re: hot air heat SOLAR.KnowledgePublications.com

re: hot air heat
11 feb 1999
i wrote: 

>...how warm can we make the holiday home if it's a 3m metric r9
>strawbale cube with no air leaks and no internal heat gain?
 
>    25 kwh = 6h(t+dt-0c)9m^2x6w/m^2-c    air heater day loss
>          + 18h(t-0c)(9m^2-2a)/r9        south wall night loss
>          + 18h(t-0c)2ax6w/m^2-c         damper night loss
>          + 24h(t-0c)45m^2/r9            other 5 surfaces
>
>so t = (25k-324dt)/(462+212a)            equation 1.
>
>using one empirical chimney formula, the airflow volume is about
>0.2asqrt(hxdt) m^3/s and the heatflow into the cube is about
>250asqrt(h)dt^(3/2) watts when the air heater is working, so if h = 3m,
>
>  dt = ((138t+212a)t/(433a))^(2/3)       equation 2.

oops. i goofed. if h = 3m, the heatflow is 433adt^1.5 watts. over
6 hours, that's 2598adt^1.5 watt-hours, which equals the loss from 
the south wall at night and the other 5 walls, ie 138t + 212at, so

   dt = ((138+212a)t/(2598a))^(2/3)       equation 2 (new, improved!)

this lowers dt and the air heater loss, which warms up the cube... 

10 for a = .1 to .2 step .02
20 for trial = 1 to 5
30 t=(25000-324*dt)/(462+212*a)
40 dt=((138+212*a)*t/(2398*a))^(2/3)
60 next trial
65 print a,t,dt
70 next a

run

 .1            45.25841      9.664856
 .12           45.47994      8.738399
 .14       --> 45.55485      8.029573  
 .16           45.53318      7.46661
 .18           45.4451       7.006726
 .2            45.30979      6.622667

making each damper about 1.5% of the wall area works well here. 
again, the performance is not very sensitive to the damper area.

nick