In the frame of the creation of a thermal software tool at the FH Aachen a conductive calculator has been established in the form of a MATLAB program. The motivation was the implementation of star coupling links. Generally, the proper calculation of linear conductors is a crucial part of the analysis process and determines the quality of the results to a large extent. For the time being, the focus in this work has been set on quadrilaterals and triangles. The difficulty lies in the proper calculation of the conductors in combination with the differing shapes of the discretization. The results obtained from analytical methods, commercially available tools as well as the methods developed in the course of this work clearly identify a common trend. Especially problematic is the calculation of triangles as they are not easily described by analytical means but they are significant to the variability of the model discretization. Hence, they are inevitable. The quadrilaterals produced mostly satisfying results but among the highly deformed quadrilaterals divergences could also be seen.
Still, it appears that the impact of triangles is much greater. As a result, the major focus of this work is on triangles to reduce the errors they impose. In this work a new method to calculate triangles has been developed and is currently being verified and tested along with multiple others. One of those is especially suited for quadrilaterals developed in the course of a diploma thesis at the TU Munich and another general method was developed earlier on in this project which uses the geometric center as a reference. While the latter two methods heavily depend on the geometry of the thermal nodes, the method developed in this work for triangles uses a different approach. The triangle is being tightly suspended in the middle of a rectangle as shown in Figure 1. Doing so divides the rectangle into two quadrilaterals adjacent to the triangle in the middle. Those and the outlining rectangle are analytically solvable and thus the conductor of the triangle can be deduced. Repeating the process along every edge results in a system of conductors that can be converted into an equivalent system of conductors originating from a non-geometric center to each edge using the general equation for star couplings.
For the proper verification of the methods, simple shapes like the strip shown in Figure 2 yield the advantage of an analytical solution and thus are used for the verification. Further the shapes are discretized by a fine mesh and processed using the FeMap internal steady state solver. These results are included in the verification and used as a reference as well. For additional testing more complex shapes are considered now using FeMap as the reference as analytical solutions of these are difficult to find.
The results of the work and a demonstration of the current state of the developed program will be shown in the presentation.
Figure 1: A triangle suspended in quadrilaterals along each edge
Figure 2: Two equally long strips with the same properties and heat loads but different discretization