## 5 Measured Results
### 2D Heat Transfer of Irregular Shapes Test  
To test if the various node types as listed in Table 7 are functioning correctly, different boundary conditions will be implemented, and the results produced via the Python script will be validated against the results produced in Ansys. It should be noted that all tests conducted are done with a mesh size of 65 \(\times\) 65, an \(h\) value of 25 W/m\({}^{2,\circ}\)C, and a \(k\) value of 60.5 W/m\({}^{\circ}\)C is used as the material is assumed to be structural steel. These values were obtained from the materials database included within the Ansys GRANTA Edupack software [1]. All tests conducted in Ansys also use a mesh element size of 0.015 m to replicate the distance between each node in the Excel sheet. Table 12 shows the various nodal equations being tested in the Python script and compares them with the results produced in Ansys. Figure 11: Comparison of contour plot produced for different mesh sizes. Figure 10: Plot of log iteration against time taken for different mesh sizes. \begin{table}
\begin{tabular}{c c} \hline \hline
**Node Test Conducted** & **Results (Python Script vs. Ansys)** \\ \hline Interior node & \\ \hline Internal corner node with convection & \\ \hline Plane node with convection & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Summary of nodal testing conducted. Row 4--External corner node with convection (all boundaries are conduction except 1, 2, and 6):  
Row 5--Insulated node or surface of symmetry (all boundaries are conduction except 2 is insulated):  
As shown in Table 12, the code is not limited to solving heat conduction only, it can be used for convection as well. As mentioned in the conclusion section, despite the disparities between the results in ANSYS and the code, it highlights the underlying limitations of the code. Hence, the similarities in results do outweigh the differences as the differences only occur on the boundaries where convection is applied. Through extensive nodal testing, it has been observed that all nodal equations integrated into the Python script function effectively, exhibiting a degree of accuracy comparable to results generated in Ansys simulations. Notably, as the number of boundary conditions increases in the Excel sheet, the Python script requires more iterations and time to complete the Gauss-Seidel iterations. Nevertheless, it stands as a viable alternative to other software for 2D steady-state conduction heat transfer of irregular shapes, given its accessibility as free and open-source software. The Python script demonstrates capability in simulating 2D steady-state conduction heat transfer on irregular shapes with diagonal lines by amalgamating various node types involving convection, as outlined in Table 6, to simulate diagonal boundary conditions where convection occurs. While the interior node equation suffices for conducting heat on diagonals, the script faces limitations in simulating insulated planes on diagonals due to constraints in Equation (13), applicable only to nodes aligned in straight horizontal or vertical lines. Notably, for testing conducted on irregular shapes with diagonal lines, material properties assumed for structural steel--specifically, an h value of \(25\,\mathrm{W}/\mathrm{m}^{2}\)\({}^{\circ}\)C and a k value of \(60.5\,\mathrm{W}/\mathrm{m}\)\({}^{\circ}\)C--are utilized, sourced from the materials database within Ansys GRANTA Edupack software. The boundary conditions and results obtained to assess conduction on irregular shapes with diagonal lines are depicted in Figure 12a, alongside outcomes derived from both the Python script and Ansys simulations in Figure 12b. The boundary conditions and results produced to test for convection on irregular shapes with diagonal lines are shown in Figure 13a together with the results produced by the Python script and Ansys in Figure 13b. Figure 12: Irregularly shaped model used to test for conduction on irregular shapes with diagonal lines. (**a**) Boundary conditions applied with simplified Excel model designer.