Last winter, standing in a cold kitchen pouring away a washing up bowl of warm water, I started thinking. We hear a lot about recovering heat from extracted air, but we allow a lot of warm-water to go down the drains. If my hastily-conducted ‘research’ is correct then water contains 4 times as much energy per kilogram as air (at the same temperature).
I’ll add the (probably wrong) maths and assumptions below, but so far I think a shower contains a potential 6800Kj for heating outside winter-air.
Even a toilet (which contains room-temp water) could have 336Kj.
From a kitchen you could extract air with energy of only 36Kj per hour.

So my question is: why do these systems not exist?

Some other points:
Do the sewers need hot water to flush out fats etc.?
Some air heat recovery systems claim efficiency of up to 95% which I don’t believe for a second. Are air-based systems more (or less) efficient than water-to-air ones? What is the temperature drop before water gets to the heat-exchanger?
Air systems will clog up with moisture, dust, and oils from sweat. Water-based systems could clog up very quickly with fats etc.
Showers, washing-machines, dishwashers, toilets are occasional-use, so make available a large amount of energy all at once, rather than a steady trickle throughout the day (but that energy is produced when the house is populated).

Water is commonly used to store thermal heat energy. Energy stored – or available – can be calculated as
E = cp dt m (1)
where
E = energy (kJ, Btu)
cp = specific heat capacity (kJ/kgoC, Btu/lb oF) (4.2 kJ/kgoC, 1 Btu/lbmoF for water)
dt = temperature difference between water stored and the surroundings (oC, oF))
m = mass of water (kg, lbm)
Room temp is about 20degrees. Outside winter temp averages 4c. Hot-water temp is about 55-60c.

A washing-up bowl contains 10litres. Temperature might be 45c when you pour it away.
That is 1050KJ of energy if heating up inside air, and 1722Kj when heating outside air.

A shower uses between 30-60 litres of water (I’ll assume 45 litres). Average temp 40.
That’s 6804KJ when heating up outside air.

Flushing a toilet uses 5 litres in a low-flush (13 litres in the old-style).
That’s 336KJ when heating outside air.
(Toilets receive water from the mains or a tank in the loft which will almost certainly be below room-temp, so the water takes heat from the room)

Heat-recovery from stale air:
Density of air is approx 1.2kg/sq.m . Heat capacity of air is 1Kj/kg (depending on humidity etc).
Average kitchen 30 cubic metres? One air change per hour in a kitchen?

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