The question was somewhat unclear, at first I was assuming the question was about installing a wind turbine to a car to make motive power. Yes, somewhat counterintuitively, such a wind powered car will work if properly designed, even if you have a headwind! No law of physics would be violated: conservation of energy is satisfied and the conservation of momentum is satisfied (you are using the wheels to transfer the momentum of the wind to become added momentum of planet Earth). The performance of such a wind-powered car would be horribly low, though (I expect any wind turbine whose weight the car is capable of supporting would result in at most 1 km/h speed, probably much lower than that).
However, if I understood the question correctly, it was instead about using some magical fan thing to help the alternator, relieving the engine from working hard to power it.
There are very well-established laws, the first and second laws of thermodynamics.
The first law of thermodynamics is the conservation of energy. You cannot create or destroy any energy, you can just change its form (note: mass is one form of energy according to Einstein). If you install a fan, you have to power it somehow, e.g. with electricity. Any energy you use to drive the fan can reduce the energy to run the alternator, but that energy has to come from somewhere. It is coming from the battery, charged by the alternator, driven by the internal combustion engine. So, the very engine whose load you are about to decrease has to drive the increased load of the fan.
Typically, the efficiencies are nowhere close to 100%. In this very setup, I assume the "help" to the alternator would be so minimal that >99% of your energy would be wasted and less than 1% of it would actually help the alternator.
The second law of thermodynamics says that disorder (entropy) only increases and never decreases. This gives the maximum efficiency for heat engines and refrigerators / AC systems. For AC and refrigerator, it can be over 100%, but for an equivalent heat engine, it is less than 100% by the same amount, so that the AC/refrigerator efficiency times equivalent heat engine efficiency is always at most 100% -- so no free lunch there, either.
Both of these laws are extremely well tested. Any violation of these laws could be exploited to demonstrate a working perpetual motion machine.
So far, nobody has demonstrated a working perpetual motion machine despite numerous attempts. By the sheer number of people attempting it, I'd say these laws are the best-tested laws of physics.
There are, however, some ways to obtain wasted energy in a car, turning it to useful energy:
- Turbochargers use exhaust energy and exploit it to cram more air into the engine, creating more power and better fuel economy
- In theory, you could use a device similar to a turbocharger to create electricity, charging the battery.
- The turbocharger should make it apparent that the exhaust contains lots of wasted energy. A better cycle such as simulated Atkinson cycle instead of Otto cycle can help to turn more of that energy into motive power (and is used at least in Toyota hybrids).
- The efficiency of an alternator is actually quite poor. Modern hybrids use motor-generators instead that have better efficiency.
- Regenerative braking can charge the battery, turning braking energy into useful energy.
By the way, if you think you could omit the fan and drive the wind turbine by the headwind a car typically experiences when driving fast, that would increase the wind resistance, thus increasing the load of the internal combustion engine.
