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re: thermal mass for large thermosyphon solar air heater
16 nov 2003
david delaney   wrote:

>...i propose a heat store having two constituent
>heat-storing masses. one of the constituents, a
>very permeable stack of concrete building blocks,
>has a large concrete-air heat-transfer surface
>area and a small thermal mass. the other
>constituent, a stack of drums of water, has a
>large thermal mass and a small drum-air
>heat-transfer surface area. both constituents
>share a single insulation envelope and operate
>within a single unpartitioned volume of air.

your web site diagram

seems to have blocks and drums on the same level, which surprises me,
since you seem to like stratification. why not put the drums on top
of the blocks?

or make a 4'x12'x8' tall "shelfbox" with 12 4'x8'x2" deep shelves on
4" centers in the lower 4' and 6 4'x8'x6" deep shelves on 8' centers in
the upper 4'. this would store 15,360 btu/f with 3,456 ft^2 of surface
and 38 ft^2 of "long side permeability," vs 3,411 btu/f and 1,963 ft^2
and 34 ft^2 in the 5.2'x11.3'x7.6' block pile. you'd need 216 ft of 30"
round poly film duct (or vinyl or epdm, at a higher cost) and 4' welded-
wire fence at a cost of about $200. 

>for carefully chosen circumstances, the performance of
>the two-component heat store should be similar to
>the performance of a heat store having the sum of
>the surface areas and the sum of the thermal
>masses of the two constituent heat storing masses.

it seems to me there are at least 2 other ways to model this:

1.  tc                        td
    |   rc =          rd =    |
    |1/(1.5x1961)  1/(1.5x323)|
    |----www----/ ----www-----|
    |            s            |
   --- cc=3411 btu/f         --- cd = 8276 btu/f
   ---                       ---     
    |                         |
    -                         -

>during the day the temperature of the concrete blocks will rise faster than
>the temperature of the water.  during the night, the concrete blocks
>transfer heat slowly by convection and radiation to the water drums. because
>the concrete blocks will give up heat more easily to cool air than will the
>water drums, the concrete blocks also supply most of the daily heat needs of
>the building and most of the daily heat losses from the heat store.   as the
>temperature of the water drum mass rises, the temperature of the concrete
>block mass cools to meet it, and becomes ready for efficient absorption of
>heat from the solar air heater the next day. (the concrete mass and the
>ratio of concrete surface to drum surface must be sized to make this true.)

it seems to me the drums and concrete will never be exactly the same
temperature. the circuit above has c = cccd/(cc+cd) = 2415 btu/f and
r = rc + rd = 0.002404 f-h/btu and rc = 5.8 hours. if switch s is closed
at dusk when tc(0) = 100 and td(0) = 80, and we wait forever, they both
become tf = (tc(0)cc+td(0)cd)/(cc+cd) = 85.8. after only 18 hours, tc
= 85.8+(100-85.8)e^(-18/5.8) = 86.5 and td = 85.8-(85.8-80)e^(-18/5.8)
= 85.6, if i did that right.

>the temperature of the concrete mass will descend below the temperature of
>the water mass if the night-time heat withdrawals and losses from the heat
>store are large enough. the water drums will become the main source of heat
>output only when the temperature of concrete is distinctly less than the
>temperature of the water.

like, after a few cloudy days. wouldn't you rather have a stratified store
then? how do you get the heat out of this overhead store without fans?

>during the day the temperature of the concrete blocks will rise faster than
>the primary consideration in sizing the concrete block stack is the
>combination of the amount of energy that must be collected in one day and
>the temperature range of the air from which the energy must be collected.
>the desired one-day energy collection divided by the thermal mass of the
>concrete equals the rise in the average temperature of the concrete required
>to store that amount of energy. this required temperature rise must be less
>than the difference between the average temperature of the air from the air
>heater and the temperature of the concrete at the beginning of the day.

it might look like this on an average day, with rcc = 1.2 hours and rcd
= 17.1 hours and ta = 100 f for 6 hours per day and 70 f for 6 hours per
day, which makes...

2.   ----------------------------ta
    |                         |  
    |                         |  
    w                         w  
    w  1/(1.5x1961)           w  1/(1.5x323)
    w                         w
    |  tc                     |  td
    |                         |
   --- cc=3411 btu/f         --- cd = 8276 btu/f
   ---                       ---     
    |                         |
    -                         -

tcl = 70+(tcu-70)e^(-18h/1.2h) = 70 and tcu = 100+(70-100)e^(-6/1.2) = 99.8
and tdl = 70+(tdu-70)e^(-18/17.1) = 45.6+0.349tdu = 55.9+0.246tdl = 74.2 and
tdu = 81.8. wouldn't you rather have a stratified store, with drums on top?
how can we calculate its performance?

>it will be important not to overload the heat store.  an air heater capacity
>suitable for december in ottawa will certainly overload the heat store in
>february. seasonal shading will have to be provided for the air heater. some
>form of emergency heat dumping may have to be provided.

venting sounds easy, with fixed overhang shading. are you worried about
overheating the house, or fires, or melting plastic drums? a hotter store
might provide more energy to heat water for showers in summertime...


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