to increase fuel economy by assisting acceleration?
Energy can be neither created nor destroyed but can be converted to various forms. Therefore it should be 'possible' to convert the heat energy wasted in vehicle exhaust into stored electrical energy, possible using a thermal pile, special battery and DC drive motor. The extra equipment would add weight to the vehicle increasing the fuel consumed and would have to be efficient enough to pay its own way.
Theoretically, this could be done, but the cost involved in practice would be quite high as to make the whole exercise not worth it. It might be easier to design fuel efficient vehicles which dissipate less heat than to convert excess heat from the engines into storable energy.
Yes, that is precisely what a turbocharger does. A good portion of the waste heat is converted to mechanical energy which is then used to pressurize the intake air/fuel charge. Modern vehicles, even without turbos, do a relatively good job of not wasting much of the heat energy. Some turbodiesels get up around the 50% efficiency range. That may not sound so great, but it does represent well, considering cost.
It is possible but not practical. If you consider the amount of energy available and the best efficiency of of any system that could be installed to harness that energy then factor in the loss of efficiency to the primary system (engine) due to extra weight and add in the cost of such a system, you end up with a negative. 2 extra points due to misinformation on other answers 1.A turbo does not recover heat from the exhaust. 2. A vehicle engine is a heat engine therefore its maximum theoretical efficiency is partly due to the ambient temperature at which it exhausts. If you put a heat exchanger on this to recover heat, you will raise the cold temperature of the heat engine and reduce its efficiency, therefore the only recoverable heat is the low grade heat from the engine body and cooling system.
The idea has merit. Theoretically the numbers work, and what ever you develop would take the place of the existing coolant system. Thus little additional weight would be created. Also, if the system could be efficient enough to account for sufficient generated heat, the vehicle profile may be able to eliminate the air passed through for the radiator heat exchanger. This would improve aerodynamic opportunities. Still, we need a material that would champion this thought.