## 6 Thermal System Design
### Defining the Thermal Load
During the eclipse phase the CubeSat will experience extremely low temperatures; due to the fact the only heat input is infra-red radiation from Earth with a value of 198 Wm\({}^{-2}\)[10]. No electrical power is generated during this phase, as no solar flux is incident, making it an extremely difficult environment for the CubeSat to survive. By altering the original setup to have a 70% black paint, 30% aluminum structure from pure aluminum 6061-T6 the steady-state hot-case temperature is 321.1187 K (48.11 \({}^{\circ}\)C). The minimum Cold Case steady-state temperature is given by:  
\[T_{min}=\left(T_{space}^{4}+\frac{I_{E}}{\sigma}*\frac{\varepsilon_{IR}}{ \varepsilon_{IR}^{*}}*\frac{A_{p}}{5*A_{p}}\right)^{0.25} \tag{73}\]  
Inputting the original material set-up, the cold case steady-state temperature is found to be 102.813 K (\(-\)170.187 \({}^{\circ}\)C). This temperature extreme cause complete shutdown of the electrical system, leading to mission failure. If Earth-facing material was altered to 70% black paint and 30% 6061-T6 aluminum the cold case temperature is found to be 172.951 K (\(-\)100.0489 \({}^{\circ}\)C). The selection of the black paint covered face is critical to the success of the shuttle mission. The reduction in the cold case temperature is vital; however, a heating system would still require integration into the CubeSat to ensure temperatures do not exceed the critical values of the CubeSat's electrical components [10]. Steady-state analysis does not provide an accurate method of temperature estimation, particularly for the cold case. As the CubeSat would enter the eclipse phase with internally stored energy within the CubeSat's material mass from the hot-case heating action due to incoming flux from the Sun and Earth. An accurate estimation of the cold case temperature would be given by conducting a transient analysis upon the CubeSat's eclipse orbit. This would ensure the initial temperature reached from heating, and the material mass and geometry of the CubeSat gave a much more accurate estimation of the CubeSat's eclipse cold case minimum temperature. A transient study would also map the temperature drop as a function of time [65]. It would therefore be possible to program the electrical systems heater to switch on a certain critical time in the eclipse phase, just before the minimum operating temperature of the electrical system was reached to conserve stored power in the battery. A transient load case is ideally modelled in a software CAD analysis package, for example SolidWorks, which is explored in Section 6.2[65]. It should however be considered that a thermal load will be placed upon the CubeSat due to heat generated by resistance in electrical components. The worst case hot scenario factoring in heat dissipation is given by [10]  
\[T_{max}=\left(T_{space}^{4}+\frac{I_{s}}{\sigma}*\frac{A_{P}}{5*A_{p}}*\frac{ A_{ss}}{\varepsilon_{IR}^{*}}+\frac{I_{E}}{\sigma}*\frac{A_{P}}{5*A_{p}}*\frac{ \varepsilon_{IR}}{\varepsilon_{IR}^{*}}+\frac{0.34*I_{s}}{\sigma}*\frac{A_{P}} {5*A_{p}}*\frac{\varepsilon_{SB}}{\varepsilon_{IR}^{*}}+\frac{\dot{Q}_{p}}{ \varepsilon_{IR}^{*}*\varepsilon*A_{p}*\sigma}\right)^{0.25} \tag{74}\]  
From the electrical system the average power consumption of constantly active components throughout the cycle was found to be 2.665 W. Given an average efficiency of 70% [21] the heat dissipation in the device is assumed to be 30% of the 2.665 W power draw, which is equal to a dissipated heat of 0.7995 W.  
\[\dot{Q}_{p}=0.7995\;\mathrm{W}\]Inputting this power dissipation into the starting material composition model yields a maximum hot-case steady-state equilibrium temperature of 324.021 K (51.021 \({}^{\circ}\)C).