SAR antenna remains pointed towards the Earth for a long time, thereby reducing the satellite's attitude adjustment time during and after imaging and data transmission. Statistics were compiled on the orbital heat flux of the satellite in all directions (Table 3), solely using the Beta angle as the comparison variable. According to the thermal design strategy, the antenna is primarily influenced by the heat flux in the +Z direction, whereas the platform is predominantly affected by the heat flux in the +Y, \(-\)Y, and \(-\)Z directions. Owing to the constant temperature of the support plate, the antenna and the platform are fully thermally decoupled. It is evident that the extreme operating conditions of the antenna and the platform are not aligned. Therefore, the satellite's extreme high- and low-temperature operating conditions are determined by combining the orbits of the two Beta angles, which, in reality, does not occur. Table 4 outlines the assumed extreme operating conditions for the orbit and the power consumption of the satellite in numerical thermal analysis. Apart from the entries listed in the table, the disparities between the two extreme operating conditions also encompass differences in the surface coating, variations in the shunt of the solar array, and differences in the satellite's attitude. The extreme working conditions of the satellite are the superposition of various conditions, such as the power consumption and heat flux in space. These environmental conditions are applied in simulation analysis and thermal test verification. The thermal design should ensure that the temperature margin of each component on the board is at least 5 \({}^{\circ}\)C under extreme conditions. Figure 5: The orbit schematic (from the perspective of the sun). \begin{table}
\begin{tabular}{c c c c} \hline
**Item** & **Beta Angle 59\({}^{\circ}\)** & \multicolumn{2}{c}{**Beta Angle 87\({}^{\circ}\)**} \\ \hline Solar constant [W/m\({}^{2}\)] & & 1367 & \\ Albedo & & 0.3 & \\ Planetary flux [W/m\({}^{2}\)] & & 239.2 & \\  & Solar & Infrared radiation & Solar & Infrared radiation \\ +X side heat flux [W/m\({}^{2}\)] & 221.8 & 52.3 & 29.6 & 54.6 \\ \(-\)X side heat flux [W/m\({}^{2}\)] & 206.8 & 50.4 & 29.8 & 48.9 \\ +Y side heat flux [W/m\({}^{2}\)] & 10.9 & 57.6 & 0.1 & 58.1 \\ \(-\)Y side heat flux [W/m\({}^{2}\)] & 926.8 & 60.2 & 1380.1 & 58.6 \\ +Z side heat flux [W/m\({}^{2}\)] & 140.6 & 204.0 & 37.8 & 203.5 \\ \(-\)Z side heat flux [W/m\({}^{2}\)] & 41.6 & 1.0 & 27.8 & 2.1 \\ \hline \end{tabular}
\end{table} 
Table 3: Orbital conditions and heat flux statistics. Figure 6 illustrates the thermal analysis model for the satellite antenna and the platform, which are independently modeled and simulated. During the modeling process, non-critical areas are simplified. In the analysis model, the satellite platform utilized 9843 nodes, while the antenna employed 8649 nodes. When conducting thermal analysis of the antenna, the temperature distribution of the platform has no impact on the antenna, as the temperature of the support plate remains constant. On the other hand, when conducting thermal analysis of the platform, the temperature of the antenna influences the thermal control power of the support plate. Therefore, under extreme low-temperature conditions of the platform, a constant temperature boundary of \(-10\)\({}^{\circ}\)C is set for the antenna, while under extreme high-temperature conditions, a constant temperature boundary of \(20\)\({}^{\circ}\)C is set for the antenna.