When you consider analytical solutions to heat transfer in welding with (for example) the source term as a double-ellipsoidal, sometimes one coordinate have the "-vt" and the heat equation in unmodified. But sometimes the heat equation is modified to include a flow term coming from a transformation due to a moving solid model. What is the correct approach? I believe that this has to do with the frame of reference, one moving with the source and the other fixed, but I am not sure. Can anyone help me?

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