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## Main Question or Discussion Point

I am trying to model the cooling of an object (for example, a sheet of glass) placed outside at night. At the moment I am only considering heat loss by radiation.

I know that the net radiation from the object will be:

R

where:

R

R

R

I have come across a formula which does the above, but also takes into consideration the absorptivity of the sheet of glass at the 8-14μm wavelength (I have only considered emissivity of the glass in this wavelength as I'm only concerned with thermal radiation heat loss to the sky).

The formula is:

R

where:

ε

α

ε

T

T

A = the area of the object

What I would like to know is where does the ε

Can anyone help?

I know that the net radiation from the object will be:

R

_{net}= R_{obj}- R_{sky}where:

R

_{net}= the net radiation from the objectR

_{obj}= the total thermal radiation from the objectR

_{sky}= the thermal downwelling radiation from the skyI have come across a formula which does the above, but also takes into consideration the absorptivity of the sheet of glass at the 8-14μm wavelength (I have only considered emissivity of the glass in this wavelength as I'm only concerned with thermal radiation heat loss to the sky).

The formula is:

R

_{net}= A((ε_{obj}^{2}/α_{obj}^{2})σT_{obj}^{4}- ε_{sky}σT_{amb}^{4})where:

ε

_{obj}= the emissivity of the object at 8-14μmα

_{obj}= the absorptivity of the object at 8-14μmε

_{sky}= the emissivity of the skyT

_{obj}= the temperature of the objectT

_{amb}^{4}= the ambient air temperatureA = the area of the object

What I would like to know is where does the ε

_{obj}^{2}/α_{obj}^{2}bit come from? I know if I wasn't considering absorptivity then it would just be ε_{obj}, but why are ε_{obj}and α_{obj}now squared? I have since lost where I saw it, and I'm pretty sure there wasn't an explanation there anyway. I have searched all over for a derivation of it but have had no luck.Can anyone help?