Is it reasonable to use the Stepan-Boltzman law when dealing with gases?

[suibhne]

Homework Statement

The Stephan Boltzmann Law used in black body cavity situations is sometimes used when dealing with gases, is this a valid use of the equation?

Homework Equations

H=AekT^4
H is heat current in radiation
A is the area
e is the emissivity
k the Stephan Boltzmann constant

The Attempt at a Solution

 

[CFDFEAGURU]

I use the Stefan-Boltzmann constant routinely in the calculation of the radiant heat flux from a gas to an adjoining surface.

The method that I use was developed by Hottel and requires determining radiation emission from a hemispherical gas mass at a temperature Tg to a surface element dA1, which is located at the center of the hemisphere's base.

The following is from "Fundamentals of Heat and Mass Transfer" 2nd Edition by Incropera and Dewitt

Emission from the gas per unit area of the surface is expressed as

Eg = $$\epsilon$$$$\sigma$$$$T^{}4$$

where $$\epsilon$$ is the gas emissivity
T is the temperature of the gas raised to the fourth power
$$\sigma$$ is the Stefan-Boltzmann constant

The gas emissivity is determined by correlating available data involving the temperature, the total pressure of the gas, the partial pressure of the radiating species, and the radius of the hemisphere.

Results for the correlation decribed above are available in graphical form for common product of combustion gases such as H2O and CO2.

Now you also have to consider the mean beam length for the gas geomety. (The gas geometry is defined by it's containers geometry.)

So ultimalely the original equation becomes

q = A*$$\sigma$$*($$\epsilon$$*T^4 - $$\alpha$$*T^4)

where $$\alpha$$ is the gas absorptivity, which is read from a graph.

So, my opinion is yes, the Stefan-Boltzmann constant can be used when dealing with common product of combustion gases.

Here is a link to Hottel's book.

https://www.amazon.com/dp/B0006BOZ9K/?tag=pfamazon01-20

Thanks
Matt

 

[suibhne]

CFDFEAGURU

Thanks for the reply will follow the lines you suggest.

 

[suibhne]

A CO2 molecule has two significant quantised infra red bands.
I still find it difficult to understand why some people think it is appropriate to use Stephan Boltzmann equation in this situation for an isolated molecule at STP.

 

[CFDFEAGURU]

The method that I described above is used when the gas is viewed as a continuum or a marcroscopic approach is used. This is the standard industry method for effectively dealing with those gases. I am not sure what type of equation would be used on the molecular level.

I still find it difficult to understand why some people think it is appropriate to use Stephan Boltzmann equation in this situation for an isolated molecule at STP.

I ask you then, how is a single molecule dealt with?

Thanks
Matt

 

[suibhne]

Since I do not work in the industry I do not have acess to study the effective ways of dealing with gases mixed or otherwise.
I would guess that in the case of CO2, excitation of thermal bands then by collision with say H2O would allow more permitted IR bands.
For a pure sample of CO2 gas then the mechanism must fall back on the behavior of a single molecule.
The spectrum of CO2 at IR bands and longer wavelengths look completely unlike a Stephan Boltzmann spectra.
Hence my original question.

 

[CFDFEAGURU]

Since I do not work in the industry I do not have acess to study the effective ways of dealing with gases mixed or otherwise.

Find the book "Radiative Transfer" by Hottel and Sarofim.

That will help you out.

Thanks
Matt

 

[suibhne]

I have since been told that the Stephan Boltzmann equation is not used in more recent methods dealing with heat transfer situations concerning gases.
The current method apparently takes account of the wavelength dependency and quantum nature involved to give a more realistic base to the calculation.

 

[CFDFEAGURU]

I have since been told that the Stephan Boltzmann equation is not used in more recent methods dealing with heat transfer situations concerning gases.

What is the source?

How are you treating the gas? Are you on the continuum level or the molecular level?

I have never heard of this.

"Thermal Radiation Heat Transfer" 4th Edition by Siegel and Howell use the same methods that I have described throughout this thread and it was published in 2002.

Thanks
Matt

 

[suibhne]

I was asking much the same question on scepticalscience website.
The thread was "Is CO2 a pollutant"
I used my same user name suibhne.
A dialog open up between my self and "carrot- eater" and in his second reply gave this latest information on use of Stephan Boltzmann Equation.

 

[CFDFEAGURU]

Well, I am not reading anything or believing anything from a site named scepticalscience from someone named carrot-eater. You didn't even take the time to provide a simple link to your argument.

Your original question has nothing to do with the quantum scale.

You also state that you do not work in the industry and you do not have access to laboratory equipment to perform testing on gases.

I am done with this thread. Thank you for wasting my time with stupid arguments from uncredable sources. I have given you two sources that will provide you with very helpful information on this subject.

 

[suibhne]

The sceptical science website despite its name is a site that supports the theory of AGW.
Carrot Eater I would guess from his reply works in a professional capacity in Climatology and certainly is a believer in the consensus view.
Thank you for directing me to your source- a very expensive book.

 

[Tandem78]

Thank you for directing me to your source- a very expensive book.

I found a freely downloadable set of files on the NASA library archive site. Thermal Radiation Heat Transfer, by Siegel&Howell, 3 volumes 1968-1971, NASA Ref SP-164.

Check http://ntrs.nasa.gov/search.jsp. Alternatively you can pay over $100 at Amazon for a bound copy.

T.

 

[suibhne]

Tandem78

Thanks very much, that's a big help all I need now is some paper for my printer many thanks.