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Would an unstratified mass (eg a poly film duct containing 1" of water over
a shiny ceiling, with insulation above that) be warmer with David Delaney's
flow separator or 70 F house return air filling a sunspace/air heater?
Consider 2 steady-state 8' R10 cubes with 64 ft^2 of R2 glazing with 80%
solar transmission, after a long string of 30 F average January days in
Phila, with 1000 Btu/ft^2 of sun on a south wall...
1. --------------
|fs| Tc | Cube 1 has a flow separator and a transpired
| .| | R10 mesh collector. We might assume the air hear the
| .| | glazing is about the same as the ceiling temp Tc.
S | .| 70 F | 30 F This sunspace might be uncomfortably hot, but the
| .| | amount of airflow is not limited by the cube temp.
| .| | How does the ceiling keep the cube 70 F?
| .| |
--------------
2. --------------
| . Tc | Cube 2 has a ventilation slot at the top and
| .| | R10 a transpired mesh collector and a potentially-
| .| | unreliable motorized damper at the bottom which
S | .| 70 F | 30 F is controlled by a thermostat that keeps the
| .| | cube air 70 F during the day. We might assume
| .| | the air near the glazing is about 70 F. We might
| .d | need another layer of glazing south of the mesh
-------------- to ensure this. The ceiling might keep the cube
70 F with a thermostat and a slow ceiling fan.
In each case, the glazing transmits 0.8x1000x64tft^2 = 51.2K Btu/day of sun.
In case 1,
51.2K = 6h(Tc-30)64ft^2/R2+18h(70-30)64ft^2/R12 [south wall]
+24h(Tc-30)64ft^2/R10 [ceiling]
+24h(70-30)4x64ft^2/R10 [remainder of cube.]
which makes Tc = 96 F, if I did that right.
In case 2,
51.2K = 6h(70-30)64ft^2/R2+18h(70-30)64ft^2/R12 [south wall]
+24h(Tc-30)64ft^2/R10 [ceiling]
+24h(70-30)4x64ft^2/R10 [remainder of cube.]
which makes Tc = 128 F.
Nick
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