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In order to check that the net heat flow to the domain is zero, we need to export the data heat flux from the bottom and right edges to MATLAB for numerical integration. Insert Directional Heat Flux results along the Right Edge. (Right Click) Solution > Insert > Thermal > Directional Heat Flux. Rename this result qx at right edge.

Choose Path for the Scoping Method, set Right Edge for the Path and X axis for Orientation, as seen below. 

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

The next step is to export the data to text files that can be read into MATLAB.  To do so, select qy at bottom edge. In the tabular data displayed in the bottom right corner, (Right Click)> Export. Save the file as We already exported qy at the bottom edge to qy_bot.txt on the Desktop. Similarly, save the data for export qx at the right edge as to qx_right.txt.

We have written a MATLAB script that reads in the ANSYS results for data files containing heat flux along the bottom and right edges and does the necessary numerical integration to calculate the total heat flowflux. Download the MATLAB script by right-clicking the link and saving to the Desktopdirectory containing qy_bot.txt: post.m. Running the file will graph the heat flux along each edge, as well as calculating calculate the total heat flow 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 in the tree, change the element size in sizing and click on Solve. The plot below contains information from 1x1, 2x2, 3x3, 5x5, and our 10x20 element mesh.  Note how as the mesh elements get 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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