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re: heat storage "portable heater" ??
9 nov 2000
toby wrote:
>> >>any thoughts on something to set on top of a woodstove then move
>> >>to heat a small area?...
>> an 8" cube with 2.7 ft^2 of surface and 4 btu/h-f of cube-to-room air
>...how about a 2' by 2' by 1" box, holding approiximately the same
>volume of 140f water) with 8.7 sqft of surface and 13 btu/h-f...
ok, approiximately.
>let's say only 3 r20 walls border with 10 btu/h-f room-to-outdoor
>conductance at the 34f outdoors...
so this "8' cube" is now an unusually-shaped room with a total of 5 walls,
and 3 of the r12 outside walls have become r20 walls. with no windows? :-)
>and 2 r20 walls with 6 btu/h-f room-to-indoor conductance border the
>74f room with the woodstove;
so 2 of the walls have sort of disappeared, with zero heat loss or gain,
if the "small area" were also 74 f...
>and an r20 floor with 3 btu/h-f room-to-ground conductance
>borders the 54f ground.
is seems unreasonable to assume that the ground under this outside room
would be so warm in the winter. and what's the floor area of this odd
5-sided room?
>the heat flowing out of the 74f room, would be:
>outside: (74-34)10=400btu/hr
>woodstove room: (74-74)6=0 btu/hr
>floor: (74-54)3=60 btu/hr
>total: 460 btu/hr
ok...
>a rough cut at finding the heat flowing out of the water "box" into the
>room is:
>
>(140-74)13 = 858 btu/hr
that works for the first few seconds...
>refining this, the water's thermal capacitance is:
>64 btu/cuft/f * [1"*1'/12" * 2'*2'] = 21 btu/f
so this "10 or 15 pound heater" has now grown to
21 pounds plus the weight of the container...
>the thermal time constant: 21 btu/f / [13 btu/h-f] = 1.6 hours
>
>so, after 1 hour, the water temperature is:
>
>tw = 140 - (140-74)exp(-1/1.6) = 105f
>
>the heat which left the water is:
> (140-105)f * 21 btu/f = 735 btu
wrong, but irrelevant.
here's an approximate thermal equivalent circuit...
74 f
|
1/13 | 1/10
t ---www---*---www--- 34 f outside walls
|
| 1/6
*---www--- 74 f inside walls
|
| 1/3
---www--- 54 f floor
with a thevenin equivalent circuit like this:
74 f
|
1/13 | 1/19
t ---www---*---www--- 49.8 f
the series resistance is 0.1296, with rc = 2.72 hours. the heater can only
keep the room warm until t = 109.4 f, when t = -2.72ln(59.6/(140-49.8)
= 1.13 hours...
>now add, 300 btu/hr jiva's bodie produces...
>and add, 340 btu/hr from the 100w light bulb..
>
>we have way more heat than what we need.
it might help to assume there's a lead smelter in this small space.
>may jesus bless,
> toby
it might help to whistle ("...if i only had a brain.")
nick
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