the form of a kettle What is the best form for a kettle, that is, to have the water boil the fastest? I am particularly interested in the following case: for one given kettle (whose volume is constant) containing different volumes of water.
I do not like to wait for my coffee in the morning.
[EDIT] Suppose that the heat source is uniform and flat only under the kettle.
 A: Well, I'd say have a thin flat base of a well-heat-conducting material as big as your heat source (to maximize heat transfer to the water) and a well-insulated sphere cap (for minimum surface area to minimize heat loss) of your specified volume on top. 
If everything but your base is adiabatic you don't even have to care about the form of the kettle :-P
A: Industrial steam generators in power applications do, in fact, look rather different from your ordinary steam kettle.  Here is an example image.

There is a lot going on here, but the important part to focus on are the thick vertical lines that represent a "baffle" that separates the inflowing feedwater + recirculated saturated liquid from the steam generating region.  At this point I'm almost sure you have no idea what I'm saying so I should start from the top.  The "hot side" is the "primary coolant" marked on the image.  The function of the steam generator is to boil the "secondary" water with the heat from the hot side.  The incoming secondary water is called the feedwater.  This flows over tubes containing the hot liquid and partially boils.  After it partially boils, the steam bubbles are separated from the liquid part and the steam is taken to where it will be used and the liquid is sent back to flow over the hot tubes.
It is possible, although not assured until engineering analysis is done, that a "baffle" type of structure could improve the performance of a kettle as well.  It would be a cylindrical structure close to the walls, resting above the bottom of the kettle, with a top below the water surface.  The reason has to do with the circulation.  In a kettle, gravity performs the function of steam separation and circulation.  As I'm pointing out here, industrial steam generators use gravity (sometimes with the aid of pumps) for the task of circulation and steam separation but the functions are distinguished in the geometric design of the apparatus, which is carefully optimized to obtain better performance.
In a ordinary kettle, no internal structures are present so the liquid, powered by density difference between hot and cold, mixes however nature intends.  It is still possible in this configuration that fairly local isolated hot and cold eddies will form which is less efficient for mixing, and the baffle structure could largely prevent that.
A drawback, however, is that using a baffle causes the steam to separate more efficiently which is actually undesirable in a kettle.  The function is usually to produce hot liquid, not steam, and designs with a baffle would produce steam sooner while leaving the rest of the liquid further from boiling point.
