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The passive warm bedroom.

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Posted by zoe_lithoi on December 10, 2013, 5:37 am
 
Greetings,

How does a family of 5 (3 adults, 2 kids) keep warm in 20degF temperature i
n their modular home when they cannot afford electricity or propane?

Let's put all 5 of them in a 10x12', R20 bedroom. Then let's put 2 layers o
f  $1 R7.7 4'x8' insulation foam board on the ceiling and 4 walls. The mat
tresses would take up about the entire floor providing approix. R15 on the  
floor.  

The calculations after my signature indicate theoretically, that after 1 ho
ur the room temperature is 51, after 2 hours it is 63, and after 3 hours, i
t is 69degF.

Home Depot has R7.7 foam board insulation for $1 (R-Tech 2 in. x 4 ft. x 8
 ft)  

2 layers of this would be ~R15. To cover the walls and ceiling of a 10'*12'
 room with 2 layers of this foam board insulation, you would need about 30  
boards, i.e. $00. Ouch. BUT it's better than paying the 'typical' $00 per
 month for the heating bill for a 6 month winter ($800).  

-------------------

To heat this room to 70degF without adding any insulation would require a 5
00Watt space heater (plus the 5 people). I'm guessing it's about 20cents pe
r kilowatt, so the cost would be 10 cents per hour, or $.40 per day or $2
 pre month or $32 for a 6 month winter.

Toby


The surface area of the 4 walls, floor, and ceiling would be:

A = 4*8*12 + 2*8*10 + 2*10*12 = 2^4 * [24+10+15*49 ~= 16*50 =  
800sqft

There is 300 Btu/hr for a sedentary adult, so let's estimate, with kids, 25
0btu/hr and average, i.e. the amount of heat entering the room from sleepin
g people:

H = 5*250Btu/hr = 1250 Btu/hr

The Heat leaving the room, of Temperature, Trm, to the 20degF outside thru  
the 800sqft of R20 walls, floor, and ceiling is:

(Trm - 20)degF*800sqft / R20 hr-sqft-degF/Btu] = (Trm - 20)* 40 Btu/hr

The amount of heat the air in the 1000cuft (8'*10'*12' = ~1000cuft) room  
 absorbs to go from 20degF to Trm is:

(Trm - 20)degF * 1/55 Btu/F /cuft  * 1000cuft ~= (Trm - 20) * 20 Btu
I guess in the first hour this would be:

(Trm - 20) * 20 Btu/hr

The heatflow equation then, is:

1250 Btu/hr = (Trm - 20) * 20 Btu/hr + (Trm - 20)* 40 Btu/hr
1250  = (Trm - 20) * 60
Trm = 1250/60 + 20 = 41F

Since the room is now heated to 41F, the 2nd hour would be:

1250 Btu/hr = (Trm - 41) * 20 Btu/hr + (Trm - 20)* 40 Btu/hr
1250  = 60Trm - 820 -800
Trm = [2870]/60 = 48degF

Since the room is now heated to 48F, the 3rd hour would be:

1250 Btu/hr = (Trm - 48) * 20 Btu/hr + (Trm - 20)* 40 Btu/hr
1250  = 60Trm - 960 -800
Trm = [3010]/60 = 52degF

The 4th hour might be 55, the 5th hour might be 56 or 57....
Halfway thru the night, it's still cold

---------------------------------------------------------------------------
--  
Suppose we added R15 foam insulation  to the ceiling and walls. We'll assum
e that the mattresses covering the floor add R15 to the floor, so that now,
 we have R20 + R15 = R35 everywhere
---------------------------------------------------------------------------
--  

(Trm - 20)degF*800sqft / R35 hr-sqft-degF/Btu] = (Trm - 20)* 23 Btu/hr

The heatflow equation then, is:
1250 Btu/hr = (Trm - 20) * 20 Btu/hr + (Trm - 20)* 23 Btu/hr
1250  = (Trm - 20) * 43
Trm = 1250/43 + 20 = 49F

Since the room is now heated to 49F, the 2nd hour would be:

1250 Btu/hr = (Trm - 49) * 20 Btu/hr + (Trm - 20)* 23 Btu/hr
1250  = 43*Trm - 980 - 460
Trm = 2690/43 = 63F

Since the room is now heated to 63F, the 3rd hour would be:

1250 Btu/hr = (Trm - 63) * 20 Btu/hr + (Trm - 20)* 23 Btu/hr
1250  = 43*Trm - 1260 - 460
Trm = 2970/43 = 69F

After the 3rd hour, the room is comfortable (69degF).

