# Thermal Control of CubeSat Electronics Using Thermoelectrics
## 3 Results and Discussion
### Benefits of the Thermoelectric Module  
Figure 3a,b present plots of the system's thermal resistance versus the heat pumped at the cold-side of the thermoelectric module, that is the heat removed from the warm object, such as a CPU, for example. Figure 3a presents data for the module's performance extracted at 25 \({}^{\circ}\)C and Figure 3b shows the same analysis for 75 \({}^{\circ}\)C performance. A deeper discussion of what \(R\) corresponds to, in terms of the physical characteristics of the radiator, will be discussed later.  
Lines on each of Figure 3a,b represent the benefit or detriment enacted by the addition of a thermoelectric module for cooling. The value assigned to each line (in the legend) represents this numerically (in \({}^{\circ}\)C), where positive (red) values show that the temperature at the cold-side of the module would be hotter than the equivalent scenario where no thermoelectric module is used and heat rejection occurs using just a radiator. Likewise, negative (blue) values indicate that the thermoelectric module cools to a temperature below that achieved with a radiator alone. As an example, the bold dashed line indicates that the thermoelectric device would cool a CPU to a temperature 5 \({}^{\circ}\)C below that for a radiator alone, when 35 W is removed from the cold side of the device (i.e., when the CPU power is 35 W) and the radiator has a thermal resistance of 0.45 \({}^{\circ}\)C/W.  
The black line represents conditions i.e., required heat to be removed versus radiator thermal resistance, where a thermoelectric module in combination with a radiator would perform equally as well as the radiator alone. In this case, there is therefore no benefit in implementing a thermoelectric solution.  
The red lines indicate conditions where introducing a thermoelectric system would actually increase the temperature of the CPU being cooled. This is most common in the top, right-hand side of Figure 3a,b, where the quantity of heat being removed is high, as is the thermal resistance of the system. This is somewhat counterintuitive initially, since one might expect that thermoelectrics would be of added benefit when the radiator performance is limited or when more heat is generated and requires removal. However, this is not the case, since to pump heat from the cold side, the thermoelectric device consumes electricalenergy which generates extra \(I^{2}R\) heat, adding to that which must be dissipated by the radiator at the module's hot-side.  
Nevertheless, thermoelectric cooling does make sense for a range of conditions, especially in the bottom, left-hand side of Figure 3a,b, when a good quality radiator is employed. In a limited number of cases, it is possible to cool the CPU to 45 \({}^{\circ}\)C below that which can be achieved with just a radiator.  
Figure 3: The thermoelectric system’s thermal resistance versus the heat pumped at the cold-side of the thermoelectric module. The black line represents conditions i.e., required heat to be removed versus radiator thermal resistance, where a thermoelectric module in combination with a radiator would perform equally as well as the radiator alone. Blue lines indicate conditions where the thermoelectric module provides benefit, whereas red lines indicate conditions where the thermoelectric module is detrimental. The legend indicates (in \({}^{\circ}\)C) how much the benefit/detriment is. (**a**) Presents data for the module’s performance extracted at 25 \({}^{\circ}\)C and (**b**) shows the same analysis for 75 \({}^{\circ}\)C.  
This analysis indicates that careful consideration of the cooling requirements and the thermal resistance of the refrigeration system are crucial in advance of selecting an active thermoelectric-based cooling solution. The slight differences between Figure 3a,b show that it is important to also consider the working temperature(s) of the thermoelectric module and identify its performance accordingly.