[Greenbuilding] Solution sought for heat rising problem

[nick pine]

Sacie Lambertson wrote:

>... currently in Vermont; staying in a lovely house with a big 30'x30', 
>tall 25'+ living room converted from a barn.  In addition to a radiant 
>heated concrete floor, a new pellet stove that blows heat into the space 
>has recently been installed.  About a third of the room is divided by a 
>loft space that forms an extension to the larger room underneath and a bed 
>room above.  The very high ceiling for the entire space is contiguous.

Sounds lovely.

>How to bring the rising warm air down to the occupied space below?

Natural convection? I picture a warm air column rising from the center of 
the floor to the center of the ceiling, then losing heat to the ceiling and 
spreading outwards to the walls and windows and losing more heat and falling 
downwards near the walls and moving in to the center of the floor and 
warming and rising up in the center again.

With 900 ft^2 of R40 ceiling and 2040 ft^2 of R30 walls, the part of the 
space above 8' would have a 900ft^2/R40 + 2040ft^2/R30 = 90.5 Btu/h-F 
thermal conductance to outdoor air, so it would require (70-30)90.5 = 3620 
Btu/h if it's 70 F indoors and 30 F outdoors. One empirical chimney formula 
says cfm = 16.6Asqrt(HdT), and 3620= cfm x dT with A = 450 ft^2 and H = 25' 
makes dT = (3620/(16.6x450sqrt(25)))^(2/3) = 0.21 degrees F, with 3620/0.21 
= 17130 cubic feet per minute of airflow, a lot. In this wintertime model, 
the average air temp would DEcrease with altitude.

Gary Reysa measured a 1 F temp increase (not much) between 6' and 14' 
heights in a room at 
http://www.builditsolar.com/Experimental/StratificationTest/stratificationtest.htm

>The space is well insulated but at the same time it has many windows, at 
>least ten.

... 10 3'x6' R2 windows near the top would make the upper space conductance 
900/40+180/2+(2040-180)/30 = 174.5 Btu/h-F and raise the upper heat loss to 
(70-30)174.5 = 6980 Btu/h with a  (6980/(16.6x450sqrt(25)))^(2/3) = 0.33 
degree F temp diff. Still not much. The temperature difference would be 
larger with less airflow if the "chimney area" were smaller, eg if most of 
the warm air rose up in a narrower column. And if the windows were all on 
one upper wall, the convection loop could be cylindrical with a horizontal 
axis instead of toroidal, with a vertical axis.

> It would not be practical nor would it look good to install a beam across 
> the space from which a fan could be hung.

How about an interesting transparent polycarbonate film shallow convex 
quonset arch structure to close up the gap at the loft level and keep the 
upper space cooler? It could be 20' wide x 30' long, with 9 $36 doubled 1x3 
bows with 1x3 spacer blocks and a 2' rise and a 20' length under 8 4'x20' 
HP92W 10 mil R1 polycarbonate strips and 3 1x3 purlins perpendicular to the 
bows. This would pass most of the light and views from above and reduce the 
upper space conductance from 174.5 Btu/F to 1/(1/600+1/174.5) = 135 Btu/h-F 
and reduce the heat loss to (70-30)135 = 5407 Btu/h and reduce the upper 
space temp to 30+5407/174.5 = 61 F. With 4 pulleys and 2 ropes attached to 
the center purlin, it could be raised to the ceiling in summertime.

Topher <topher at greenfret.com> writes:

> For my house (well insulated and well sealed), I have never seen more than 
> a 5 degree difference.

Warmer above in wintertime?

> The math looks like...  2048 ft^3 of air space *  0.018 BTU/ft^3-degree = 
> 37 BTU / degree * 5 degrees delta = 184 BTUs.  With a 100 cfm fan we move 
> that every 20 minutes.  If the heat magically regenerates...

I lost you there. If it were warmer above and a fan made the air temp 
constant all over, it seems to me that would only reduce the heat loss from 
the space above to the outdoors by the amount of the initial 
overtemperature.

Nick