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Straw-infilled-Pallet Winter Greenhouse.

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Posted by zoe_lithoi on November 30, 2014, 5:28 pm
 
Straw-infilled-Pallet Winter Greenhouse.
Greetings,

My son and I are building a 80" x 80" x 8'(tall) 'winter' Greenhouse made o
f pallets screwed together and stuffed with straw for insulation (R10?).  I
t has plastic stapled to the inside which should prevent heat loss by conve
ction. The Roof has masonite siding on it in case of rain. We will have 200
 of grow lights which will also serve as the primary heat source. The groun
d will be either a heat source or a heat sink (not sure yet.....). The goal
 is to keep the temperature above freezing so the seedlings don't die.

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

A = 4*7*8 + 7*7 = 273 sqft

The heat from the growlights
Hgl = 200W * 3.41 Btu/1Watt-hr = 682 Btu/hr

Hgnd = ground heat will be called:  
For now, we will assume that heat from the growlites will enter the ground.

Hrm =  heat leaving the room of Temperature, Trm, thru the 273sqft of R10
 walls and ceiling to the 20degF outside  is:

Hrm = (Trm - 20)degF*273sqft / R10 hr-sqft-degF/Btu] = (Trm - 20)* 27 B
tu/hr

If the room gets new air each hour equivalent to it's volume, then the air-
exchange heat loss for the amount of heat the air in the 400cuft (8'*7'*7')
 room  absorbs to go from 20degF to Trm is:

Hair = (Trm - 20)degF * 1/55 Btu/F /cuft  * 400cuft ~= (Trm - 20) * 5 B
tu/hr

The heatflow equation then, is:

Hgl = Hgnd + Hrm + Hair
682 = Hgnd + (Trm - 20)* 27 + (Trm - 20) * 5

For now, let's assume the heat flow into or out of the ground is 0, i.e.:
   Hgnd = 0

682 = (Trm - 20)* 27 + (Trm - 20) * 5
682 = 33*Trm - 20* (27 + 5)
682 = 33*Trm - 660
1342 = 33*Trm
Trm = 1342/33 = 41degF

If the outside temperature was 0degF, then
Trm = 682/33 = 21degF
--- daid seedlings

So we need to look at the ground temperature.

In the above calc's, Trm is between 20 and 40degF. The Ground temperature,  
for the southwest (NEvada, Utah, Arizona), 4inches deep (the approix depth  
heat can travel in the ground in 1 hour --- see the 'daycreek' thread in th
is group), is about 50degF. So as long as the greenhouse temperature, Trm,  
is below 50degF, then the ground is a heat source and supplies heat to the  
greenhouse.

-----------------------------  

-SAND Heat capacity 2.5 BTU/(F-sqft-in)  
-SAND Resistance    0.083 hr-sqft-F/(BTU-in)  

From past calculations and real-world example (daycreek.com), ground heat t
ravels about 4inches per hour, so:

-SAND Heat capacity 2.5 BTU/(F-sqft-in) * 4inch =  10 BTU/F-sqft  
-SAND Resistance    0.083 hr-sqft-F/(BTU-in)  * 4inch = 0.33 hr-sqft-F/Bt
u

The surface area of the ground is:
7' x 7' = ~50sqft

Hgnd = (50degF - Trm)*50sqft / [0.33 hr-sqft-F/Btu]
Hgnd = (50degF - Trm) * 16.5 Btu/hr
    
-------------------
Now let's include the ground heat in the heatflow equation which again is:

Hgl = - Hgnd + Hrm + Hair
682 = -(50degF - Trm) * 16.5 + (Trm - 20)* 27 + (Trm - 20) * 5
682 = (+16.5+27+5)*Trm - 50*16.5 - 20* (27 + 5)
682 = 44*Trm - 825 - 660
2167 = 44*Trm
Trm = 2167/44 = 49degF

Now, if the outside temperature is 0degF (instead of 20degF):
682 = (+16.5+27+5)*Trm - 50*16.5 - 0* (27 + 5)
682 = 44*Trm - 825  
1597 = 44*Trm
Trm = 1507/44 = 34