---------------------------------------------------------------------------
--  
Suppose we added R20 foam insulation  to the ceiling and walls. We'll assum
e that the mattresses covering the floor add R20 to the floor, so that now,
 we have R40 everywhere
---------------------------------------------------------------------------
--  

(Trm - 20)degF*800sqft / R40 hr-sqft-degF/Btu] = (Trm - 20)* 20 Btu/hr

The heatflow equation then, is:
1250 Btu/hr = (Trm - 20) * 20 Btu/hr + (Trm - 20)* 20 Btu/hr
1250  = (Trm - 20) * 40
Trm = 1250/40 + 20 = 51F

Since the room is now heated to 51F, the 2nd hour would be:

1250 Btu/hr = (Trm - 51) * 20 Btu/hr + (Trm - 20)* 20 Btu/hr
1250  = 40*Trm - 1020 - 400
Trm = 2670/40 = 67F

Since the room is now heated to 67F, the 3rd hour would be:

1250 Btu/hr = (Trm - 67) * 20 Btu/hr + (Trm - 20)* 20 Btu/hr
1250  = 40*Trm - 1340 - 400
Trm = 2990/40 = 75F

After the 2nd hour, the room is comfortable (67degF). After the 3rd hour, t
he room is getting toasty (75degF).

-----------------------  
2 layers of the R7.7 4'x8' 2inch thick, foam board on the 4 walls and ceili
ng works out to about 30 boards.

2 layers * [2*8*10 + 2*8*12 + 10*12]/(4*8)
= 2 layers * 8*[20 + 24 + 15]/(4*8)
= [20 + 24 + 15]/2)
= 29.5 boards  

-------------------------------------

How big of a space heater would you need if you didn't insulate the room at
 all?

Let's say we wanted the room to be 70degF. and the heat from the space heat
er is Hsh

The heatflow equation given above becomes:  

Hsh + 1250 Btu/hr = (70 - 20) * 20 Btu/hr + (70 - 20)* 40 Btu/hr
Hsh + 1250 = 50 * (40+20)  
Hsh + 1250 = 50 * (60)  
Hsh + 1250 = 3000  
Hsh = 3000 - 1250 = 1750 Btu/hr = 1750 Btu/hr * 0.293 Watts/BTU/hr  
= 512Watts  


Posted by Morris Dovey on December 10, 2013, 6:37 am
 
On 12/9/13 11:37 PM, zoe_lithoi wrote:

Depending on how the home is sited, you might be able to try something  
like this: http://www.iedu.com/Solar/Panels/index.html  

--  
Morris Dovey
http://www.iedu.com/Solar/  


Posted by zoe_lithoi on January 10, 2014, 5:56 pm
 Greetings,

It appears there are many online articles claiming they can, along a turned
 on computer, for example, heat a room with candles... and include making a
 radiant heater out of 4 'tea candles' costing 1 british pound ($.65) for  
100 of them, the candles burn for about 4 hours. Is this fact or fiction? O
ne of the complaints was that no thermal calculations were done to support  
said claim, taking into account the size and insulation of the room, nor re
lating it's performance to how cold it is outside.  

My calc's below show that the claim is reasonable for a well-insulated room
 (R20) heated by 5 people and 4 British Tea candles.... 58degF for the 1st  
hour, and 70degF for the next.

One video is at:

http://www.whydontyoutrythis.com/2013/11/how-to-easily-heat-your-home-using  
-flower-pots-and-tea-lights.html

The 'Characterization of Candle Flames' paper can be read at:
http://fire.nist.gov/bfrlpubs/fire05/PDF/f05141.pdf  

The candle was calculated as 779Watt which can be converted to be 263 BT
U/h
So, 4 candles would yield about 1000 Btu/hr for 4 hours. Our goals is to ma
ke it thru an 8 hour nite, so we would need 8 candles per nite which would  
cost 8 *$.64/100 = 0.13 (13 cents), so over 1 month, it would cost about
 50cents.

Let's add candle light heat to the calculations I made earlier in this thre
ad about heating a a 10x12', R20 bedroom with the heat from 5 people, total
ing about 1250Btu/hr with an outside temperature of 20degF.... resulting in
 a 41F room temperature. So the 4-candle heater 'claim' doesn't seem like i
t would do much good on a 20degF night.... even if combined with heat from  
an approix. 200 Watt (680btu/hr) computer.  

Calculations are below my signature.

