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a solar barbecue?
2 jun 1996
can we make a permanent outdoor solar cooker that looks something like this,
and stays hot for 24 hours a day, day after day all year?

           south view                    east view
    ---------------------------          ------------------
   |                           |        |  r30 movable cover
   |      ----------------     |        |            -----------
   |     |  cooking area  |    |        |           |  cooking area
    ---------------------------   ---   |------------------
   |  air  |            | air  |        |/    .    <== cooler air  
   |   in  |            |  in  |        |  r  .    .   from masonry shelf
   |---------------------------|   |    |  3  /-------------------------
   |       |     air    |      |        |  0  s    warmer air to shelf ==>
   |       |     out    |      |   |    |     s
   | - - -  ------------  - -  |        |  -  s  -   --------------------
   | ^      vent area av   ^   |   |    |     s     |         r30 here too
   | |                     |   |        |     s     |
   |  -glazing starts here-    |   |    |     s     |  strawbales and mortar?
   |                           |   |    |     s     |
   |                           |        |     s     | r30 wall
   4'?                         |        |     s     |
   |       glazed area a       |   h    |<-g->s<-g->|
   |                           |        |     s     |      storage area?
   |                           |   |    |     s     |
   |                           |        |     s     |
   |                           |   |    |     s     |
   |                           |        |           |
   |            4'?            |   |    |\        / |
 -  ---------------------------   ---   |-----------| - - - - - - - - - -
                                         -- two layers of glazing?

perhaps a simple passive air heating system a la norman saunders, pe, or
steve baer, in which the sun shines through two or three outer layers of
glazing, onto a porous absorber surface, with an air gap of dimension g 
between the glazings and the absorber, and another between the absorber
and the wall.

cooler air from a high-thermal-mass masonry shelf, eg some concrete blocks
with their holes running north and south, would be persuaded to flow down 
between the colder glazing and the absorber, then  up  through the air gap
between the absorber and the wall. this would be more thermally efficient
than a more typical system in which the solar heated air is in contact with
the cold outer glazing. the shelf would have a tight-fitting cover. 

we might start with an r30 wall, say 6" of fiberglass and 2" of foam behind a
piece of dark cement "wonderboard." no backdraft dampers, because at night
the cool air would form a stagnant pool that just stays in the air heater
pocket, since cold air sinks, while the warmer air stays trapped in the roof
shelf, like an igloo, which has the entrance below the floor.

the width of gap g determines the airflow resistance, in part. steve baer
says g might well be h/15, eg 4" for an 4' high wall. the vent area av might
be about 5% of the glazed area. the porous absorber might be one or more
layers of black aluminum window screen, with an absorbing area of up to 5
times the window area, large enough so that most of the heat from the absorber
is transferred to the flowing air, vs having a small-area hot absorber that
loses a lot of heat to the glazing by radiation. one might measure success by
glazing and absorber temperatures, the lower the better. one way to measure
these temps is to use an exergen d501 scanning thermometer (about $1000.)

one way to look at the airflow is to blow some smoke into the collector. the 
useful heat output of the collector is proportional to the product of the
air velocity and the temperature difference between the input and output air.
50% solar collection efficiency would be a good target...

suppose our perpetually-hot outdoor solar barbecue/shrine were 8' wide x
4' tall, with a white ground reflector in front to the south, and reflective
wings to the side to bounce most of the sun onto a 4' x 4' vertical collecting
surface below the south edge of the grille/high-thermal-mass shelf, which
might be 2' x 4' x 2' thick. what would the temperature of the shelf be,
after a long string of average january days, in abilene, tx, where the
average outdoor temp is 43 and the average amount of sun that falls on a
south wall is 1,400 btu/ft^2/day?

first let's find the solar input. nrel measured 1,400 btu with a ground
reflectivity of 0.2, but a white surface, eg white paint, might have a
reflectivity of 0.8, to the sun becomes 1.8x1,400/1.2 = 2,100 btu/day.
next we have the 2:1 non-imaging concentrators which raise this to about 
4,200 btu/ft^2/day, as they bounce all the winter sun from +/- 45 degrees (?)
azimuth from 32 ft^2 of south-facing wall onto 16 ft^2. the total sun in is

ein = 16 ft^2 x 4200 btu/ft^2/day = 67,200 btu/day.

how much heat would leave the cooker during a 24 hour day? if the masonry shelf
has a temperature t, and a surface area of 8 ft^2 each for the top and bottom
and 8 ft^2 each for the north and south sides, and 4 ft^2 each for the east
and west sides of the shelf, the energy eout that flows out of the cooker
during an average january day will be roughly 

eout = 6 hr(t-43)16ft^2/r2           for the collector face during the day
    + 18 hr(43-43)16ft^2/r2          ie 0, for the collector face at night
    + 24 hr(t-43)40ft^2/r30          for all other surfaces, 24 hours a day

     = (48+32)(t-43) = 80t.
if ein = eout, t = 43 + 67,200/80 = 883 f. this is promising, altho it will
be a lot cooler, since radiation loss will become significant at this temp.
the porous absorber would help reduce that loss, by absorbing some of the
heat that tries to radiate back out the glazing from the absorbing surfaces
further in. this could use some experiments with numbers of layers and solar
and airflow porosities, including some layers made of rusty metal mesh, which
has selective surface properties. a solar crabtrap. suppose the shelf temp
were 400 f, 24 hours a day, in january. the cooking temp could be less, if
there were some way to regulate the heat.

how would this temp change with time, eg on a day without sun? suppose we made
the shelf mostly out of steel, weighing 489 pounds per cubic foot, with a
heat capacity of about 60 btu/f-ft^3 (vs about half that for concrete or 1/3
that for sand--lots of old pieces of steel buried in sand? bury the pot in
the hot sand too?) then we'd have a thermal mass of 60x2x4x2 = 960 btu/f, in
our 4 ton shelf. this solar cooker would be theftproof and tornado proof. it
might make a nice outdoor addition to a public park, or a school, as well as
a private backyard.

on a cloudy day, the rc time constant would be

rc = (30ft^2-btu/hr-f)/40ft^2(960btu/f) = 720 hours, or 30 days. not bad...

if the shelf started out at 400 f on a cloudy week, after 5 days the
temp would be t(5) = 43 + (400-43)exp(-5/30) = 345 f... not bad...

some useful rules of thumb:

q (cfm) = 16.6 av sqrt(h delta t), for an open chimney, in which
               av is the smaller vent area in square feet,
	       h is the chimney height in feet, and
	       delta t is the input/output air temp difference (f).

u = 0.174e-8 ac (t+460)^4  btu per hour is re-radiated by an ac ft^2
               non-selective surface at temperature t (f).  

full sun is about 300 btu/ft^2/hour.

1 btu will heat about 55 ft^3 of air 1 degree f.


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