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I am completely clear on what you are proposing and have been for some time. My last post essentially proves that a car does not produce anywhere near enough hot gas to create a bubble of warm air around it and so any gas expelled forward will just remain in the boundary layer anyway. That would not modify the effective shape of the car and so CD would remain the same and the density used in calculating drag would remain the same free stream density as it is without any forward exhaust.
Now, supposing that the engine actually did make enough hot exhaust to generate a bubble of any meaningful size that would actually change CD (by changing the effective shape of the car seen by the free stream), that could possibly be advantageous purely from an aerodynamics standpoint. The bubble shape would have to be just right, though, as a car typically has a lower drag coefficient than does as sphere. However, even if this was done, you still have to push all of that incoming air out of the way to make space for your bubble, so the engine is now working extra hard to eject a stream of exhaust forward with enough force to create a bubble out in front of the car. Even doing this a foot in front of a car would require quite a bit of forward momentum in the exhaust. Now your forward exhaust, which requires more engine power to generate, is also acting as a forward-acting thrust. You've now double penalized yourself.
I also have no doubt that on a busy highway, the temperature will rise above ambient by a few degrees due to passing cars. Of course, this already happens, so it's not that much of an improvement.
Finally, if your car is driving into a warmer pocket of air, the lower density means your car engine is going to run less efficiently since it's taking in less air per volume for combustion.
Now, supposing that the engine actually did make enough hot exhaust to generate a bubble of any meaningful size that would actually change CD (by changing the effective shape of the car seen by the free stream), that could possibly be advantageous purely from an aerodynamics standpoint. The bubble shape would have to be just right, though, as a car typically has a lower drag coefficient than does as sphere. However, even if this was done, you still have to push all of that incoming air out of the way to make space for your bubble, so the engine is now working extra hard to eject a stream of exhaust forward with enough force to create a bubble out in front of the car. Even doing this a foot in front of a car would require quite a bit of forward momentum in the exhaust. Now your forward exhaust, which requires more engine power to generate, is also acting as a forward-acting thrust. You've now double penalized yourself.
I also have no doubt that on a busy highway, the temperature will rise above ambient by a few degrees due to passing cars. Of course, this already happens, so it's not that much of an improvement.
Finally, if your car is driving into a warmer pocket of air, the lower density means your car engine is going to run less efficiently since it's taking in less air per volume for combustion.