Hybrid Car – More Fun with Less Gas

An attic radiator

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Posted by Nick Pine on June 16, 2007, 11:39 am
Chris writes


But more IS better, no? Adding vents between soffit and ridge vents
can only raise the total attic airflow and lower the temperature.  

Sounds good in summertime. Or maybe not... 10 years ago I replaced
my 1820 stone farmhouse 12/12 pitch south roof with a single layer
of Dynaglas corrugated clear polycarbonate over the 24'x32' insulated
floor, with 2 turbine vents and 4 windows near the floor. The turbine
vents were probably unnecessary. They have hatches beneath that can
be closed in wintertime. The north roof is galvanized steel over
cedar shingles.

When I tried moving hot air down the stairs and into the basement
and back into a 32'x12'-deepx16'-tall greenhouse sunspace and up to
the attic again with a $00 250 W 2800 cfm 311 F spec Multifan in
a basement window and a one-way plastic film damper in the attic
stairway door, that didn't move or store enough heat, despite 2" of
polyurethane foam over the outside of the stone walls and 50 tons
of water in the basement in about 200 plastic 55 gallon drums, so
I'm thinking of hanging some $0 used car radiators under the ridge
to collect heat in hot water, like Nathan H. did in Australia.

Nathan ran their attached 12 V fans at 60 W reduced power, after
discovering that more fan power didn't increase the air-water heat
transfer. How hot can the motors run without damage? Do they follow
the "fan laws" with power proportional to cfm^3? I'd like to collect
about 50K Btu/day of heat in 140 F water for showers in summertime,
and more in the winter for space heating near Phila. A car radiator
might move about 100K Btu/h with full water and airflow, about
800 Btu/h-F, like a $00 MagicAire SHW2347 2'x2' horizontal duct
heat exchanger moving 45K Btu/h from 125 F water into 1400 cfm of
68 F air with a 0.1" H20 air pressure drop.

My roof might transmit 0.9x250x32'x20'xcos(45-26.5) = 136.6K Btu/h
of full sun (250 Btu/h-ft^2) on 12/21 at noon. With 640 ft^2 of R1
glazing, an equivalent circuit might look like this, in a fixed font:

      ---                               1/640
  ---|-->|--------                    ---www---
 |    ---    |                       |
 |           |       Thevenin        |
 |   1/640   |       equivalent:     |
 |----www----                        |
 |                                   |
 |  34 F                             |  34+136.6K/640 = 247 F
---                                 ---
 -                                   -
 |                                   |
 -                                   -  

Adding a radiator:
    1/640  |  1/800
 |   ------------>   |
 |         I         |
 |  247 F            |  140 F
---                 ---
 -                   -
 |                   |
 -                   -

I = (247-140)/(1/640+1/800) = 38K Btu/h, with attic air temp
Ta = 140+38K/800 = 188 F. I could move the Multifan up to
the attic, or maybe make a 10'x2'x2' duct below the radiator
to improve thermosyphoning airflow with a cool air column...

If the MagicAire unit cools 125 F air to Ti with 45K = 1400(125-Tho)
at full flow, Tho = 93 F, approximately, with effectiveness
E = (125-93)/(125-68) = 0.564. If E = NTU/(NTU+1), NTU = E/(1-E)
= 1.293 = AU/Cmin = AU/1400, so AU = 1810 Btu/h-F. With less flow,
eg C cfm, we might have E = 1810/(1810+C) = (Ta-Ti)/(Ta-140) (1)
and Ta = 247 - C(Ta-Ti)/640 (2) and C = 16.6x2'x2'xsqrt(10'(Ta-Ti),
ie dT = (C/210)^2 (3) using an empirical thermal chimney formula,
and Ta = 247-CdT/640 (2) and dT/(Ta-140) = E, with dT = Ta-Ti.

Plugging (3) into (2), Ta = 247 - C^3/(640x210^2), and plugging these
into into (1) gives C = (2.23x10^9-473C^2)^0.333. Plugging in C = 1000
on the right makes C = 1306 on the left. Repeating makes C = 1125, 1177,
1164, 1167, 1166, and 1167, so dT = (1167/210)^2 = 30.9 F, with attic
air temp Ta = 191 and Ti = 160 inside the down-duct, so we would collect
about 1167x30.9 = 36K Btu/h... 2 radiators could collect more, with
separate chimneys, or a common chimney with one at the top and one at
the bottom, if the chimney is inside a house collecting heat from
a sunspace during the day and distributing heat to the house at night.

What moisture?

You might exhaust the swamp cooler into the attic ("up ducts")
to keep it cooler and move the cooler indoors and turn it on
with a thermostat when the indoor temp reaches 80 F and turn
on an exhaust fan with a humidistat when the indoor RH reaches
56% (this is an efficient corner of the ASHRAE comfort zone.)

Warm air rises... cfm = 16.6Avsqrt(HdT) with equal vent areas Av
in ft^2 and an H foot height difference and a dT (F) temp diff.

Wisconsin code officials forced Soldier's Grove solar attic owners
to line them with drywall to avoid fires, until the town pharmacist
pointed out that their carbon vs time/temp graph was in degrees C
with a log scale, and they were interpreting it as if it were in
degrees F with a linear scale and wrongly predicting fires every
20 years, vs every 20 centuries :-)


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