"Spehro Pefhany" wrote in message
...
On Thu, 29 Oct 2009 12:46:13 -0400, "Ed Huntress"
wrote:


"Bill Noble" wrote in message
...


"Ignoramus10802" wrote in message
...
On 2009-10-29, Pete C. wrote:

Ignoramus10802 wrote:

On 2009-10-29, Stormin Mormon
wrote:
Please forgive me while I troll for a moment.....

Is it energy saving to turn the thermostat down, when
leaving the house? I mean, the furnace has to run to catch
up when I get home. I have a way of looking at the matter.
I'll explain my point of view after the argument is
underway.


Imagine for a minute that you have to leave house for a month.

Would it be energy efficient to turn thermostat down? Of course, as
less heat will be produced for a whole month, with only a few minutes
to catch up.

The same applies to only one day.

i

It's far more complicated than that. Factors such as insulation / heat
loss, type of heating, multi-stage heating, electric backup heat on
heat
pumps, etc. all come into play in determining the away duration and
temp
reduction where savings begin, and in some cases (typically high
efficiency homes) it can require a multi day absence to see any
savings.

This is patently untrue.

I

Correct - whatever the net effect of insulation is, there is a net
negative heat flux from the house to the outside. The flux is
proportional to the temperature difference (the exact equation will
depend
on the radiation, convection and conduction components - radiation alone
is governed by the Stephan-Boltzman equation). The larger the
difference
the greater the flux. Averaged over any period of time, any time spent
with the thermostat set lower will yeild a lower internal temperature,
hence less heat flux. Whether that is enough to show up in your bill is
another question, but from a energy savings point of view, it is
incontestible.

The confounding issue, though, is the thermal mass of the house. That's
why
the DOE explanation says that the savings occur when the temperature
inside
the house has stabilized at the lower temperature.

When you shut off the furnace, the thermal mass of the inside of the house
is what's giving up heat to the outside. That's stored energy that came
from
the furnace heat. When you raise the temperature, you have to restore that
heat to the thermal mass. So with the furnace off and the temperature
inside
of the house dropping, you're losing stored heat. When you turn the
thermostat back on, you have to restore that lost heat, which will also
heat
up the atmosphere inside of the house (which is a very small portion of
the
total inside thermal mass).

That's what I read from their description, anyway, and it comports with
things I've read about it from other sources. There is no (theoretical)
net
gain or loss when the thermal mass is put through the cycle of cooling
down
and heating up. The savings occur when the temperature is reduced and
stabilized.

The furnace is supplying an average of so many BTU when it is running
(assuming the usual on/off type of furnace).

The house is losing so many BTU when it is at temperature T0 inside,
and the losses will always Be LESS when the temperaure is closer to
the outside temperature (assumed to be lower, of course).

Right. But the integrated savings over time will be around half (without
doing the math) of what one would have if the temperature of the house
actually dropped to its final temperature and stayed there for a long time.

In other words, if the house temp keeps dropping through the day to, say, 55
deg F, and then you set the thermostat back up to your normal temperature of
70, the whole cycle is one of loss from the thermal mass, then restoration
of the heat stored in the thermal mass. If your house is well-insulated, you
wind up with half of the savings (slightly more; it's a calculus problem and
the physics involve exponential decay, but averages will do for this
discussion) you'd have if you either left the thermostat set at 55 for a
couple of days, or if you had a lightly-built house with poor insulation and
the temperature dropped quickly when you turned down the thermostat.

According to DOE (and I've seen that information before), the savings
resulting from shutting off the furnace over a short period of time are
quite small, even on a per-hour basis, because the mean temperature of the
house is a lot higher than its temperature when you come home. They say
that, on the average, lowering the temperature 10 - 15 deg during the
workday, and lowering it again to some unspecified lower temp while you
sleep at night, saves, typically, 10% of your heating bill.

Just as an example, say you saved 10 cents/hour when the temperature of the
house remains at 55 over several days. But if you let it drop to 55 and then
immediately turn up the thermostat to 70, you only save 5 cents/hour. And
you have to wait for the house to heat up.

And here's a more telling example. Say the temperature outside is 50 deg,
your normal house temperature is 68 deg., and your house is well-insulated
and contains a lot of masonry, plaster walls, and other stuff with high
thermal mass. You shut off the thermostat completely when you leave for work
in the morning. When you come home, you turn it back up. The temperature in
the house is 60 at that time. I think everyone can see that the savings due
to the mean temperature differential is quite small. But many people are
going to think that, because the furnace was off all day, they're saving a
day's worth of fuel. Not.


When the house is cooling, the thermal mass is supplying part of the
heat to the outside.

If your furnace is *off*, the thermal mass is supplying 100% of the heat to
the outside.

When the house is heating up, the furnace is
supplying heat to warm the thermal mass, PLUS the heat which is being
lost to the outside.

Right.


The heat lost to the outside during the cooling *that is supplied by
the thermal mass* is made up for that part of the heat supplied by the
furnace to heat the house back to T0, so that part IS a wash.

Right.


What's missing is that for for every second the house is at a lower
temperature than T0, the heat loss to the outside is less, so even if
it cools down and immediately is heated up there will be an energy
saving.

Yes, but a much smaller one than most people would think, since their
furnace was off for a whole day.


If it was linear (which it isn't, but bear with me) then say the
outside temperature was 25F and the internal temperature was 75F.
The loss is k*(75-25) = k*50, where k is a constant. Now allow the
house to cool to 50F over an hour, then heat it back up again to 75F
over another hour. The heat loss to the outside during that time is
k*(62.5-25) = 37.5*k, which is 25% less (62.5F is the *average* inside
temperature over those two hours).

Right. So it's 25% less heat loss than you have at your normal temperature,
even though the temperature inside the house dropped to 50 deg. But most
houses don't lose heat that quickly. As a practical matter, you're only
gaining around half of what some people would expect by letting the
temperature drop to 50 deg and then heating the house back up.

Chances are the heat loss is
actually worse than linear (convection and radiation are worse, and
conduction is linear), so this should be conservative. Now if it's 25%
of 2/24 of a day, that's not very much (about 2% saving) but it is
going to be a saving.

Without getting into the math or the other routes for heat transfer, the 2%
is the point. You need to let the house stabilize at the lower temperature
before you're getting the kind of savings that most people think they should
get.


This all assumes that a house is decently insulated and that the thermal
mass of the house is substantial. Of course, the thermal differential
between the inside and outside temperatures are always at work, suggesting
that there is less heat loss with each degree of reduction of inside
temperature, as you say. But the DOE's reference to actual testing agrees
with the fact that, as soon as you turn the thermostat down, you begin
losing *stored* heat, and when you turn it back up, 100% of that lost heat
must be restored, regardless of actual thermal losses through the walls
and
ceiling.

Yes, that *part* of it is a wash.