If a 400Watt growlite were used, and it was 0degF
Hgl = 1364Btu/hr
Then:
1364 = 44*Trm - 825  
2189 = 44*Trm
Trm = 2189/44 = 50degF

If there were not any growlites, and it was 20degF outside, then:
0 = 44*Trm - 825 - 660
1485 = 44*Trm
Trm = 1485/44 = 34degF

The lowest daily low temperature in Las Vegas Nv for the month of July is 4
0degF
See: https://weatherspark.com/averages/31890/1/Las-Vegas-Nevada-United-Stat  
es

Daytime temperatures are normally in the 50's and 60's.

Using Outside temperature of 40degF, with a 200W growlight we get:

682 = (+16.5+27+5)*Trm - 50*16.5 - 40* (27 + 5)
682 = 44*Trm - 825 - 1320
2827 = 44*Trm
Trm = 2827/44 = 64degF


Using Outside temperature of 40degF, without a 200W growlight we get:

0 = (+16.5+27+5)*Trm - 50*16.5 - 40* (27 + 5)
0 = 44*Trm - 825 - 1320
2145 = 44*Trm
Trm = 2145/44 = 49degF

So, one might have a thermostat to power the growlights if the temperature  
dropped below 45degF.... AND Further, put the growlites on a timer to give  
it 12 hours each day (so the plants can get light) during night-time hours  
when it is coldest outside.

200W * 1kW/1000W * $.11/kW-hr * 12hr/day = 0.26cents/day
--> $/month
--> $8/Winter (6-months)

Toby

Posted by zoe_lithoi on December 25, 2014, 5:53 pm
 
Greetings,

I took some temperature readings with a usb-type data logger for 2 days. on
e day had some 200Watt grow lights on, while the other did not. The 2 logge
rs, unfortunately were not very accurate because to start with, I had them  
both inside a room next to each other, and one read 80degF while the other  
read 82degF. I put one outside, and the other inside the greenhouse. I'm pa
sting the spreadsheet data here, and am not sure how it will appear when it
's processed by Google.

            No Lights    200W Lights    Notes
            Tmp-I    Tmp-O    Tmp-I    Tmp-O    
Date        Time    Inside    Outside    Inside    Outside    
12/22/14    1616    80    82            Both Temp Probes
                            In House
12/22/14    1816    63                
12/23/14    0    57    56            
12/23/14    700    52    53            low Tmp-I & Tmp-O
                            Equalization: No Heat
                            Flow into or out of
                            Greenhouse
12/23/14    830    52    55            
12/23/14    1306        82            High Tmp-O
                            Heat into Ground
12/23/14    1420    62    69            High Tmp-I
12/23/14    1545    62    64            
12/24/14    0            50    35    
12/24/14    300                30    
12/24/14    500            43    30    
12/24/14    545            43    30    

I estimate the 'ground temperature' equals 53degF by noting that with the l
ights off on  12/23/14 for a period around 700 (7am), the outside temperatu
re and inside temperature were about equal. I call this equalization. There
 was no heat flowing into the greenhouse from the outside, and there was no
 heat flowing into or out of the greenhouse through the ground. This was an
other way to confirm my estimate in the previous posting on this thread whe
re I said the ground temperature about 4inches deep was about 50degF. IT's  
not quite that simple. The temperatures 7 hours earlier at 0am on 12/23/14  
show heat flowing from the greenhouse to the outside. This heat is being su
pplied by the ground. So what has happenned is that the ground temperature  
had heated up (charged up) prior to that, and now this thermal capacitor wa
s discharging. The ground temperature had to have been greater than the gre
enhouse temp (57). What this tells me is that the ground temperature cycles
 on that day from about 53 to 58F.

