# The Thermal Analysis and Heat Dissipation Structure Optimization of a Propeller Driver System
## 2 Thermal Analysis of Propeller Driver
### Grid and Solution Domain Setting  
As natural convection is the primary mode of heat transfer in our study, the computational domain was set up as depicted in Figure 2. The distance of the enclosure in the direction of gravity was set to be 1-2-times the height of the model, while the distance of the enclosure in the opposite direction of gravity was set to be 2-times the height of the model. For all other directions, the enclosure distances were set to be 1-2-times the size of the model [32]. The distance of the enclosure in the direction of gravity was set to 110 mm, while the distance of the enclosure in the opposite direction of gravity was set to \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component Name** & **Material** & \multicolumn{2}{c}{**Thermal Conductivity**} \\  & & **(W/(m-K))** \\ \hline U1 & silicon & 419 \\ U2 & silicon & 419 \\ U3 & silicon & 419 \\ U4 & silicon & 419 \\ Driving plate & FR4 & 0.3 \\ Base & Al6063 & 201 \\ Heat sink & Al6063 & 201 \\ Column & Plastic Package & 5 \\ Column & Cu & 385 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The material property parameters of components. 198 mm. For x directions, the enclosure distances were set to117 mm and 118 mm. The dimensions of the computational domain were set to be 315 mm in length, 381 mm in width, and 551 mm in height. The boundaries of the domain were all set as open boundaries, with an ambient temperature of 25 \({}^{\circ}\)C and a gauge pressure of 0 Pa. Gravity was set to act in the negative Y direction. The fluid used was air at 1 atm. At these conditions, the density of air is 1.1614 kg/m\({}^{3}\), the thermal conductivity is 0.0261 W/(m\(\cdot\)K), and the specific heat capacity is 1005 J/(Kg\(\cdot\)K). The grid encryption scheme is as follows: the minimum and the maximum grid sizes for the zone near heat sink and PCB layers were set to 3 mm and 4 mm, respectively. Discretize the whole computational domain with grids that have sizes between 1 mm and 4 mm. The grid aspect ratio is 3.989. There are 2,405,352 grids in the model, as shown in Figure 2b. Then, increase the grid density. Setting the maximum mesh size of the drive unit to 3 mm and 2.5 mm, respectively, the number of meshes in the model increased to 4,225,221 and 6,341,556. The calculation results are shown in Table 3. Under the three grid models, the calculation results have no obvious change. Therefore, the 2,405,352 grid system was used in the following simulation cases, as shown in Figure 2b. Before performing numerical calculations on the model, it is necessary to consider the flow state of the fluid. In this paper, the \(Ra\) of the fluid can be calculated using Equations (10) and (11) [31; 32]. \[Gr=\frac{ga\Delta t\mathrm{i}^{3}}{\
u^{2}} \tag{10}\]  
\[Ra=Gr\times\Pr \tag{11}\] \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Maximum Grid Size (mm)**} & \multirow{2}{*}{**Number of Grids**} & **Monitoring Point** \\  & & **Temperature** (\({}^{\circ}\)**C**) \\ \hline
4 & 2,405,352 & 54.84 \\
3 & 4,225,221 & 55.61 \\
2.5 & 6,341,556 & 55.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mesh independence verification. Figure 2: (a) Computational domain. (b) discretized grid. From experimental results, as shown in the Section 2.5, assuming the wall temperature is 65 \({}^{\circ}\)C, the fluid temperature is 25 \({}^{\circ}\)C, and the bulk temperature is 45 \({}^{\circ}\)C. The kinematic viscosity of the air is 1.75 \(\times\) 10\({}^{-5}\) m\({}^{2}\)/s, and the Prandtl number is 0.6985. The characteristic dimension for free convection from the horizontal plate is chosen as 150 mm. Then, the Rayleigh Number is calculated to be about 9.5 \(\times\) 10\({}^{6}\). According to the data, the flow state of the fluid is turbulent [31]. Therefore, the calculation model is selected as the Automatic Algebraic Turbulence model. This iteratively solves the method using the SIMPLE method.