You can’t do it with aluminium or copper at all. There will be no heat to conduct, so hold it as long as you like.
As an example, induction heating is a commonly used method in zone melting for Si-purification [0].
The effect is more pronounced in ferromagnetic materials because a larger flux is induced.
You can put a few mm thick piece of steel on top of the hob and then set your copper pan on that, as a workaround.