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re: a.c. house holds heat?
27 aug 2001
jean p nance   wrote:

>    we live in a very well  insulated house with central air conditioning.
>it is small, 940 sq feet, and a.c. costs are not high. in summer we tend
>to set the thermostat at 76 or 78. if nights are hot, it may run a bit all
>night, to hold the thermostat temperature.
>    now that days are still hot but nights are cooler we have a problem.
>even with a few windows open, when the temperature goes down into the
>60's at night, or even the 50's, the house holds its heat. last night we
>forgot to set the thermostat back to 74, left it at 77. this morning,
>with an outdoor temperature at 66, the house was still 77  when we woke
>up. it just won't cool down. is this just stored heat in walls and

could be, and that could be an advantage in weather like this.
if the house can store heat it can store coolth.

>can anyone suggest a remedy?

maybe you need to move more nightime air through the house. to find out,
you might measure the indoor air temp tis, wall temp tm, outdoor air
temp ta, and exhaust air temp tx. the thermal mass of the walls tries
to cool off through an internal airfilm conductance u (which can be
raised, ie improved, with a ceiling fan) in series with a ventilation
airflow conductance h... (tm-tis)u = (tx-ta)h, with h in cfm.

steve baer says this equation is useful because if you measure tx and ta
and approximate tm and tis and find that u/h = (tx-ta)/(tm-tis) is large,
say 3 or more, you know that you can greatly benefit by increasing h,
that is by increasing the airflow through the room.

consider a 10' cube with r20 insulation (g = 600ft^2/r20 = 30 btu/h-f)
and 600 ft^2 of 1" drywall (c = 600 btu/f, and rc = 20 h) and a fan that
moves h cfm of outdoor air through it during the night, with a ceiling
fan that makes 130 fpm (an upper limit where papers begin to fly) near
the walls and ceiling so u = 1200 btu/h-f near the mass surface. 

if q = (tm-tis)u btu/h flows out of the mass and the indoor air temp
tis = ta + q/h/2, then q = (tm-ta)2hu/(2h+u), right? so dtm/dt = -q/c
and tm = ta+(tm-ta)exp(-t/tau), where tau = (2h+u)c/(2hu), for cooling.
making tau 3 hours requires h = 120 cfm, 1.2 cfm/ft^2 of floorspace.

nrel says phila has 67.2/76.7/86.1 average min/24h/max temps in july,
something like 72 f average at night and 81 during the day. if the mass
has temp tmd at dusk and tmm in the morning, 12 hours later, tmm
= 72+(tmd-72)exp(-12/3) = 70.7+0.0183tmd and tmd = 81-(81-tmm)exp(-12/20)
= 75.4-0.01tmd, so tmd = 76.1 and tmm = 72.1, with 78% rh at dawn (ick.)
more mass or insulation or airflow would lower the temps. some licl
could lower the rh...

>we are now considering a  couple of solar fans on the roof.
>easier to install than electric but they won't run at night.
>what about just wind powered roof fans? 

holes in the roof are good, especially in 2-story houses.
cfm = 16.6avsqrt(hdt), with a vent area av in ft^2, an
elevation difference h in feet, and a temp diff dt (f).


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