Subject: sunspace/solar closet symbiosis

From: [email-masked] (Nick Pine)
Date: 28 Aug 1996 01:21:08 -0400

Solar closet glazing loss ends up warming sunspace air, which warms the house,
so that heat is not really lost. This symbiosis is similar to what Bill
Shurcliff calls "Khanh's radically new approach to increasing the useful
output of a flat plate collector panel: scheme employing a cheap, laterally-
contiguous slave panel," in _New Inventions in Low-Cost Solar Heating--
100 Daring Schemes Tried and Untried_, except that Khanh just used his
"sunspace heat" to keep the collector warmer, with a larger 2nd layer of
glazing, and a dark surface below the collector.

Just adding another layer of glazing to a solar closet is different. How can
we compare these two situations, with 36 F outdoor air and 1000 Btu/ft^2/day
of sun? Suppose each R1 sunspace glazing below were 2'x 2', and the R1 solar
closet glazing were 2'x 1', and there were perfect insulation to the north,
(or the south, down under) and at night...

 Warmstore with two layers of glazing    warmstore behind sunspace

             .........                          .........            
             .   .   .                          .   .   .            
          Tw .   .   . 36 F                   1'.   .   .  36 F          
             .   .   .                       Tw .   .   .            
             .   .Ts .      sun                 .   .   .       sun      
             .   .   .                          .   .   .            
             .   .   . 2'                       .....   .            
             .   .   .                          .       .            
             .   .   .                          .       .            
             .   .   .                          .  Ts   .            
             .   .   .                          .       .            
             .   .   .                          .       .            
             .........                          .........            

In the first case, 4K Btu = 6hr(Tw-36)4ft^2/R2, so Tw = 36 + 4K/12 = 369 F.
(Ignoring radiation loss.)

In the second, 4K = 6hr(Ts-36)4ft^2/R1, ie 4K =  24Ts - 24x36 and 
	       2K = 6hr(Tw-Ts)2ft^2/R1, ie 2K = -12Ts + 12 Tw,
                                        ie 4K = -24Ts + 24 Tw, so
                                           8K =         24 Tw - 24x36, so
                                           Tw = (8K+24x36)/24 = 369 F.

Looks the same, if neither is providing any useful heat to the house... 

But, suppose we remove 3500 Btu/day of heat for the house,
>from  the solar closet, in the first case, and
>from  the sunspace, in the second case. Then

In the first case, 4K Btu = 6hr(Tw-36)4ft^2/R2 + 3500,
so Tw = 36 + (4K-3500)/12 = 78 F.

In the second, 4K = 6hr(Ts-36)4ft^2/R1 + 3500,
           ie 500 = 6hr(Ts-36)4ft^2/R1, ie 500 =  24Ts - 24x36 and 
	       2K = 6hr(Tw-Ts)2ft^2/R1,  ie 2K = -12Ts + 12 Tw,
                                         ie 4K = -24Ts + 24 Tw, so
                                          4.5K =         24 Tw - 24x36, so
                                            Tw = (4.5K+24x36)/24 = 224 F.

The daytime "sunspace" temp would be 36 + 3500/6xR1/4ft^2 = 146 F in the
first case. The daytime sunspace temp would be 36 + 500/12 = 78 F in the
second case. The lower temperature behind the outer glazing means lower 
losses to the outdoors, and a more usable space for people and plants.
Radiation losses magnify this effect. One might use IR-transparent
polyethylene or Mylar film for the sunspace glazing in the second case,
but perhaps not in the first. 

If I'm doing this right, and we figure that the warmstore has to be at least
80 F to keep the house warm on a cloudy day, there is NO useful stored heat
in the first case, while the solar closet in the second case stores (224-80)
= 144 Btu/lb of water for cloudy weather in the second case, at a high enough
temperature to heat water for showers, as well (altho doing that, eg with a
fin-tube convective loop through a water heater upstairs, will lower the
closet temperature, requiring more closet glazing.)

Nick