The bottom of a pan is made of a 4-mm-thick aluminum layer. In order to increase the rate of heat transfer through the bottom of the pan, a design was proposed for the bottom that consists of a 3-mm-thick copper layer sandwiched between two 2-mm-thick aluminum layers. Assume a perfect contact between the layers. Will the new design conduct heat better

Yes, the new product will not conduct heat better

Explanation:

The bottom of the former product is made up of a 4mm thick aluminum layer

The new design is made up of two 2mm thick aluminum layer with a 3mm thick copper layer sandwiched in between.

These two materials are great conductors of heat.

As for copper, if one end is heated , the other ends rapidly reaches the same temperature, Copper is known as the best conductor of heat, that is, allows quick heat transfer. This ability of copper makes it highly used in applications where quick heat transfer is important, like the saucepans where rapid heat transfer is required.

As for aluminum, it is also a great heat conductor and twice as good as copper.

But the heat conductivity of copper is greater than aluminum and this will allow  a faster heat transfer between the layers.