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re: solar collector panel insulation
10 jul 2000
tim dierauf  wrote:

>hi nick,

hi tim,

>> >...with a low flow system, we can assume that we have 70f inlet and
>> >130f outlet. thus, a mean plate temperature is 100f. we can then use
>> >this to approximate losses.

>> losses to some lower outdoor temperature. for instance, on a 30 f day,
>> a collector with a mean plate temp of 100 f and r1 glazing might lose
>> (100f-30f)/r1 = 70 btu/h to the outdoors. that's 420 btu over 6 hours.

>> >now, let's consider a panel with a high fluid flow where there is
>> >only a 10f increase across the panel. assuming our tank starts off
>> >isothermal at 70f, then the mean plate temperature would be 75f --
>> >nice and low...

>> the second example, the mean plate temp might be
>> 75 f for the first hour, with a 45 btu/ft^2 loss
>> 85 f for the 2nd                55
>> 95 f for the 3rd                65
>> 105 f for the 4th               75
>> 115 f for the 5th               85
>> 125 f for the 6th               95, ie a
>> 100 f average temp, with a     420 btu total loss...
>ahhh, i disagree with your assumption that it will take only an hour to
>ratchet the storage up 10f for each time period. the time constant will be
>an exponential decay with the mean storage temperature looking something
>like (i hope this comes of with proportional font):
>mean storage temperature
>|                                                                        *
>|                                                    *
>|                                     *
>|                          *
>|                  *
>|            *
>|        *
>|     *
>|   *
>|  *
>| *
>-------------------------------------------------------------------> time

this collector loss would be higher than in the linear case, since
it spends less time at the lower temps and more at the higher temps.
>i'm not a betting man, but i will state that for most "typical"
>installations a low flow system will out perform a high flow system
>if the storage is allowed to stratify.

well, what do we mean by "outperform"? fig. 12.5.1 on page 498 of
duffie and beckman's 1991 solar engineering shows a nice gain in solar
fraction for low flow systems, based on wuestling's 1985 simulation
studies. i had the impression that this gain had more to do with the
stratified store (backup heat less frequently needed) than increased
collector efficiency. now i'm not so sure. 

i'm also not sure why the low-flow system has such a pronounced peak
at a certain flow. lower than that and the output temp is high enough
that collector efficiency suffers? higher than that and the output temp
is low enough that the upper tank temp is too low, and backup heat is
required more often?

and does this apply to systems in which the solar fraction is 100% by
design, eg solar houses with no backup heating systems, in which
performance (rarely) suffers, but backup fuel is never used? norman
saunders calculates that backup heat (or a sweater) would only be needed
over short times every 35 years or so in his solar houses. he uses
gaussian stats to show that these events would be almost as rare as
100 year floods :-) the usual concept of "solar fraction" seems to have
little meaning here.


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