## 3 Passive Thermal Control Methods
### Passive Radiator
Figure 4:0  
where \(\alpha\) is absorptivity of the radiator surface, \(q_{s}\) is the incident solar flux on the radiator panel, \(Q_{in}\) is the heat to be rejected. By knowing \(Q_{internal}\) and other environmental heat loads, radiator area can be calculated using Equation (16) assuming that the view factor is 1 for preliminary calculations. If the radiator design calculations are carried out for GEOsatellites, \(Q_{allbedo}\) and \(Q_{IR}\) are generally ignored as the effect of earth's albedo and IR flux are insignificant (approximately <0 [11]) because as the altitude increases, environmental loads from earth decreases rapidly. One exception to this is the case of cryogenic systems, which operate at very low temperatures that even small environmental heat loads from earth are significant to the thermal design [11]. The radiator panel for the 6U satellite platform is optimized for two design parameters. * Radiator size: Radiator panel is allowed to vary in size for maximum radiating capacity. Length and width of the radiator are varied while keeping the thickness constant. * Radiator Thickness: Radiator thickness is varied while keeping the surface area constant. Radiating temperature of the radiator for both of these conditions are varied as the input heat load remains same. To account for varying orbital thermal loads, performance studies were carried out for two orbital worst-case conditions. A few assumptions made for this performance study were,  
* The radiator loses heat only by radiation mode of heat transfer
* Calculations are done for steady state conditions with constant properties
* Radiator temperature is assumed to be constant across thickness
* Heat loss from the edges is negligible. * Incoming solar flux is negligible as the radiator looks into deep space all the time in the orbit and mounted below the solar panel. * Radiator plate is considered to be at a uniform temperature initially. * Material properties do not change with respect to the temperature. * Earth shine and planetary radiation are taken into consideration. Firstly, a body-mount radiator is studied. Based on the advanced standard for Cube-Sats [4], the maximum surface area of the body-mount radiator on a 6U satellite is not more than 200 mm \(\times\) 300 mm. However, full surface area cannot be utilized due to a few mechanical constraints, and hence the maximum area is assumed to be 290 mm \(\times\) 180 mm (0.0522 m\({}^{2}\)). Similarly, the size of the radiator panel for a 27U satellite is considered to be 300 mm \(\times\) 300 mm (0.09 m\({}^{2}\)). The Figures 5 and 6 illustrate the orientation of the body-mount and deployable radiators for 6U and 27U satellites with respect to the sun. Figure 4:1 BMR-Satellite Orientation with respect to Sun. As can be seen in Figure 7, total heat rejected by both the body-mount (BMR) and deployable radiators (DR) are increasing exponentially (due to fourth power of T) when the temperature of the radiator is increased for a constant radiating surface area of 0.2 m\({}^{2}\). Total heat rejected for the deployable radiator is higher because of double-active radiating surfaces, whereas the BMR has a single-active radiating surface. For the above calculations, it is assumed that the radiating surfaces are coated with black paint which has an emissivity of 0.85. The radiator is mounted below the solar panel for the 6U configuration, so they do not absorb much heat if exposed to the sun but, typically the radiators are painted white. Figure 8 illustrates the relationship between radiator area (\(A_{rad}\)), temperature (\(T_{rad}\)), and total heat to be dissipated (\(Q_{internal}\)). For a constant temperature, the total heat loss into deep space increases with increase in radiator surface area, and this variation is plotted for different radiating temperatures. Placement of the radiator panels on the satellite body is another important decision as the radiator should not be exposed to solar radiation, which is a major heat source.