## 6 Thermal System Design
### Thermal Load Case Testing (SolidWorks)  
To conduct thermal modelling of the CubeSat's orbit, it is firstly necessary to create a simplistic steady-state model [9]. The generated CAD geometry will be a shelled rectangular body with a wall thickness of 1.27 mm to replicate the thickness of the Pumpkin Monocoque. A steady-state model does not require an accurate estimation of thickness and geometry, as this simplistic calculation generates an equilibrium temperature based on the heat balance equation \(\dot{Q}_{in}\ =\ \dot{Q}_{out}\)[9]. A steady-state analysis can incorporate surface to ambient or surface to surface radiation in the SolidWorks program. Selecting the ambient option will replicate the load conditions, dissipating heat to the surrounding background space environment. Once the two components were modelled it is necessary to assign material properties to the bodies. The material properties, listed in Table 30, are extremely important for an accurate analysis. To provide comparable results to the first-hand calculations, the weighted emissivities and absorptivities are applied [9]. For a steady-state calculation, material density and thickness does not factor; however, it will be important during the transient calculations, as the rate of heat loss and absorption will depend on the material geometry. This 3U CubeSat geometry, Figure 49 was then loaded into the thermal analysis window of SolidWorks. A standard mesh was then applied to the geometry with a coarse mesh size of 13.8 mm shown in Figure 50. This value was found to be suitable via a mesh convergence study, as by default SolidWorks only produces results when convergence is lower than a 0.1% value [58]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material Configuration** & **Averaged Emissivity** & **Averaged Absorptivity** \\ \hline
70\% Solar Cell, 30\%, Aluminum & 0.62 & 0.76 \\
100\% Aluminum Face & 0.08 & 0.379 \\
70\% Black Paint, 30\% Aluminum & 0.654 & 0.7927 \\ \hline \hline \end{tabular}
\end{table} 
Table 30: Initial Material Properties for Steady-state Analysis. Thermal loads are then applied to the model, simplistically modelling a thermal load case similar to that encountered during the worst case hot phase in orbit. It is firstly assumed that both faces housing the Clyde-Space XTJ solar cells are perpendicularly incident to the incoming solar flux, which has an intensity of 1369 Wm\({}^{-2}\) illustrated in Figure 51. In reality, it is highly unlikely that this loading scenario would be encountered [9]. Figure 49: Cold Case Altitude Control Block Diagram. Figure 50: Steady-state Mesh Configuration. The incoming albedo and Earth's infra-red radiation were applied to the bottom face, as shown in the figure below (Figure 52). It is assumed that the Albedo and IR incoming fluxes are perpendicular to this face, which is the lower face, positioned towards Earth during orbit. The value of incoming applied Albedo is 488.733 W and Earth's infra-red 197.96 W. These values are found in the first-principle calculations based on an orbit height of 600 km. To create a steady-state heat transfer scenario, it is also necessary to model the heat exhaustion from the \"cool\" faces coincident with the background temperature of space of 3 K experiencing no heating effect due to the incoming flux. This heat removal from the system, \(\dot{Q}_{out}\) will allow SolidWorks to define a steady-state equilibrium temperature for the CubeSat in the worst case thermal load scenario [9]. The initial chosen material for the heat expulsion faces is 70% black paint coating and 30% aluminum, which has an averaged emissivity of 0.654. The material selection for these faces will be altered to pure aluminum 6061-T6 to observe the effect upon the equilibrium temperature once the initial temperature has been determined by the SolidWorks Thermal simulation solver.