Let's make a better estimate of the overall thermal resistance of the Green
house by looking at the temperatures around 1420 to 1545 on 12/23/14. The g
reenhouse temperature, Trm, was 62F, and the outside air temperature was ab
out 65 to 66F (taking into account the 2deg temperature error mentioned abo
ve. In the last posting, I estimated that it had an R10 "R-Value" over a 27
3sqft surface area (walls and ceiling). Lets call this Rgv

Hrm =  heat entering the greenhouse room of Temperature, Trm, from the ou
tside air of temperature To, thru the 273sqft of Rgv walls and ceiling
Hrm = (To - Trm)degF*273sqft / Rgv hr-sqft-degF/Btu]  
Hrm = (To - Trm)*273/Rgv Btu/hr

Hgnd = ground heat  entering the greenhouse room of Temperature, Trm, thr
u the 50sqft of R0.33 dirt with temperature Tg  
Hgnd = (Tg - Trm)*50sqft / [0.33 hr-sqft-F/Btu]
Hgnd = (Tg - Trm)*150 Btu/hr

If the room gets new air each hour equivalent to it's volume, then the air-
exchange heat loss for the amount of heat the air in the 400cuft (8'*7'*7')
 room  absorbs to go from To degF to Trm is:  

Hair = (To - Trm)degF * 1/55 Btu/F /cuft  * 400cuft  
Hair = (To - Trm)* 5 Btu/hr

And lastly, there is another source of heat flow radiative in nature, Hrad,
 which for now we will assume is 0.

Kierkoff's Current (Heat) flow equation is:
  Hrm + Hgnd + Hair + Hrad = 0
  (To - Trm)*273/Rgv  + (Tg - Trm)*150 + (To - Trm)*5 + 0 = 0
  (To - Trm)*(273/Rgv + 5) + (Tg - Trm)*150 = 0

Now let's look at the data at 1420 to 1545 on 12/23/14 as stipulated:
Trm = 62F
To = 66F (The temperature range wa sfrom 69 to 64, but remember that this
 temperature probe recorded a 2degF higher temperature at the same location
 and time as the other probe, so the temp range was really 67 to 62. AT 62,
 it would be the same temperature as the other probe. So we will look at th
e 66F.)
Tg = 57F (in reality it could be anywhere between 55 to 58F, but since it
's at the hottest part of the day and still charging up, 57F is a reasonabl
e estimate IMO.)

(66 - 62)*(273/Rgv + 5) + (57 - 62)*150 = 0
(4)*(273/Rgv + 5) - (5)*150 = 0
(4)*(273/Rgv + 5) - (5)*150 = 0
1092/Rgv + 20 - 750 = 0
1092/Rgv = 730
Rgv = 1092/730 = 1.5  

huh. I would have expected more....

I'll have to relook at this and look at the data better.... and look at the
 radiative heat

Toby

On Sunday, November 30, 2014 9:28:27 AM UTC-8, zoe_lithoi wrote:

 of pallets screwed together and stuffed with straw for insulation (R10?).  
 It has plastic stapled to the inside which should prevent heat loss by con
vection. The Roof has masonite siding on it in case of rain. We will have 2
00 of grow lights which will also serve as the primary heat source. The gro
und will be either a heat source or a heat sink (not sure yet.....). The go
al is to keep the temperature above freezing so the seedlings don't die.

10 walls and ceiling to the 20degF outside  is:

 Btu/hr

r-exchange heat loss for the amount of heat the air in the 400cuft (8'*7'*7
') room  absorbs to go from 20degF to Trm is:

 Btu/hr

, for the southwest (NEvada, Utah, Arizona), 4inches deep (the approix dept
h heat can travel in the ground in 1 hour --- see the 'daycreek' thread in  
this group), is about 50degF. So as long as the greenhouse temperature, Trm
, is below 50degF, then the ground is a heat source and supplies heat to th
e greenhouse.

 travels about 4inches per hour, so:

 40degF

e dropped below 45degF.... AND Further, put the growlites on a timer to giv
e it 12 hours each day (so the plants can get light) during night-time hour
s when it is coldest outside.


