# Thermal Control of CubeSat Electronics Using Thermoelectrics
## 3 Results and Discussion
### Radiator Size  
This assessment was carried out for a single thermoelectric module to manage a heat load of up to approximately 50 W using a module that is 40 mm \(\times\) 40 mm \(\times\) 4 mm. However, the findings are expected to be scalable, given the scalability of thermoelectric modules, both to larger and smaller sizes, e.g., two modules could be used to cool a 100 W heat load and so on. The caveat is that the size of the radiator would need to scale too.  
To enhance this assessment, an estimate of the radiator size that would enable a given thermal resistance, is presented in Figure 5. Here the radiator emissivity is set to 0.95. The radiator is assumed to radiate to deep space, at a temperature of 3 K. Since the thermal resistance will vary as a function of radiator temperature, Figure 5 presents trend lines for four different radiator temperatures (25 \({}^{\circ}\)C, 50 \({}^{\circ}\)C, 75 \({}^{\circ}\)C and 100 \({}^{\circ}\)C).  
As expected, Figure 5 shows that the thermal resistance of the radiator reduces for a greater radiator temperature, or for a larger radiator area. What is also clear, is that a relatively large radiator is required to achieve a thermal resistance that would provide enough cooling to make a thermoelectric system viable. For example, for a radiator at 75 \({}^{\circ}\)C, a 1.4 m\({}^{2}\) radiator would be required to achieve a thermal resistance of 0.3 \({}^{\circ}\)C/W. Given that CubeSats consist of units with approximately 0.1 m-long sides, meaning a radiator placed on a single 1 U surface is only 0.01 m\({}^{2}\), it seems that many conditions where thermoelectric modules could provide a cooling benefit would be undermined by the requirement for an unrealistically large or complex radiator, e.g., a deployable radiator [2]. This calculation is also a best-case-scenario, since no thermal resistance for the thermal strap is included, i.e., essentially the radiator is in direct contact with the surface to be cooled. In reality the thermal strap would impose an additional thermal resistance.  
It is therefore likely that, in the vast majority of cases, a thermoelectric system for CubeSat thermal management would not be feasible due to the large radiator that would be required, as well as the added complexity, mass and cost involved in the deployment of a thermoelectric system in the first place, which only provide benefit within a small range of operating conditions. That said, for this small range it is also possible that thermoelectric cooling could be used to actually reduce the radiator size. This idea is explored in another study by these authors [16].  
Research aimed at improving thermoelectric modules is extensive and focuses on improving coefficient of performance. Indeed a significant COP enhancement would increase the range of operating conditions where thermoelectric cooling would be viable. This task in non-trivial however, since it relies on an improvement in thermoelectric material properties. These are inter-related, for example thermoelectric figure-of-merit improves by increasing electrical conductivity and decreasing thermal conductivity. Usually an increase in one, also increases the other, hence large improvements in this field are difficult to achieve.