Which is a more efficient way to boil water – a shallow wide pot or a narrow deep pot? Assume the same amount of water, the same flame on the heating element (I use a gas stove) and that both pots cover the flame pretty much entirely and are the same material.
if the narrow pot extended well beyond the flame, so heat wouldn’t escape before being transferred to the pan then that would be more efficient because of less surface area to loose heat.
What about the sides of the pot?
Surface area always speeds up heat transfer.
A wide base means the pot can pick up more heat from the burner. But… after a certain size, any additional increase won’t produce much additional benefit.
A wide top could lead to more heat loss and evaporation, but putting a lid on the pot should minimize that.
It will depend on the size of the burner relitive to the pot.
More surface area of base = more transfer of heat. Think about the effect of more surface area of a heat sink.
My physics teacher in high school told us a story about a new type of pan he’d developed with some friends in college, which had a number of concentric rings on the bottom to increase the surface area dramatically. He said it worked very well but nobody wanted to produce it because it was very hard to clean.
That said, I think a classic kettle shape probably works best - it has a wide bottom with a narrowing top, and it’s almost completely closed.