Posted by zoe_lithoi on December 25, 2014, 7:03 pm
 Greetings,

So, I'm refining my calculations by taking account the heatflow thru the do
or which I had just reckoned as part of the straw-infill greenhouse.

The ~2'x7' plywood 'door'has an Rvalue of about R0.5 hence the heatflow thr
u the door
Hdr = (To-Trm)*14sqft/R0.5sqft-degF-hr/Btu  
Hdr = (To-Trm)* 28 Btu/hr

The surface area of the walls and ceiling can now be reduced by this 14sqft
 as well, from 273 to 259sqft:  
Hrm = (To - Trm)*259/Rgv Btu/hr

Kierkoff's Current (Heat) flow equation is now :  
  Hrm + Hdr + Hgnd + Hair + Hrad = 0  
  (To - Trm)*259/Rgv + (To-Trm)* 28 + (Tg - Trm)*150 + (To - Trm)*5 + 0 =
 0  
  (To - Trm)*(259/Rgv + 28 + 5) + (Tg - Trm)*150 = 0
  (To - Trm)*(259/Rgv + 33) + (Tg - Trm)*150 = 0

Now let's look at the data, as in the previous posting at 1420 to 1545 on 1
2/23/14 as stipulated:  
Trm = 62F  
To = 66F
Tg = 57F  

(66 - 62)*(259/Rgv + 33) + (57 - 62)*150 = 0  
(4)*(259/Rgv + 33) - (5)*150 = 0  
(4)*(259/Rgv + 33) - (5)*150 = 0  
1092/Rgv + 132 - 750 = 0  
1036/Rgv = 618  
Rgv = 1036/618 = 1.7

It 'still' should be more.
If the ground temp is 58 instead of 57.
(4)*(259/Rgv + 33) - (4)*150 = 0  
1092/Rgv + 132 - 600 = 0  
1036/Rgv = 468  
Rgv = 1036/468 = 2.2


Toby

On Thursday, December 25, 2014 9:53:43 AM UTC-8, zoe_lithoi wrote:

one day had some 200Watt grow lights on, while the other did not. The 2 log
gers, unfortunately were not very accurate because to start with, I had the
m both inside a room next to each other, and one read 80degF while the othe
r read 82degF. I put one outside, and the other inside the greenhouse. I'm  
pasting the spreadsheet data here, and am not sure how it will appear when  
it's processed by Google.

 lights off on  12/23/14 for a period around 700 (7am), the outside tempera
ture and inside temperature were about equal. I call this equalization. The
re was no heat flowing into the greenhouse from the outside, and there was  
no heat flowing into or out of the greenhouse through the ground. This was  
another way to confirm my estimate in the previous posting on this thread w
here I said the ground temperature about 4inches deep was about 50degF. IT'
s not quite that simple. The temperatures 7 hours earlier at 0am on 12/23/1
4 show heat flowing from the greenhouse to the outside. This heat is being  
supplied by the ground. So what has happenned is that the ground temperatur
e had heated up (charged up) prior to that, and now this thermal capacitor  
was discharging. The ground temperature had to have been greater than the g
reenhouse temp (57). What this tells me is that the ground temperature cycl
es on that day from about 53 to 58F.

enhouse by looking at the temperatures around 1420 to 1545 on 12/23/14. The
 greenhouse temperature, Trm, was 62F, and the outside air temperature was  
about 65 to 66F (taking into account the 2deg temperature error mentioned a
bove. In the last posting, I estimated that it had an R10 "R-Value" over a  
273sqft surface area (walls and ceiling). Lets call this Rgv

outside air of temperature To, thru the 273sqft of Rgv walls and ceiling

hru the 50sqft of R0.33 dirt with temperature Tg  

r-exchange heat loss for the amount of heat the air in the 400cuft (8'*7'*7
') room  absorbs to go from To degF to Trm is:  

d, which for now we will assume is 0.

is temperature probe recorded a 2degF higher temperature at the same locati
on and time as the other probe, so the temp range was really 67 to 62. AT 6
2, it would be the same temperature as the other probe. So we will look at  
the 66F.)

it's at the hottest part of the day and still charging up, 57F is a reasona
ble estimate IMO.)

he radiative heat

de of pallets screwed together and stuffed with straw for insulation (R10?)
.  It has plastic stapled to the inside which should prevent heat loss by c
onvection. The Roof has masonite siding on it in case of rain. We will have
 200 of grow lights which will also serve as the primary heat source. The g
round will be either a heat source or a heat sink (not sure yet.....). The  
goal is to keep the temperature above freezing so the seedlings don't die.

