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1) Given the following tank of water with four heating elements in two groups, A and B, where the elements in each group are switched on and off together, what is the optimal way to heat the tank of water from cold (e.g. 10'C) to hot (e.g. 65'C)?

2) Once hot, what is the best way to keep the water in the tank hot?

Water tank with heating elements diagram

The real life scenario is that I have an electric boiler which heats the water inside the tank and then when you want central heating it begins cycling around the system. For hot water it transfers the heat from the water in the boiler to the potable water on demand.

I run this thing for 10 hours a day, but I feel like that could be optimised (depending on usage, of course) but I'm trying to get my head around some basic stuff first.

Thanks in advance for any help!

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closed as off-topic by ZeroTheHero, user191954, Kyle Kanos, stafusa, John Rennie Oct 9 '18 at 16:25

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  • $\begingroup$ This seems to be more of an engineering problem than a scientific one, so you may get better answers posting in the Engineering Exchange. $\endgroup$ – Charlie Oct 8 '18 at 23:20
  • $\begingroup$ From an energy efficiency standpoint, I don't think it really matters how you divide a given amount of input heat energy among the two heater groups. For energy efficiency what matters is the amount of insulation that you have around the tank. To make sure that the heated water is well circulated in the tank, though, it may make sense to dump most or all of the heat energy into the lower heaters since hot water rises. I think that both gas and electric water heaters heat the water at the bottom of the tank, and that may be the reason. $\endgroup$ – Samuel Weir Oct 8 '18 at 23:47
  • $\begingroup$ Thanks folks - appreciate you taking the time to reply. $\endgroup$ – brindy Oct 9 '18 at 14:59

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