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re: hair brained solar cistern???
14 dec 2002
toby  wrote:

>professor pine,

i'm not a professor, toby, altho it may seem so from your
incompetent viewpoint. you may improve. miracles happen :-)
 
>you wrote:
>"meanwhile, toby continues to simulate heat gain over months."

with changing weather. but the sand can only store enough house heat
for a few hours...

>you did the same, i quote a line from your computer program:
>
>    "for day = 1 to 200"

sure, to find steady state temperatures within a degree or so,
using the same weather every day. daestrom did this too.

>a-la-n's solar cistern has been working for the last 1.5 months
>providing 99% of the heat for the house.

has alan ever mentioned 99%?

>sure it won't provide 'nuff heat when it's -25f which requires 25k btu/hr.

as i recall, your claim was 25k btu/h at -20 f.

>it's been providing up to 15k to 20k btu/hr,  24 hours a day for
>the last 1.5 months.

would alan agree with this statement?

>...heat doesn't flow through 2 feet in an hour as your above model implies.

there you go again :-)

>you stated: "your head will probably feel better if you ignore
>toby's hairbrained traveling heat calcs. "

still true :-)

>daestrom tried to get it through you thick nick skull:
>
>" what you're not considering here nick is the slab's heat capacity. 
>most of the heat does not travel through all 2 feet...

the only heat that doesn't flow through the 2' of sand is the heat
that escapes through the bottom and edges. where does it come from?
where else would it go?

>> ...with moist sand... we might be looking at something like this:
>> 
>>                      t1        t2        t3
>>     0.00068   0.0011 |  0.0011 |  0.0011 | 0.00083
>> tw ---www------www---*---www---*---www---*---www--- 70 f
>>                      |         |         |       
>>                     --- 7200  --- 7200  --- 7200    i btu/h --->
>>                     ---       ---       ---
>>                      |         |         |
>>                      -         -         -
>> 
>> ignoring the sand resistance close to the pipe, the wall conductance
>> might be 10 btu/h-f-ft^2... 750' of 3/4" pipe with 147 ft^2 of surface
>> might have a 1470 btu/h-f conductance or a 0.000608 conductance...
>> 8xr0.083/600 = 0.0011, 20x600 = 7200, and 0.5/600 = 0.00083.  
>================================================ 
>
>3 errors:
>
>1. 20*600 = 7200????

...12k, a dumb mistake.

>2. 750' of 3/4" pipe????  ---- try 1000' of 3/4" pipe

ok.

>3. 'the wall conductance might be 10 btu/h-f/ft^2????

sure. that's reasonable for plastic pipe, but it doesn't include
the resistance of the sand very close to the pipe. sand with r0.083
per inch has k = 1/(12r) = 1. including 3" of sand around each
linear foot of pipe with 0.196ft^2 of wall surface makes r = 0.51
(for the pipe wall) plus ln(3/(0.75/2))/(2pik) [= 0.33], a total of
r0.84 for a foot of pipe, or 0.00084 for 1000' of pipe.

now we have something like this:

                      t1        t2        t3
     0.00084   0.0011 |  0.0011 |  0.0011 | 0.00083
 tw ---www------www---*---www---*---www---*---www--- 70 f
                      |         |         |       
                     --- 12k   --- 12k   --- 12k     i btu/h --->
                     ---       ---       ---
                      |         |         |
                      -         -         -
or this:
               t
     0.001184  |  0.00303
 tw ---www-----*----www----- 70 f
               |    -->
              ---    i
              ---
               |
               -

if the average heatflow is i and the (in and out) water temp tw = 135 f
for 6 hours per day, t = 70+0.00303i and i = (135-t)/(0.001184x24h/6h)
= 8369 btu/h, which makes t3 = 70+0.00083x8369 = 76.9 f. t2 = 86.2 and
t1 = 95.4.

if (70-ta)278 = 8369, it looks like the sand alone can keep the house 70 f
(for a short time) until the outdoor temp drops to ta = 70-8369/278 = 40 f,
and we'd have to waste heat by ventilation to keep the house at 70 f when
the outdoor temp is above 40 f. 

if we burn wood to keep the house air 70 f as we slowly extract every last
btu from the sand, the top layer can store (76.9-70)12k = 82.8k btu. the 
others can store 194.4k and 304.8k. the total is 582k btu, the equivalent
of 582k/25k = 23 hours of house heat when it's -20 f outdoors. 

if we only burn enough wood to keep the house 60 f, we can store 202.8k in
the top layer and 314.4k and 424.8k in the other layers, a total of 942k btu.
at 60 f, the house only needs (60-(-20))278 = 22.2k btu/h, so the sand can
store the equivalent of 942k/22.2k = 42 hours of house heat.

with a -20 f house, the sand can store heat forever :-)

nick




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