I found the photo on the Internet:
And I'm wondering. How is it even possible? Does this technique have a name? Any thoughts how to do it?
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You probably need a 3D modeling tool that can emit flames and smoke. That fire is actually more smoke-y than fire. Then create a rough sketch of the model, and simulate the burning.
Now, the more realistic your simulator is, the better it will look, obviously. The best simulators use very complex fluid simulation to achieve good results. E.g. see this simulation. 4 second from 5 hours of fluid simulation with 12000000 cells....
The other way is just to get photos of fire with transparency, and composite that over the model. You can end up with good results if you have good PS skills. Even better if you can paint over, as I think the image also has manual painting in it.
UPDATE: I stumbled upon this tutorial, and maybe this is exactly what you want...