Well, there are many factors to this. Heat conductivity is only one part of a large picture. The thermal conductivity of glass is 500 times less than that of copper, but you don’t expect the boiling time to be different by 500 fold.
If we take a step back, there are at least three steps. a) The energy transfer from gas flame to the bottom of the pot. b) the energy transfer from the bottom surface of the pot to the top surface of the pot (basically, your aluminum and copper disc). c) the energy transfer to the water.
So really, what you pointed out is the second part and it is a small part compared to the other two.
In addition, don’t forget that we are talking about copper disc and aluminum disc sandwiched by stainless steel. With the stainless steel there, a lot of things are much closer.
Citing some conductivity numbers (W/m * K)
Aluminum 205
Copper 385
Steel 50.2
So the thermal resistivity numbers are:
Aluminum 0.0049
Copper 0.0026
Steel 0.020
As you noticed, steel’s resistivity is much higher than those of aluminum and copper. So when you combined them together (like layers of steel and aluminum or layers of steel and copper), then the steel is likely to play a big role in thermal resistance. Or in other words, your conductivity in that cladded material can be largely influenced by the steel.