 R10 walls and ceiling to the 20degF outside  is:

27 Btu/hr

air-exchange heat loss for the amount of heat the air in the 400cuft (8'*7'
*7') room  absorbs to go from 20degF to Trm is:

 5 Btu/hr

re, for the southwest (NEvada, Utah, Arizona), 4inches deep (the approix de
pth heat can travel in the ground in 1 hour --- see the 'daycreek' thread i
n this group), is about 50degF. So as long as the greenhouse temperature, T
rm, is below 50degF, then the ground is a heat source and supplies heat to  
the greenhouse.

at travels about 4inches per hour, so:

is 40degF

States

ure dropped below 45degF.... AND Further, put the growlites on a timer to g
ive it 12 hours each day (so the plants can get light) during night-time ho
urs when it is coldest outside.


Posted by zoe_lithoi on December 25, 2014, 7:23 pm
 Greetings,

I am continuing to refine my calculations. This time by taking into account
 the radiative heat flow.

The room Temperature, Trm is 62F. The surface temperature of the floor is p
erhaps, TflaF

Now, radiant heatflow is generally calculated with the temperatures
in degree Rankine, not Fehrenheit. To convert:

Trankine = Tfehrenheit + 460

The standard radiation function is defined as follows:
Qrad = S*E*F*A*(Trm^4 - Tfl^4)  
where:  
S   = Stefan-Boltzmann Constant (SBC) = 0.119 x 10-10 BTU/Hr*in^2*R^4
      Note: this is a constant, and R4 means Rankine (as opposed to
            Fehrenheit) raised to the 4th power..
     =  0.119 x 10^-10 BTU/Hr*in^2*R^4  * 144 in^2/1 ft^2
     =  1.714 x 10^-9 Btu/Hr*ft^2*R^4
E   = emissivity =  0.9 (according to:
              http://ciks.cbt.nist.gov/bentz/nistir6551/node14.html )
F = geometric form factor = 1.0  
A = area   = 50 sqft (for the surface above the floor of the greenhouse
)
Qrad = radiant heat flow rate (Heat/Time)
Tfl = Temperature of the floor surface in Rankine
Trm = room temperature in Rankine

Now, radiant heatflow is generally calculated with the temperatures
in degree Rankine, not Fehrenheit. To convert:

Trankine = Tfehrenheit + 460

Qrad = S*E*F*A*( (Trm+460)^4 - (Tfl+460)^4)  

----------------------------------
Trm = 62F = 522 Rankine (The solar cistern's slab surface temperature)
Tfl = 61F = 521 Rankine
-----------------------------------

Qrad  =     FA(Tssc^4 - Th^4)  
=  1.714x10^-9 Btu/Hr*ft^2*R^4 * 0.9*1* 50ft^2 *((522)^4
-(521)^4)
=  1.714x10^-9 Btu/Hr*ft^2*R^4 * 0.9*1* 50ft^2 *(7.424 x10^10 -7.368
x10^10)
= 77.13 * 0.056 x10^10
= 4.3 Btu/hr

Kierkoff's Current (Heat) flow equation is now :  
  Hrm + Hdr + Hgnd + Hair + Hrad = 0  
  (To - Trm)*259/Rgv + (To-Trm)* 28 + (Tg - Trm)*150 + (To - Trm)*5 + 4 =
 0  
  (To - Trm)*(259/Rgv + 28 + 5) + (Tg - Trm)*150 + 4 = 0  
  (To - Trm)*(259/Rgv + 33) + (Tg - Trm)*150 + 4 = 0  