Toby

From before, the surface area of the 4 walls, floor, and ceiling would be:

A = 4*8*12 + 2*8*10 + 2*10*12 = 2^4 * [24+10+15*49 ~= 16*50 =  
800sqft

There is 300 Btu/hr for a sedentary adult, so let's estimate, with kids, 25
0btu/hr and average, i.e. the amount of heat entering the room from sleepin
g people:

H (people) = 5*250Btu/hr = 1250 Btu/hr
H (4 candles) = 1000 Btu/hr
H (total) = 2250 Btu/hr

The Heat leaving the room, of Temperature, Trm, to the 20degF outside thru  
the 800sqft of R20 walls, floor, and ceiling is:

(Trm - 20)degF*800sqft / R20 hr-sqft-degF/Btu] = (Trm - 20)* 40 Btu/hr

The amount of heat the air in the 1000cuft (8'*10'*12' = ~1000cuft) room  
 absorbs to go from 20degF to Trm is:

(Trm - 20)degF * 1/55 Btu/F /cuft  * 1000cuft ~= (Trm - 20) * 20 Btu
I guess in the first hour this would be:

(Trm - 20) * 20 Btu/hr

The heatflow equation then, is:

2250 Btu/hr = (Trm - 20) * 20 Btu/hr + (Trm - 20)* 40 Btu/hr
1250  = (Trm - 20) * 60
Trm = 2250/60 + 20 = 57.5F

Since the room is now heated to 57.5F, the 2nd hour would be:

2250 Btu/hr = (Trm - 57.5) * 20 Btu/hr + (Trm - 20)* 40 Btu/hr
2250  = 60Trm - 1150 -800
Trm = [4200]/60 = 70degF

Toby

On Monday, December 9, 2013 9:37:00 PM UTC-8, zoe_lithoi wrote:

 in their modular home when they cannot afford electricity or propane?

 of  $1 R7.7 4'x8' insulation foam board on the ceiling and 4 walls. The m
attresses would take up about the entire floor providing approix. R15 on th
e floor.  

hour the room temperature is 51, after 2 hours it is 63, and after 3 hours,
 it is 69degF.

 8 ft)  

2' room with 2 layers of this foam board insulation, you would need about 3
0 boards, i.e. $00. Ouch. BUT it's better than paying the 'typical' $00 p
er month for the heating bill for a 6 month winter ($800).  

 500Watt space heater (plus the 5 people). I'm guessing it's about 20cents  
per kilowatt, so the cost would be 10 cents per hour, or $.40 per day or $
72 pre month or $32 for a 6 month winter.

= 800sqft

250btu/hr and average, i.e. the amount of heat entering the room from sleep
ing people:

u the 800sqft of R20 walls, floor, and ceiling is:

m  absorbs to go from 20degF to Trm is:

----  

ume that the mattresses covering the floor add R15 to the floor, so that no
w, we have R20 + R15 = R35 everywhere

----  

----  

ume that the mattresses covering the floor add R20 to the floor, so that no
w, we have R40 everywhere

----  

 the room is getting toasty (75degF).

ling works out to about 30 boards.

at all?

ater is Hsh

= 512Watts


Posted by songbird on January 11, 2014, 1:48 pm
 Bob F wrote:
...

  i was thinking suffocation hazard in any room that
is tight enough to keep that much heat in.

  heat losses from highly insulated rooms are via
the doors/windows and without those you are asking
for suffocation.

  air exchangers will be very important if you want
this to fly, and then you will need a proper design
to make sure the heat is captured and not leaking.

  agreed on fire hazard too.  too many people in a
small room full of mattresses and blankets, not a
good combination with candles.

  i like the overall idea, but we keep the thermstat
set much lower so the heat needed to keep it warm is
much less.  our whole house costs about 1500/yr to  
keep warm per heating season.  not bad, but it could
be better.  i just don't want to sacrifice the views
out the patio doors and windows.  in the middle of  
the winter any light from outside is psychologically
important.

  when it was just me here most of the time i would
drop the thermostat down to 50-55F for the rest of
the house and keep this room a little warmer.  worked
fine for me, but it was too cold for visitors and that
wasted a lot of energy cycling the heat up and down.


  songbird

Posted by Morris Dovey on January 11, 2014, 7:44 pm
 On 1/11/14 11:50 AM, Bob F wrote:

That depends on the cost of the heating.

Doing whole-structure solar heating allows (on really sunny winter days)  
opening a window for comfort and fresh air. :-)

--  
Morris Dovey
http://www.iedu.com/Solar/  


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