Try this:
Create a long, narrow cylinder and parent it to the exhaust.
Apply a nearly transparent fractal texture (try Turbulence or Fractal Noise), stretched along the length and then animate the texture position.
In the transparency channel, you'll also want a gradient applied that makes the cylinder entirely transparent before it's end.
You'll probably want to apply a little refraction as well (and ensure you have ray trace refraction switched on in your scene).
This should be enough to get you going. Give it a try - tweak it - and post some renders for us.
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