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The analytical solution is contained in this csv file that contains the concentration (or equivalently, the temperature) at various radial locations.

In addition, here are the analytical solutions for alpha = 1 and alpha = 3/2.

Mesh Refinement & Smaller Pseudo-timestep

Under construction

Validation

It is always a good habit to check that the mesh is refined enough. For example, you could use an element size that is half of what was used in the videos and compare the results.

When using pseudo-transient, it is important to make sure that you are using a small enough pseudo-time-step. For example, you could use a pseudo-time-step that is half of what is used in the videos and compare the results, or you could also use one that is twice as big as what is used in the videos.

Validation

We do not have any experimental data for this problem.Under construction

References:

Under construction

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