Seeing Through the Thermal Darkness

[Nick Pine]

Laren wrote:

>>... When the sensor in the box reads warmer than the room sensor,
>>you know that the window is giving you positive Solar gain. You
>>can then calculate the amount of Solar gain, based on the difference
>>between the two temperatures, as if the window glass area were
>>simply a wall surface, heated to the temperature of its sensor
>>readout.

>So, if the room sensor says 70 F and the sensor in the small box says
>80 F...

.... the slow-moving indoor airfilm resistance is R2/3, and the solar
gain is (80-70)1ft^2/(R2/3) = 15 Btu/h-ft^2?

That could happen with an outdoor temp of 30 F and net solar insolation
I = 150 Btu/h-ft^2 and a single-pane window with R2/3 and R1/3 indoor
and outdoor air films, like this, viewed in a fixed font like courier:

R1/3 (=1-2/3)
Tb = 80 = 30+I/3 --------www---- 30 F
|
| ---
---|<--|---|
---
I = 3(80-30) = 150 Btu/h-ft^2

The rest of the window would look like this:

R1
Ti = 70 F -------www---- 30 F
|
| ---
---|<--|---|
---
I = 150 Btu/h-ft^2

with a net solar gain of 150-((70-30)1ft^2/R1 = 110 vs 15 Btu/h-ft^2,
ie 7.3X more solar gain.

Alternatively, using your calc below vs your words above, the net gain
would be (80-70F)1ft^2/R1 = 10BTU/hr-ft^2...

That's an enormous (11X) difference. What gives?

>>BUT, only if the glazing had an insulation value of R1.

Hmmm.

>>By including the insulation value of the glazing, the net heat gain
>>can be easily calculated. For instance... if a window is assumed to be
>>generic R2 double glazing... then we have a net heat gain of:
>>
>> (80-70F)3'x4'/R2 = 60BTU/hr, [ie 60/(3'x4') = 5 Btu/h-ft^2, not much]

An R2 window with an R2/3 slow-moving indoor airfilm and an 80 F box temp
on a 30 F day would transmit 38 Btu/h-F of sun:

R1.33
Tb = 80 = 30+1.33I --------www---- 30 F
|
| ---
---|<--|---|
---
I = (80-30)/1.33 = 38 Btu/h-ft^2

with a net solar gain of 38-((70-30)1ft^2/R2 = 18 Btu/h-ft^2

R2
Ti = 70 F -------www---- 30 F
|
| ---
---|<--|---|
---
I = 38 Btu/h-ft^2

vs the 5 you would predict? And with 150 vs 38 Btu/h-F of net sun,

R1.33
Tb = 80 = T+1.33I --------www---- T = 80-1.33xI = -120 F :-)
|
| ---
---|<--|---|
---
I = 150 Btu/h-ft^2,

with a net solar gain of 150-((70-(-120))/R2 = 55 Btu/h-ft^2

R2
Ti = 70 F -------www---- -120 F
|
| ---
---|<--|---|
---
I = 150 Btu/h-ft^2

vs the 5 you would predict, leaving a large thermal darkness...

Nick