## 6 Thermal System Design
### Defining the Thermal Load
\[t_{E}=\frac{1}{180^{\circ}}*\cos^{-1}(\frac{\left(H^{2}+2*R*H\right)^{0.5}}{ \left(R+H\right)*\cos(\beta)}) \tag{35}\]2  
\[t_{E}=\frac{1}{180^{\circ}}*\cos^{-1}(\frac{\left(H^{2}+2*R*H\right)^{0.5}}{ \left(R+H\right)*\cos(\beta)}) \tag{35}\]3  
\[t_{E}=\frac{1}{180^{\circ}}*\cos^{-1}(\frac{\left(H^{2}+2*R*H\right)^{0.5}}{ \left(R+H\right)*\cos(\beta)}) \tag{35}\]4  
where:  
\[t_{E}=\frac{1}{180^{\circ}}*\cos^{-1}(\frac{\left(H^{2}+2*R*H\right)^{0.5}}{ \left(R+H\right)*\cos(\beta)}) \tag{35}\]5  
\[t_{E}=\frac{1}{180^{\circ}}*\cos^{-1}(\frac{\left(H^{2}+2*R*H\right)^{0.5}}{ \left(R+H\right)*\cos(\beta)}) \tag{35}\]6  
\[t_{E}=\frac{1}{180^{\circ}}*\cos^{-1}(\frac{\left(H^{2}+2*R*H\right)^{0.5}}{ \left(R+H\right)*\cos(\beta)}) \tag{35}\]7  
\[t_{E}=\frac{1}{180^{\circ}}*\cos^{-1}(\frac{\left(H^{2}+2*R*H\right)^{0.5}}{ \left(R+H\right)*\cos(\beta)}) \tag{35}\]8  
\[t_{E}=\frac{1}{180^{\circ}}*\cos^{-1}(\frac{\left(H^{2}+2*R*H\right)^{0.5}}{ \left(R+H\right)*\cos(\beta)}) \tag{35}\]9  
\[|\beta|<\beta^{*}\]0  
\[|\beta|<\beta^{*}\]1  
\[|\beta|<\beta^{*}\]2  
\[|\beta|<\beta^{*}\]3  
The external surfaces of the CubeSat act as the interface to energy exchange with the environment, and are exposed to radiation such as solar, Albedo and IR. It is key to achieving a net energy balance to select material with suitable properties to ensure this occurs. Table 28 shows material properties for Al 6061-T6, used for the CubeSat structure, GaAs solar cells as well as black paint. As the coating is extremely thin is paint is assumed to have a negligible weight. The paint is Nextel velvet coating manufactured by 3 M. It has been certified for space exploration and extreme temperature ranges beyond which the CubeSat will experience. The larger surfaces, with dimensions 100 mm by 300 mm, of the CubeSat are composed of 70% GaAs solar cells and 30% Al 6061-T6. The smaller \"upper\" and \"lower\" surfaces of the CubeSat are Al 6061-T6 coated with black Nextel Velvet coating. The average material property for each face can be calculated using:  
\[|\beta|<\beta^{*}\]4  
\[|\beta|<\beta^{*}\]5  
\[|\beta|<\beta^{*}\]6  
\[|\beta|<\beta^{*}\]7  
Therefore:  
\[|\beta|<\beta^{*}\]8  
\[|\beta|<\beta^{*}\]9  
For the larger sides covered with 70% GaAs solar cells and 30% Al 6061-T6 the combined absorptivity and emissivity is shown below:  
\[\beta^{*}=\sin^{-1}\left(\frac{R_{earth}}{R_{earth}+H}\right)=73.4^{\circ} \tag{36}\]0  
\[\beta^{*}=\sin^{-1}\left(\frac{R_{earth}}{R_{earth}+H}\right)=73.4^{\circ} \tag{36}\]1  
To accommodate for the propulsion system, one of the smaller 100 mm by 100 mm faces will be made from aluminum and will not be coated in black paint, and the emissivity and absorptivity are standard values shown in the table; however, for the aluminum face covered in black paint:  
\[\beta^{*}=\sin^{-1}\left(\frac{R_{earth}}{R_{earth}+H}\right)=73.4^{\circ} \tag{36}\]2  
\[\beta^{*}=\sin^{-1}\left(\frac{R_{earth}}{R_{earth}+H}\right)=73.4^{\circ} \tag{36}\]3  
For the 100 mm \(\times\) 300 mm faces exposed to background space, it is desirable to have as high an emissivity as possible. This will ensure the maximum amount of heat is released to limit the internal temperature to as safe a maximum as possible. The Earth-facing CubeSat panel will be manufactured from 6061-T6 aluminum  
\[\beta^{*}=\sin^{-1}\left(\frac{R_{earth}}{R_{earth}+H}\right)=73.4^{\circ} \tag{36}\]4  
\[\beta^{*}=\sin^{-1}\left(\frac{R_{earth}}{R_{earth}+H}\right)=73.4^{\circ} \tag{36}\]5  
The results are summarized in Table 29, with the Surface Number designations matching those shown below: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Al 6061-T6** & **GaAs Solar Cells** & **Nextel Velvet Coating** \\ \hline Emissivity & 0.08 & 0.85 & 0.90 \\ Absorptivity & 0.379 & 0.92 & 0.97 \\ Density (kgm\({}^{-3}\)) & 2700 & 2100 & - \\ Conductivity (W/mK) & 166.9 & 200 & - \\ Specific Heat (J/kgK) & 980 & 1600 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 28: Material Properties Outer Face Materials [10].