Ok, here's some very basic maths with made up figures:
Assume the room temperature is freezing (0 degrees C)
LOSS OF ENERGY
The tank loses 0.1 degree of heat every minute, to the atmosphere, because of poor insulation.
Therefore it takes 1000 minutes (16 hours) for the tank to return from 100 degrees to 0 degrees C.
HEATING THE TANK
To heat the tank by 1 degree takes 0.01kWh.
So to heat the tank to 100 degrees takes 1kWh.
The immersion heater runs at 1kW, and therefore it takes 1 hour to heat the tank to 100 degrees from room temperature.
Loss of heat during this time is 0.1*60 = 6 degrees (we'll ignore this to keep stuff simple!)
HEATING THE TANK ONCE PER DAY OVER TWO DAYS
The tank is cold (0 degrees)
I turn the immersion on for 1 hour.
The tank reaches approximately 100 C.
1 kWh used
I turn it off.
The tank is cold 16 hours later (1 KW required the next day to heat the tank again)
I repeat the next morning
2 kWh used in total
HEATING THE TANK UP THEN MAINTAINING TEMP OVER 2 DAYS
- I turn the immersion on for 1 hour.
- The tank reaches approximately 100 C.
-
1 kWh used
- I leave it on
- The tank loses 0.1 C / minute
- 0.1 * 2880 (minutes in 2 days) = 228 C lost in total
- To heat 228C costs 228 * 0.01kW = 2.28kWH
3.28 kWh used in total
So, ignoring water usage, with these figures it's more efficient to heat the tank once per day.
More things to consider:
INSULATION
As we increase the efficiency of insulation (less C lost per minute), the figures converge on the same value. This value is 1kWh, the amount required to heat the tank up from cold. No energy is lost, it never needs to be switched on again.
So the more efficient the insulation, the less difference in energy use for each method, though heating once per day is always more efficient, up until 100% efficiency of insulation.
TEMPERATURE LOST
In reality, temperature is lost more quickly at higher temps. So it requires more energy to maintain the tank at 100C then it would at 50C, for example. So the heat loss is not linear, and therefore, the notion of the tank losing 0.1C/minute at 100C is unrealistic. If the insulation was this inefficient, the figures would be more like:
1 C lost per minute at 100C
0.1C lost per minute at 50C
0.01 lost per minute at 10C
So to maintain 100C, in this example, would require 10 times as much energy (30kWh). These figures aren't accurate, but again they show maintaining temperature at the hottest point uses large amounts of energy.
WATER USAGE
Usage of water replaces hot water with cold. It is effectively the same as reducing the quality of insulation. i.e. it just increases the heat loss per minute value. So with water usage taken into account, heat loss is greater (by an variable value), requiring more work to maintain the temperature.
There is no way to adjust the above figures to make it more efficient to keep the water hot. The only thing you can do is make it AS efficient, by eliminating any loss of energy by using perfect insulation.
I appreciate the maths/physics above is not perfect science, but it follows the basic principles, and I don't believe there are any other variables that affect this.
hehe. I'm glad I finally demonstrated that to myself with actual figures.
