# Thermal Optimization Design for a Small Flat-Panel Synthetic Aperture Radar Satellite
## 3 Thermal Design Strategy
### Optimization of Thermal Design for the SAR Antenna  
For large-area antennas, it is of great significance to adopt simplified thermal control measures as much as possible, as any simplification will have an exponential impact on the entire antenna manufacturing process. Each antenna subarray is equipped with four columns of T/RMs, all with the same column spacing. Additionally, two PMs are  
Figure 3: Temperature control strategy for support plate. positioned on one side of each column of T/RMs, ensuring consistent boundary conditions for each column of T/RMs. The antenna mounting plate is made of an aluminum skin-aluminum core honeycomb board, ensuring both low weight and high strength, while maintaining excellent planar and longitudinal thermal conductivity. This enables the heat generated by the components to be quickly transferred to the mounting board and dispersed after the imaging process. In addition, when MLI is uniformly arranged in the circumferential direction, the boundary of the antenna mounting plate can be considered as an adiabatic state, and the temperature variation across the entire plane can be regarded as a quasi-static process. Due to the hysteresis effect of heat transfer, T/RMs remain unaffected by the temperature rise of PM during the imaging process. In addition, a double-channel aluminum-ammonia heat pipe is positioned beneath each column of T/RMs, serving to mitigate edge effects and reduce temperature disparities arising from inconsistent heat generation among the T/RMs. Figure 4 shows an overview of the antenna mounting plate. There are gaps between the antenna mounting plate, T/RMs, and RUs, and heaters can be arranged within these gaps to ensure thermal uniformity of mounting plate. By reasonably designing the TIM within the gap, the temperature of T/RMs can be maintained in an ideal state. Specifically, no heating is required for the antenna under low-temperature conditions of the whole satellite, and the peak temperature of T/RMs under high-temperature conditions remains below the maximum permissible value, with a certain temperature margin maintained under both conditions. This design reduces satellite energy consumption which is called zero-consumption thermal control. To design an appropriate area for TIM, in this article, the power consumption of short-time imaging is averaged across the entire orbital period. Assuming that the average temperature (\(T_{\text{avg}}\)) of T/RMs under extreme high-temperature conditions is 20 \({}^{\circ}\)C, and defining the control temperature (\(T_{\text{con}}\)) under extreme low-temperature conditions as \(-\)10 \({}^{\circ}\)C, the area of TIM can be determined based on the thermal equilibrium equation. Figure 4: Thermal design strategy for antennas. Taking a single RU as the research object, and assuming there is little area of contact between the mounting plate and RU, the thermal equilibrium equation of the T/RMs is as follows. \[\frac{Q_{-zh}-\sigma T_{avg}^{4}}{1+\frac{1-\epsilon_{MLI}}{A_{kil}A_{MLI}}+ \frac{1}{A_{T/RM}X_{T/RM-MLI}}+\frac{1-\epsilon_{T/RM}}{A_{T/RM}T/RM}+\frac{T_{ RUlh}-T_{avg}}{\frac{1}{h_{T/RM-MP}}+\frac{\delta_{MP}}{\lambda_{MP}}+\frac{1}{n_{ RUl-MP}}}=\frac{P\tau}{\tau_{0}A_{T/RM}} \tag{9}\]  
\[\frac{Q_{-zc}-\sigma T_{con}^{4}}{1+\frac{1-\epsilon_{MLI}}{A_{kil}A_{MLI}}+ \frac{1}{A_{T/RM}X_{T/RM-MLI}}+\frac{1-\epsilon_{T/RM}}{A_{T/RM}T/RM}+\frac{T_{ RUlc}-T_{con}}{\frac{1}{h_{T/RM-MP}}+\frac{\delta_{MP}}{\lambda_{MP}}+\frac{1}{n_{ RUl-MP}}}=0 \tag{10}\]  
where \(A\) represents the thermal radiation area, \(T\) stands for the temperature of the components, \(Q\) represents the space heat flux, \(X\) denotes the radiation angle coefficient, and \(h\) represents the thermal conductance of the interface, which is a parameter proportional to the area it occupies.