# Numerical Analysis on the Performance of a Radiant Cooling Panel with Serpentine-Based Design
## 2 Methods
### Geometrical Setup of the Proposed Design  
The 3D design of the RCP model is created by using Autodesk Fusion 360. This software is used because it makes it easier to construct 3D modeling. The completed 3D design of the RCP is then converted into a _.step_ file. The _.step_ file of the design is then imported into SpaceClaim for flow simulation. The dimension of this model follows the parameters proposed in Table 4. The generated model of a one-inlet-one-outlet serpentine flow configuration, as modeled by using Autodesk Fusion 360 in SpaceClaim, is shown in Figure 2.  
After generating a 3D model of the RCP, a hexahedral mesh is used for the generation of mesh on the design model in Figure 3. Hexahedral mesh is chosen because it enables a more accurate result on a simple geometry model. Edge sizing is used at the inlet and outlet flow of the fluid domain. The mesh is smoothed by applying 10, 15, 20 and 25 divisions on the mentioned edge for the grid independence test, to ensure that the grid size used is suitable to obtain a converged solution.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Design Parameters** & **Value** & **Operating Conditions** \\ \hline \multirow{4}{*}{Aluminum Panel} & \(A_{r}=1.05\) & \\  & \(A_{p}=1.35\) m\({}^{2}\) & Laminar flow \\  & \(W=1.19\) m & Incompressible \\  & \(L=1.13\) m & \(T_{w,in}=15\)\({}^{\circ}\)C \\  & \(t=3\) mm & \(T_{amb}=24\)\({}^{\circ}\)C \\ \hline \multirow{2}{*}{Copper Tube} & \(D_{o}=12.5\) mm & \(\dot{m}_{in}=0.004\) kg/s \\  & \(D_{i}=10\) mm & \(AUST=24\)\({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 4: Summary of parameters and operating conditions for the simulation.  
Figure 2: 3D model of the one-inlet-one-outlet serpentine flow configuration.  
The simulation domains and boundary locations are specified after the mesh generation of the model is completed. The fluid domain is the pipe carrying chilled water, and the solid domain is the aluminum plate located below the fluid domain. Heat exchange will occur between the two domains, with the boundary conditions mentioned in Table 3. The fluid domain is set to have the properties of water, and the solid domain has the properties of aluminum.  
For the solver execution part, a laminar model is chosen because the calculated Reynolds number is in the laminar region. The energy equation is turned on as heat exchanges occur between the fluid domain and the solid domain. The solver type is pressure-based and steady-state. A steady-state simulation is faster than a transient one and is thus suitable for this study, to save time and computational load.  
For the solution part, a Semi-Implicit Method for Pressure Linked Equations (SIMPLE) is used for the pressure-velocity coupling and is set as the solution method. A second-order upwind is chosen for the spatial discretization of the momentum and energy equations, whereas the gradient discretization is based on the least-squares cell, and pressure discretization is set as second-order. The residual tolerance used for continuity, \(x\)-velocity, \(y\)-velocity, \(z\)-velocity, and energy is 0.001, which is the default value from ANSYS Fluent. Hybrid initialization is used, and 1000 iterations are chosen to make sure that the value obtained is accurate and converged.  
Finally, the results obtained in the post-processing stage are analyzed and examined for discussion. The results that will be taken for analysis are the temperature contour of the RCP, pressure contour, outlet water temperature, surface temperature of RCP, and pressure drop inside the tube. The cooling capacity and temperature distribution uniformity are determined from the surface temperature of the RCP.  
The steps above will be repeated on the other two proposed designs of the RCP flow configurations.