And remove the roof first, for more efficiency. What's the solar collection
efficiency of: a) a black metal roof, and b) the roof with a polycarb cover,
and c) the cover without the roof, in full sun (250 Btu/h-ft^2) on a 30 F
day, with 120 F air in the attic?
I took a cut at your a), b) and c), but with Tattic reduced to 90F (on
the theory that the fan would turn on when the attic temperature gets
to 90F)?
c) One layer of clear Polycarbonate glazing as the roof:
Uglaz = 1.2 (for single glazed collector including radiation)
Rglaz = 0.83
Qloss = (Tattic - Tamb)/ Rglaz = (90F-30F)/0.83 = 72 BTU/hr-ft^2
efic = (250 -72)/ 250 = 71% Wow!
b) One layer of clear Polycarb over dark metal roofing --
heat transfer by conduction through metal only (no ducts):
Rglaz = 0.83
Rattic = 0.65 (R from metal to attic -- one still air film)
Qabsorbed = (0.9 trans)(0.95 absorb) (250 BTU/ft^2-hr) =
= 214 BTU/hr-ft^2 absorbed by metal roof plate
Qattic = (Tcol - Tattic)/Rattic -- heat to attic
Qloss = (Tcol - Tamb)/Rglaz -- loss out glazing
Qattic + Qloss = Qabsorbed
(Tcol-90F)/0.65 + (Tcol-30F)/0.83 = 214
This gives Tcol = 142F
Qattic = (142F - 90F)/0.65 = 80 BTU/hr-ft^2 to attic
efic = 80/250 = 32%
Less than half as good as the clear PC only, but it might be
attractive if you already have a metal roof?
It could be made a bit better with some mild forced convection on the
inside surface of metal.
On (say) a 2000 sqft house with (1.4/2)(2000) = 1400sqft of South
facing roof it could be a whole lot of heat.
c) Dark colored metal roof only (no glazing):
Assume a 7.5mph wind -- Rout = 0.25
Rattic = 0.65 (as above)
Qabsorbed = (0.95 absorb)(250BTU/hr-ft^2) = 238 BTU/hr-ft^2
Qattic = (Tcol - Tattic)/Rattic
Qloss = (Tcol - Tamb)/Rout
Qattic + Qloss = Qabsorbed
(Tcol-90F)/0.65 + (Tcol-30F)/0.25 = 238
This give Tcol of just about 90F
Since the collector and attic are equal in temperature,
no heat is transfered to attic, and efic = 0??
If you change to no wind -- Rout = 0.65 -- then:
(Tcol-90F)/0.65 + (Tcol-30F)/0.65 = 238
This gives Tcol = 138F
Qin = (138F-90F)/0.65 = 74 BTU/hr-ft^2
efic = 74/238 = 31% -- so wind makes a lot of difference!?
But, still, the bare roof might do pretty well in the shoulder months,
and when there is not much wind?
Does this all seem about right? Did I go astray above?
Conclusions:
A roof from one layer of Polycarb would be both thermally and dollar
efficient -- you just need to embrace the transparent look?
On your PC roof, how do you collect the heat once in the attic?
How do you distribute it to the house?
Will the building code folks OK this kind of roof?
A dark metal roof with a layer of PC on the outside has fair thermal
performance, and pretty good dollar performance?
A dark metal roof only (no glazing) has poor thermal performance, but
will collect some heat on some days, and costs almost nothing?
Gary