How to explain why aluminum won't work on an induction stove?

A induction stove is a high frequency transformer. The primary winding is built into the stove, the secondary winding is the bottom of the pot or pan placed on it.

In principle, such a transformer works with all types of conductors as the secondary. The problem is, you want to have a high electric resistance in the secondary. Because that high electric resistance is what produces the heat inside the bottom of the pot or pan.

And here's where aluminum and copper drop out. They are good conductors and have a low electric resistance.

Iron in contrary has a very high electric resistance because of one special feature: because it's ferromagnetic AC currents can only flow in a very thin layer below its surface. This is called the skin effect. Again, every metal shows that skin effect, but for iron it's 80 times higher than for aluminium and copper. And so is resistance and heat production.

That's why you need an iron sheet in the bottom of your pot or pan.

Induction cooking works by inducing a field in the metal of the cooking container so that the resultant currents cause energy dissipation.

For metal in the order of say 3 to 10 mm thick, at low enough frequencies the induced fields occur throughout the metal.

As the frequency is increased the heating zone occupies an area increasingly near the exterior of the metal due to what is known as 'skin effect.
Good Wikipedia discussion here: "skin effect".

Wikipedia says:

• Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor, and decreases with greater depths in the conductor. The electric current flows mainly at the "skin" of the conductor, between the outer surface and a level called the skin depth. The skin effect causes the effective resistance of the conductor to increase at higher frequencies where the skin depth is smaller, thus reducing the effective cross-section of the conductor. The skin effect is due to opposing eddy currents induced by the changing magnetic field resulting from the alternating current. At 60 Hz in copper, the skin depth is about 8.5 mm. At high frequencies the skin depth becomes much smaller.

and, crucially:

• Skin depth also varies as the inverse square root of the permeability of the conductor. In the case of iron, its conductivity is about 1/7 that of copper. However being ferromagnetic its permeability is about 10,000 times greater. This reduces the skin depth for iron to about 1/38 that of copper, about 220 micrometres at 60 Hz. Iron wire is thus useless for AC power lines.

This combination of features, that leads to high losses in iron compared with copper, makes it useless for low loss power transmission lines BUT superior for causing inductive losses and heating when using the best practically available technology.

However, one of the factors in losses in material is the frequency of the AC field. As the frequency increases the skin depth decreases, the resistance of the conducting material increases accordingly and losses increase. For copper skin depth with frequency varies as shown in the table below. :

Skin depth in copper

[Table from Wikipedia. ]

At present consumer market power switching semiconductors are limited to maximum switching frequencies of around 100 kHz by economic considerations. Frequencies in this range re entirely adequate for heating iron cooking equipment. Typical frequencies in use are in fact in the 20-100 kHz range with around 25 kHz being common.

When (or if) developments in semiconductor switches allow economic power switching at frequencies in the 1 to 10 MHz range copper skin depths will be reduced, compared to that at 20 kHz by a factor of about 10 to 30 times. This would reduce the Copper skin depth to about that of Iron at 20 kHz. Due to the higher resistivity of iron the losses and thus the heating in Copper would still be lower but probably high enough to allow innovative Copper based heating solutions to be developed.

Copper compared to Alumium / Aluminum / Aluminium *

Aluminum skin depth is about 1.25 x that of Copper.
Aluminium resistivity is about 1.6 x that of Copper.
So Alumium heating at the same frequency is liable to be about 25% more than for Copper. Which is close enough to identical given all the second order affects liable to be encountered.

• Re Alumium / Aluminum / Aluminium - blame Sir Humphry Davy :-)