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In order to check that the net heat flow to the domain is zero, we need to export the heat flux from variation at the bottom and right edges to MATLAB for numerical integration. We already exported qy at for the bottom edge to qy_bot.txt. Similarly, export qx at for the right edge to qx_right.txt.

We have written a MATLAB script that reads in the these ANSYS data files containing heat flux along the bottom and right edges and does the necessary numerical integration to calculate the total heat flux. Download the MATLAB script by right-clicking the link and saving to the directory containing qy_bot.txt: post.m. Running the file will graph the heat flux along each edge, as well as calculate the total heat flux through each of the two edges.

We will also look at the results for the dimensionless temperature along the line y=1. To change the mesh size, go back to Mesh > Edge Sizing in the tree , and change the element size in sizing and click on Solve Number of Divisions appropriately. Click Solve. All results will be updated for the new mesh. The plot below contains information from 1x1, 2x2, 3x3, 5x5, and our 10x20 element mesh.  Note how as the mesh elements get gets finer (i.e. more elements,) the solution converges onto one line.  This is a trivial example, as it converges by 5x5 elements, but consider how mesh refinement can affect results in a complex system.

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https://confluence.cornell.edu/download/attachments/146918522/Convergence.png