The video shows how nitinol can be used to convert a temperature difference into motion.
It is in effect a
heat engine.
It all depends on the temperature range for the phase transformation.
While the phase transformation can occur in a temperature difference window of just 20 degrees Celsius, the boundaries of that window are fixed
(the height of the range depends on the titanium/nickel ratio in the alloy).
Even if the range is not that big, the cooling temperature need to be at or below the fully flexed threshold and the heating at or above the fully recovered state. So you do need a well controlled stable heat and cold source.
Stirling engines, to name one other type of heat engine, do not have those limitations.
They work if there is a temperature difference and are usually not very sensitive to the absolute temperatures. A Stirling engine that runs when one side is scorching hot and the other just boiling hot may run just as well if one side is at room temperature and the other side freezing cold.
Nitinol can't do that.
There are pros, though.
As the material itself is the actuator, nitinol engines can be mechanically simpler than other heat engines. Some machines have no moving parts other than the nitinol itself, rendering them 'solid state' machines.
Nitinol is very deformable and very resilient; it can generate large pressure when heated mildly.
It seems to improve with age, as repeated use seems to help it perfect its alloy structure by forcing misplaced atoms into position. That also makes it very stable and long-lasting.
If the goal is to generate electricity, it still has to run a dynamo.
Seebeck generators do the same and are true solid state devices. They are not very effective though.
Anyhow, all these devices do more or less the same: convert a temperature difference to another form of energy.
The problem is not the heating side but the cooling side. The less hot you want it, the larger the cooling area needs to be; exponentially so. Yes we can get a few hundred Watts from tapping exhaust or coolant heat. But we need radiators about as big as the one used for the engine.
Likewise the A/C system has a radiator that is fairly large while the heat it sheds is just a tiny fraction of the heat that the engine produces. It needs to return colder fluid, so it needs to be relatively big.
We do not need a second A/C radiator just to gain back a few hundred Watt. The extra weight and cost would kill the benefit.
Nitinol is a nice material, but not likely to make it into cars for power scavenging purposes.
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