Now let's look at the data, as in the previous posting at 1420 to 1545 on 1
2/23/14 as stipulated:  
Trm = 62F  
To = 66F  
Tg = 58F  

(66 - 62)*(259/Rgv + 33) + (58 - 62)*150 + 4 = 0  
(4)*(259/Rgv + 33) - (4)*150 + 4 = 0  
(4)*(259/Rgv + 33) - (4)*150 + 4 = 0  
1092/Rgv + 132 - 600 + 4 = 0  
1036/Rgv = 464  
Rgv = 1036/464 = 2.23

It 'still' should be more.  

Toby

On Thursday, December 25, 2014 11:03:42 AM UTC-8, zoe_lithoi wrote:

door which I had just reckoned as part of the straw-infill greenhouse.

hru the door

ft as well, from 273 to 259sqft:  

= 0  

 12/23/14 as stipulated:  

. one day had some 200Watt grow lights on, while the other did not. The 2 l
oggers, unfortunately were not very accurate because to start with, I had t
hem both inside a room next to each other, and one read 80degF while the ot
her read 82degF. I put one outside, and the other inside the greenhouse. I'
m pasting the spreadsheet data here, and am not sure how it will appear whe
n it's processed by Google.

he lights off on  12/23/14 for a period around 700 (7am), the outside tempe
rature and inside temperature were about equal. I call this equalization. T
here was no heat flowing into the greenhouse from the outside, and there wa
s no heat flowing into or out of the greenhouse through the ground. This wa
s another way to confirm my estimate in the previous posting on this thread
 where I said the ground temperature about 4inches deep was about 50degF. I
T's not quite that simple. The temperatures 7 hours earlier at 0am on 12/23
/14 show heat flowing from the greenhouse to the outside. This heat is bein
g supplied by the ground. So what has happenned is that the ground temperat
ure had heated up (charged up) prior to that, and now this thermal capacito
r was discharging. The ground temperature had to have been greater than the
 greenhouse temp (57). What this tells me is that the ground temperature cy
cles on that day from about 53 to 58F.

reenhouse by looking at the temperatures around 1420 to 1545 on 12/23/14. T
he greenhouse temperature, Trm, was 62F, and the outside air temperature wa
s about 65 to 66F (taking into account the 2deg temperature error mentioned
 above. In the last posting, I estimated that it had an R10 "R-Value" over  
a 273sqft surface area (walls and ceiling). Lets call this Rgv

e outside air of temperature To, thru the 273sqft of Rgv walls and ceiling

 thru the 50sqft of R0.33 dirt with temperature Tg  

air-exchange heat loss for the amount of heat the air in the 400cuft (8'*7'
*7') room  absorbs to go from To degF to Trm is:  

rad, which for now we will assume is 0.

this temperature probe recorded a 2degF higher temperature at the same loca
tion and time as the other probe, so the temp range was really 67 to 62. AT
 62, it would be the same temperature as the other probe. So we will look a
t the 66F.)

e it's at the hottest part of the day and still charging up, 57F is a reaso
nable estimate IMO.)

 the radiative heat

made of pallets screwed together and stuffed with straw for insulation (R10
?).  It has plastic stapled to the inside which should prevent heat loss by
 convection. The Roof has masonite siding on it in case of rain. We will ha
ve 200 of grow lights which will also serve as the primary heat source. The
 ground will be either a heat source or a heat sink (not sure yet.....). Th
e goal is to keep the temperature above freezing so the seedlings don't die
.

round.

of R10 walls and ceiling to the 20degF outside  is:

* 27 Btu/hr

e air-exchange heat loss for the amount of heat the air in the 400cuft (8'*
7'*7') room  absorbs to go from 20degF to Trm is:

 * 5 Btu/hr

ture, for the southwest (NEvada, Utah, Arizona), 4inches deep (the approix  
depth heat can travel in the ground in 1 hour --- see the 'daycreek' thread
 in this group), is about 50degF. So as long as the greenhouse temperature,
 Trm, is below 50degF, then the ground is a heat source and supplies heat t
o the greenhouse.

heat travels about 4inches per hour, so:

t-F/Btu

y is 40degF

d-States

ature dropped below 45degF.... AND Further, put the growlites on a timer to
 give it 12 hours each day (so the plants can get light) during night-time  
hours when it is coldest outside.


