How much heat from a shower goes to heating the room?
We have a 9.5 KW walk-in shower and it heats up a chilly bathroom
without the need to switch on the 2kW wall heater.
I was wondering how much heat typically gets transferred from the hot
shower water to the room air?
I hoped this had been worked out before for an average shower giving
a rule of thumb which might have said a quarter (or whatever) of the
heat gets passed to the air.
The sort of statistic which might find its way into the newspaper or
get quoted, although I hadn't heard it.
As you can see from the formula I provided, the shower/room heat
transfer is determined by the shower flow rate and the temperature loss
in the shower stream.
The temperature change in the room will, in addition to the power
transfer to the air by the shower, be a function of room air volume, the
current air temperature, and any additional cooling/air change in the room.
Unfortunatly there will not be an average answer due to the variables
involved in each installation.
But I think I answered your original question about "how much heat
typically gets transferred from the hot shower water to the room air".
The short answer is that the loss to the air is negligible when comared
to the energy that went into heating the water - certainly not a quarter
- or even a tenth of that.
You are using a flow of water (lots of it with a high energy density),
to heat small amount of air with a low energy density.
That's because when you do the sums, its not really significant, and
ultimately not really that important.
You pay the money to heat the house, you can do that by heating water
and pumping it round some radiators, and by squirting it out of a shower
head in direct contact with the air. One can argue that the shower
heating the room is a bonus from a comfort point of view, even if not
from a condensation one.
You already have enough information. If it warms it up as effectively as
a 2 kW heater, it is 2 kW.
There is no *general* answer because it depends on too many parameters,
not least the flow-rate of any extractor fan.
I find the best combination is to run a dehumidifier in the room
whilst having a shower. The room gets nice and toasty, and I can
shave afterwards as the mirror doesn't fog up.
My dehumidifier is a condenser type that draws about 200w. But the
effect in a shower room seems much more than that, so I guess there's
quite a bit of heat coming from condensing the water vapour.
I did some calculations a while back, when I was thinking about
putting a heat exchanger/extractor fan in the bathroom - if I
calculated correctly, and recall correctly, most of the energy
will be in the water in the air, rather than the air itself. So
I stuck with the dehumidifier. I did make some rather off the cuff
assumptions about the amount of water in the air, though - something
like comparing the heat capacity of a litre or so of water to the
heat capacity of a bathroom-full of air.
In spite of various eminent contributions, I still think it is a pretty
daft calculation, especially if you have an extractor fan. Hot water
comes out of the shower, some of it evaporates (stealing a lot of energy
as latent heat). You extract this vapour which then dumps the energy
into the plume outside.
Of course you get it back if you run a dehumidifier inside, or if it
condenses on the walls and ceiling.
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