Seth Olsen brought to my attention an interesting paper Quantum tunneling affects engine performance.
The authors consider a specific chemical reaction that occurs in diesel engines. The rate of this hydrogen abstraction reaction, shown below, is modified by quantum tunneling below the energy barrier associated with the transition state.
This reaction is one of hundreds happening in an engine but it turns out the ignition time of the diesel engine is quite sensitive to the rate at which this specific reaction occurs. The authors estimate the ignition time could vary by up to ten per cent due to tunneling.
I don't know anything about diesel engines.
But I do see a little bit of a falsification problem with the papers claim. The reaction rate also varies with small changes in the barrier height [see Table 1]. The latter is difficult to calculate accurately. One way to separate out the effect of tunneling is to do an isotope substitution. Deuterium will have less tunneling than hydrogen. But, it also has a different barrier due to the zero point correction. Similar issues come up in trying to establish the contribution of tunneling to proton transfer reactions in enzymes.