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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.

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How about an immersion heater? –  leftaroundabout Jun 17 '11 at 18:35
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You must also specify the form of the heat source, because otherwise I'd say: Maximize the size of the heat source and have a really flat kettle (more like a huge frying pan). This maximizes the surface that's in contact with the heat source. –  Lagerbaer Jun 17 '11 at 20:38
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I think Isaak wrote this question before he had some coffee in the morning. –  Georg Jun 18 '11 at 10:11
    
@Georg : funny, it's true I am quite tired for the moment. @Lagerbear : I edit the post. Thanks for your remark. –  Isaac Jun 20 '11 at 12:35
    
Is an automatic timer too prosaic? –  Jen Aug 19 '11 at 20:49

2 Answers 2

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

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Does it take into account the motion of the fluid? –  Isaac Jun 20 '11 at 13:28
    
No, but I'm not sure if this is relevant. You'll probably get Rayleigh-Benard cells for most shapes which are flat-ish ( i.e. optimize heat transfer from the heat source). en.wikipedia.org/wiki/Rayleigh%E2%80%93B%C3%A9nard_convection –  Christoph Jun 21 '11 at 15:11

Industrial steam generators in power applications do, in fact, look rather different from your ordinary steam kettle. Here is an example image.

Steam generator for thermal plant

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.

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Interesting picture! A steam generator with inlet/outlet of a coolant, but no heat source is to be seen, strange! And: what is the connection to the question of Isaak? –  Georg Jun 20 '11 at 20:39
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I'm suggesting that the best "form" of a kettle to boil water faster would possibly entail a flow separator. This is a possible improvement through the design of the device, whereas the only other advice I see here amounts to suggesting that the heat transfer coefficient be improved. –  Alan Rominger Jun 20 '11 at 21:24
    
Is it really possible You do not know what "heating water to boil" in the context of coffee making means? Isaak needs some hot water for his coffee, no steam! And again: where is the heat source in that steam boiler? –  Georg Jun 20 '11 at 22:22
    
@Georg the heat source is the primary coolant, as this is a steam generator design from a pressurized water reactor. The commonality is the need to mix the water using exclusively natural circulation. Exposing the lowest $T$ water to the heated surface is a common objective of both steam generators and a kettle to heat up water. With a flow path going upwards through a column and then down through a downcomer, the lowest $T$ water in the system is constantly being exposed to the heated surface. This is also true, but probably less-so in single phase mixing in an ordinary kettle. –  Alan Rominger Jun 20 '11 at 22:46

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