re: low-mass sunspace question SOLAR.KnowledgePublications.com

re: low-mass sunspace question
25 jun 1996
from this afternoon's email...

>awhile ago (may 8, to be exact) you posted in alt.energy.renewable a 
>comparison of a high-mass sunspace to a very low-mass sunspace.  i like the
>idea of the low-mass alternative with a solar closet in a well insulated
>part of the house.

ok...

>in the post your calculations are based on maintaining the sunspace at 80f
>during the day.  you also mention that the water in the solar closet starts
>out at 130f and cools to 80f as its heat is needed to maintain the house
>temperature.  my question is, how does the water get up to 130f?  

the solar closet has an air heater on the south insulated side, so the sun
shines through the sunspace glazing, then through the solar closet air heater
glazing, and heats up the air inside the closet air heater to about 130 f. 

>i assume there is some kind of heat exchanger transferring the heat in the
>80f sunspace air to the water in the solar closet. 

no. there's no air exchange between the sunspace and solar closet, just sun, 
passing through the sunspace, then thru the solar closet glazing. a lot of
people seem to miss this. perhaps it needs a better explanation. 

>as i understand it, the sunspace air must be allowed to get hotter than 130f
>at some time to get an efficient energy transfer.

no. take a look at this two dimensional version:

           s1              s2               s3
32 f       |     t1        |       t2       |       70 f
outdoors   |               |                |       house
           |               |                |
1 ft^2 of  |    1 ft^2 of  |  1 ft^2 of r10 |
r1 glazing |    r1 glazing |         wall...|
           |               |                |
           |               |                |
1200 btu   |    sunspace   |  solar closet  |
per ft^2   |               |                |
of sun over|               |                |
a 6 hour   |               |                |
day -->    |               |                |
           |               |                |
 
if surface s2 were dark-colored, with an infinite r-value, so there were no
other place for the solar energy to go, the average 200 btu/hour of sun would
raise temperature t1 until all the heat that came into the s1 glazing went
back out through the glazing, so 200 = (t1-32)x1ft^2/r1, or t1 = 232 f. right?

now suppose s2 is perfectly transparent, with an r-value of 1, and s3 is dark,
with an r-value of 10. what will t2 be? here's the electrical analog:

     ------------
 |  | 200 btu/hr |
||--|   ----->   |-------     (the sun is a current source.)
 |  |            |       |
     ------------        |
                         |
32 f ---www--------www---------www--- 70 f
        r1    |    r1    |     r10
             80 f        t2

say enough hot air is bled out of the sunspace into the house to keep the
sunspace at 80 f. then we have 200 = (t2-80)1 ft^2/r1 + (t2-70)1ft^2/r10,
ie 200 = t2 - 80 + 0.1t2 - 7, ie 287 = 1.1t2, or t2 = 261 f, so you see the
solar closet can be a lot warmer than the sunspace, when there is no air
exchange between them, just sun passing through one space and into the other.

if each glazed surface were perfectly transparent, and there were n panes
of glass, each having an r-value of 1 (counting the still air film), and the
last surface were perfectly insulated, the temperature t in the last space
would be such that 200 = (t-32)/n, ie t = 32 + 200n. you can see something
like this if you put an oven thermometer on the lawn on a sunny day and cover
it with a few panes of glass, eg a few old storm windows. the thermometer
goes up to a few hundred degrees quickly, and the grass quickly turns brown.
the same thing happens inside a solar water heating panel on the roof, if
the pump fails, which is called "collector stagnation." 

nick