"Randy" wrote:

I am planning on building a solar heater on my shop (south side), the
size would be 12'x40'...

R19 walls and an R60 roof and 102 ft^2 of R2 windows and 0.5 ACH of air
leaks and a 34x54/R60 = 31 Btu/h-F roof conductance and 102/2 = 51 for
windows with 136' of non-collector wall with (12.5x136-102)/R19 = 84 and
0.5x12.5x34x54/60 = 191 for 191 cfm of air leaks totals 357 Btu/h-F.

... With a 70 F shop air temp, R1 Dynaglas... with 90% solar transmission
might collect 0.9x902 = 812 Btu/ft^2 and lose 6h(70-26)1ft^2/R1 = 264
for a net gain of 548, ie 12x40x548 = 263K Btu/day.

If the shop is used 6h/day and it doesn't store much heat, it needs about
6h(70-26)357 = 94.2K Btu/day, which leaves 168.8K for the house, collected
at 168.8K/6h = 28.1K Btu/h. A 2'-4' deep heater with 70 F air in the space
between black fiberglass window screen with 67% open area with the top of
the screen attached to the south edge of the heater ceiling and the bottom
attached near the shop wall and 150 F air in the space under the heater
ceiling might heat 150-28.1K/1600 = 132 F water with 320' of fin-tube pipe
or 2 used 800 Btu/h-F auto radiators. Hot collector air might thermosyphon
up, travel through the radiators and then back down a duct into the bottom
of the collector, with a fan and a shop temp thermostat and an occupancy
sensor to keep the shop 70 F.

How can we predict the performance of an air heater with a mesh absorber
with some warm shop air flowing from south to north through the mesh and
hotter air thermosyphoning from the space above the mesh through some auto
radiators and back down a duct into the lower part of the heater, to
the north of the mesh? The shop air flow tends to keep air moving into
the mesh, like a breathing wall, but if we reduce the flow of shop air,
at some point, hot air will want to naturally circulate south from the top
of the space to the north of the mesh through the mesh, downwards next to
the cool glazing, and back north through the mesh near the bottom.

So at the top of the mesh we have 70 F air to keep the shop warm flowing
north through the mesh fighting 150 F air that wants to naturally circulate
south through the mesh, because its hot air column to the north of the mesh
is lighter than the 70 F column of air next to the glazing. If the 70 F air
weighs 0.075 lb/ft^3 and 140 F air weighs 0.075(460+70)/(460+150) = 0.065
lb/ft^3 and the heater is 12.5' high, the 150 air bouyancy force would be
12.5(0.075-0.065) = 0.0125 psf, or 0.0024 "Hg, within the range of a fan.

The shop needs 15.7K Btu/h, ie 15.7K/(150-70) = 200 cfm min, ie 0.4 cfm/ft^2
of mesh. If cfm = 27900Asqrt(dP) with A in ft^2 and dP in psf, each square
foot of mesh needs an A = 0.4/(27900sqrt(0.0125)) = 0.00013 ft^2 hole, ie
a 0.018 in^2 hole, ie a 0.15" hole. We might jab 1/4" holes with flaps using
a pencil through dark Typar mesh on a 1' grid behind the window screen and
use a smaller fan to move 10 cfm of 70 F air through the mesh when the flaps
are closed and the 200+ cfm fan isn't running.

Nick