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re: cooling the home
9 jul 2002
alan gottschald  wrote:

>i live in upstate ny, when it's hot it tends to be humid...

nrel says the average daily july temp in syracuse is 70.4 f, with
an average daily max and min of 81.7 and 59.0 (vs 67.2 in phila,
where night ventilation works most of the time) and humidity ratio
w = 0.0114, ie pa = 29.921/(1+0.62198/w) = 0.539 "hg... 75 f air
at 100% rh has ps = exp(17.863-9621/(460+75)) = 0.887, so warming 
outdoor air to 75 would make the rh 100pa/ps = 61%. not bad. you
might lower it more with a window ac with restricted airflow.

>we have a modern factory built house, it's well insulated... in summer
>it gets warm and retains the heat. short of putting mirrored panels on
>the roof and windows and forcing everyone to turn off every applience
>(computers,tv's and such i'm at a loss on how to cool it down cheaply.

more cfs vs incandescents could help, and external window shading and
a whiter roof and more attic ventilation, eg holes in soffits and gables.

a 500 btu/h-f house using 528 kwh/month (2500 btu/h) of indoor electrical
energy would be 2500/500 = 5 f warmer than outdoors, on average, with no
deliberate heating or cooling. a 2000 cfm fan would raise the conductance
to about 2500 btu/h-f and reduce the indoor-outdoor difference to 1 f... 

is there a basement? a square foot of concrete d inches thick has an
r0.2d resistance and about 25d/12 btu/f of capacitance, so rc = 0.42d^2,
0.42 h for 1", 1.6 for 2", and 3.75 for 3", with c = 25x3/12x2048ft^2
= 12.8k btu/f for the floor and walls of a 32x32x8' basement. say we
cool it with 61 f air for 6 hours on an average night with a fan and
turn off the ac and circulate air between basement and house during
the day if the house rh is less than 60%...

with 1.5 btu/h-f-ft^2 of wall conductance to slow-moving air and r0.3
of concrete conductance, the basement wall's resistance is about
(2/3+0.3)/2048 = 0.000472 f-h/btu. a 2k cfm fan adds 1/2k in series,
for a total conductance g = 1029 btu/h-f, with rc = 12.4 hours. 

if the basement cools from td (max) to tm = 61+(td-61)exp(-6/12.4) from
midnight to 6 am and the average outdoor temp from 6 am to midnight is
73 f and the constant house temp is th, it needs 18h((73-th)500+2500)
= (td-tm)c btu of cooling for 18 h, so th = 78-1.42(td-tm).

assuming td = 73 f, tm = 68.4 at 6 am, and th = 71.5. if td = 71.5,
tm = 67.5 and th = 72.3. td = 72.3 makes tm = 68.0 and th = 71.9, so
tm = 67.8, then 67.84, then 67.78, so it looks like the house could 
be 78-1.42(71.98-67.78) = 72.03 f over a long string of average days. 

a larger fan could keep it cooler. at 4k cfm, g = 1385 btu/h-f, so
rc = 9.2 hours. td = 71 f makes tm = 66.2, then 66.3, so th = 71.1.

we might add some sealed 4"x10' pvc water pipes under the rafters to
increase the mass. with 56 pounds of water and 10 ft^2 of surface and
1.5 btu/h-f-ft^2 in slow-moving air, rc = 56/(10x1.5) = 3.7 hours,
like the basement walls... 100 pipes would make c = 18.4k btu/f and  
g = 1900 btu/h-f at 4k cfm, so rc = 9.68 h and th = 78-2.04(td-tm),
which leads to tm = 65.8 and td = th = 70.

nick




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