Posted by zoe_lithoi on December 25, 2014, 7:51 pm
 Greetings,

Something is not right.  

I'm looking again at 2 things.
1. Rechecking the thermal resistance in the ground. We are looking at BTU p
er hour.  Heat travels about 4" through the ground in 1 hour. (see the appe
ndix after my signature).
2. There is what is called a 'warm-still' air resistance in series with the
 ground. It is small, and normally does not need to be taken into acount.
  
R0.67 sqft-hr-F/Btu for the warm air film

-----------------------------------  

In 1 hour, the heat is supplied to the air by the 4" of dirt.
Dirt has an Rvalue of R0.083/inch

R0.083/inch * 4 = R0.33 sqft-hr-F/Btu for 4 inches of dirt
plus
R0.67 sqft-hr-F/Btu for the warm air film
= R1 sqft-hr-F/Btu

This is 3 times greater than my earlier value I used which was R0.33. So re
calculating the heat through the floor:

Hgnd = ground heat  entering the greenhouse room of Temperature, Trm, thr
u the 50sqft of R1 dirt with temperature Tg  
Hgnd = (Tg - Trm)*50sqft / [R1 hr-sqft-F/Btu]  
Hgnd = (Tg - Trm)*50 Btu/hr

Kierkoff's Current (Heat) flow equation is now :  
  Hrm + Hdr + Hgnd + Hair + Hrad = 0  
  (To - Trm)*259/Rgv + (To-Trm)* 28 + (Tg - Trm)*50 + (To - Trm)*5 + 4 =  
0  
  (To - Trm)*(259/Rgv + 28 + 5) + (Tg - Trm)*50 + 4 = 0  
  (To - Trm)*(259/Rgv + 33) + (Tg - Trm)*50 + 4 = 0  

Now let's look at the data, as in the previous posting at 1420 to 1545 on 1
2/23/14 as stipulated:  
Trm = 62F  
To = 66F  
Tg = 58F  

(66 - 62)*(259/Rgv + 33) + (58 - 62)*50 + 4 = 0  
(4)*(259/Rgv + 33) - (4)*50 + 4 = 0  
1092/Rgv + 132 - 200 + 4 = 0  
1036/Rgv = 64  
Rgv = 1036/64 = 16.2

That is much more realistic!!!...  
My original estimation was R10.... Maybe 16.2 is too large.
Let's go back to the earlier posting which used Tg as 57.
(66 - 62)*(259/Rgv + 33) + (57 - 62)*50 + 4 = 0  
(4)*(259/Rgv + 33) - (5)*50 + 4 = 0  
1092/Rgv + 132 - 250 + 4 = 0  
1036/Rgv = 114  
Rgv = 1036/114 = R9

This seems the best fit.
Let's look at even more data.

Toby

Toby

Appendix: Heat travels about 4inches into the ground in 1 hour.  
Let's look at the depth, D, below 1 sqft of slab surface, As, heat
will travel in 1 hr, t:
  t = time = 1hr
  As = 1 sqft
  tr = thermal resistivity = 1.7 hr*ft*F/Btu  
          (fig 11-1 of  my earth-coupled heat transfer book)
  Cv = 30 Btu/F/cuft
  td = thermal diffusivity = 1/tr*C
-*-*-*-*-*-*-*-*-*
C = 30 Btu/F/cuft * D*1sqft = 30D Btu/F
  td = 1/[(1.7 hr*ft*F/Btu)*(30D Btu/F)] = 1/51D  sqft/hr

D = (1/51D sqft/hr)/(D ft) * 1 hr  
D = 1/[51*D^2]  
D^3 = 1/51 = 0.31 ft
D = (1/51)^(1/3) = 0.307' = 3.7"

On Thursday, December 25, 2014 11:23:10 AM UTC-8, zoe_lithoi wrote:

nt the radiative heat flow.

 perhaps, TflaF

= 0  

 12/23/14 as stipulated:  

e door which I had just reckoned as part of the straw-infill greenhouse.

 thru the door

sqft as well, from 273 to 259sqft:  

 = 0  

on 12/23/14 as stipulated:  

ys. one day had some 200Watt grow lights on, while the other did not. The 2
 loggers, unfortunately were not very accurate because to start with, I had
 them both inside a room next to each other, and one read 80degF while the  
other read 82degF. I put one outside, and the other inside the greenhouse.  
I'm pasting the spreadsheet data here, and am not sure how it will appear w
hen it's processed by Google.

 the lights off on  12/23/14 for a period around 700 (7am), the outside tem
perature and inside temperature were about equal. I call this equalization.
 There was no heat flowing into the greenhouse from the outside, and there  
was no heat flowing into or out of the greenhouse through the ground. This  
was another way to confirm my estimate in the previous posting on this thre
ad where I said the ground temperature about 4inches deep was about 50degF.
 IT's not quite that simple. The temperatures 7 hours earlier at 0am on 12/
23/14 show heat flowing from the greenhouse to the outside. This heat is be
ing supplied by the ground. So what has happenned is that the ground temper
ature had heated up (charged up) prior to that, and now this thermal capaci
tor was discharging. The ground temperature had to have been greater than t
he greenhouse temp (57). What this tells me is that the ground temperature  
cycles on that day from about 53 to 58F.

 Greenhouse by looking at the temperatures around 1420 to 1545 on 12/23/14.
 The greenhouse temperature, Trm, was 62F, and the outside air temperature  
was about 65 to 66F (taking into account the 2deg temperature error mention
ed above. In the last posting, I estimated that it had an R10 "R-Value" ove
r a 273sqft surface area (walls and ceiling). Lets call this Rgv

the outside air of temperature To, thru the 273sqft of Rgv walls and ceilin
g

m, thru the 50sqft of R0.33 dirt with temperature Tg  

e air-exchange heat loss for the amount of heat the air in the 400cuft (8'*
7'*7') room  absorbs to go from To degF to Trm is:  

 Hrad, which for now we will assume is 0.

t this temperature probe recorded a 2degF higher temperature at the same lo
cation and time as the other probe, so the temp range was really 67 to 62.  
AT 62, it would be the same temperature as the other probe. So we will look
 at the 66F.)

nce it's at the hottest part of the day and still charging up, 57F is a rea
sonable estimate IMO.)

at the radiative heat

e made of pallets screwed together and stuffed with straw for insulation (R
10?).  It has plastic stapled to the inside which should prevent heat loss  
by convection. The Roof has masonite siding on it in case of rain. We will  
have 200 of grow lights which will also serve as the primary heat source. T
he ground will be either a heat source or a heat sink (not sure yet.....).  
The goal is to keep the temperature above freezing so the seedlings don't d
ie.

 ground.

t of R10 walls and ceiling to the 20degF outside  is:

0)* 27 Btu/hr

the air-exchange heat loss for the amount of heat the air in the 400cuft (8
'*7'*7') room  absorbs to go from 20degF to Trm is:

0) * 5 Btu/hr

 i.e.:

rature, for the southwest (NEvada, Utah, Arizona), 4inches deep (the approi
x depth heat can travel in the ground in 1 hour --- see the 'daycreek' thre
ad in this group), is about 50degF. So as long as the greenhouse temperatur
e, Trm, is below 50degF, then the ground is a heat source and supplies heat
 to the greenhouse.

d heat travels about 4inches per hour, so:

  

qft-F/Btu

ain is:

uly is 40degF

ted-States

erature dropped below 45degF.... AND Further, put the growlites on a timer  
to give it 12 hours each day (so the plants can get light) during night-tim
e hours when it is coldest outside.


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