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Eric Hasamann January 9, 2008 13:51

how to define the emissivity
Hello, everyone, I wanna simulate radiation heat transfer in a duct. When defining the material properies, however, I dont know how to set the emissivity of the fluid, in which 70% is CO2. In the 'materials panel', only absorption coefficient is required, but I am confused to see the unit of it is 1/m, because as i got from Heat and mass transfer lecture, Absorption coefficient doesnt have unit and its value is equal to the emissivity. Based on my calculation, the emissivity is about 0.2 as there's dust inside. So would anybody tell me how to define this value to the material, and what's the relationship between the emissivity and absorption coefficient described in Fluent?

Many thanks,

Eric Hasamann

Rami January 10, 2008 03:20

Re: how to define the emissivity
You confuse between two properties, which have some similarity:

The absorption coefficient is a property of a participating (or semi-transparent) medium, and is the relative amount of power absorption along a ray as it passes through the material volume, and its units are indeed (1/length).

Emissivity, absorptivity (and also reflectivity and transmissivity) are properties of a surface, and are dimensionless. The absorptivity is the relative amount of absorbed power in the surface relative to the incident power. You may read about these properties in any standard textbook on radiation (e.g., Siegel & Howell or Modest).

Eric Hasamann January 10, 2008 10:09

Re: how to define the emissivity
Hey Rami, Thanks for your answer. I am trying to tell the difference by reading textbooks. But would you please tell me how to define the emissivity? I am really a newie in Fluent. Thanks a lot. Eric

Rami January 10, 2008 10:34

Re: how to define the emissivity
Hi Eric,

I am new to Fluent as well, but I'll see if I can help nevertheless. However, in order to answer, you should give more details relevant to the radiative heat transfer.

If the gas is almost transparent (i.e., non-participating,), the radiation transfer is merely at the walls. In this case you may use one of the simpler models (e.g. s2s), which is more limited, and need only the prescription of the walls emissivity. Unfortunately, some of these models have other limitations as well, and you should check if they are still applicable to your problem.

On the other hand, if the gas contribution to radiation (by absorption, emission and/or scattering) is not negligible, you may need to use one of the more enhanced models, e.g., dom, and there you should give the medium radiative properties (the absorption and scattering coefficient and possibly the scattering phase function) in addition to the wall emissivities and other required data.

You'll have to gain some insight on these terms from the textbooks, and also define more precisely your needs.

Eric Hasamann January 10, 2008 12:12

Re: how to define the emissivity
Hey Rami, The following I give a very brief description to the project, hoping you can get some information. In order to remove carbon, steel is usally heated up to about 1900K, and then oxygen is introduced and reacts with carbon which givis off flue gas. Then the flue gas, sucked by a vaccum pump, passes through a long pipe. And here comes the problem, we want to know the temperature profile of the flue gas and the wall of the pipe in order to avoid pipe cracking caused by dramatic temperature change.

As we know, heat is transfered from the flue gas to the pipe wall by radiation and convection, but the convection heat transfer coefficient is very small comparing that of radiation for high temperature gas espcially a dustful gas. What I wanna simulate is this process, the heat transfer from the flue gas to the wall of pipe, in which the emissivity of the gas should be defined I think. Personally, I dont think s2s is the proper model.

Actually it's not a compex case, and I have finished the work by matlab. But I find Fluent is really an amazing code and it sparkls my interesting and makes me start the jouney. I really appreciate your help. Eric

Allan Walsh January 10, 2008 15:03

Re: how to define the emissivity
This subject can get difficult quickly, at least beyond my scope, but here are some quick pointers.

The emissivity (or absorptivity if it is a grey gas) is related not only to the gas composition but also the length that radiation has to travel. In your class, you probably used the mean beam length to get the emissivity of the gas based on the CO2 concentration.

So, the absorption coefficient in Fluent (with unit of 1/length) is divided by the mean beam length (or some other distance such as the cell width) to get non-dimensional absorptivity/emissivity. Fluent gives several options to relate the absorption coefficient to emissivity since the length is dependant on the geometry.

The P1 radiation model in Fluent should be suitable for your case. First set up a simple problem like a grey gas between two black plates of known temperature for which we have an analytical solution. Then choose a reasonable abs. coeff. to get an expected emissivity, given the distance between plates, and solve for the heat fluxes to the plates. Satisfy yourself that it works for the simple case and then use this same method for your duct. Good luck.

Eric Hasamann January 11, 2008 08:08

Re: how to define the emissivity
Hey Allan, Do you meant absorptivity/emissivity=absorption coefficient* mean beam length ? Up to now, I tried use DTRM model for simulation, and changed the absorptivity coefficient from 0.1 to 1, actually 0.1,0.5 and 0.9 were empoyed in order to find some helpful hints. I will try P1 later. Thanks so much for your help. Eric

opaque January 11, 2008 12:59

Re: how to define the emissivity
Dear Eric and Allan,

Let me clarify the picture a bit.

Radiation heat transfer is a volumetric phenomena that is characterized by the absorption, scattering and emission of energy. For highly absorbing materials (also called opaque materials), the energy is absorbed in a infinitesimal layer within the material; therefore, it can be modeled as a surface instead of a volume. To characterize these surfaces the concept of absorptivity, reflectivity and transmissivity have been introduced to represent the interaction of incoming radiation with these surfaces (noticed I am not including emission). These parameters are not material properties, but characteristics of the surface that include roughness, material properties, wavelength, coating effects, etc.

For semi-transparent materials like CO2, or H2O, the absorption coefficient, and scattering coefficient material properties are required to describe the radiation transfer. They are not related, nor to be confused with the emissivity.

The absorption coefficient for CO2, H2O, CO and gases in general are a function of wavelenght, pressure and composition of the mixture. There are several models available on how to estimate these numbers and how to proceed with the modeling. Your best source is a real textbook on thermal radiation, for example,

Radiative Heat Transfer, Michael Modest,

Thermal Radiation Heat Transfer, R. Siegel and J. Howell

Thermal Radiative Transfer and Properties, M. Brewster

On a separate topic, beware of using the local cell length scale into the radiation modeling. That makes your results mesh dependent and therefore unreliable. Stick to physical concepts or models.

On the radiation model: Allan recomendation to use P1 is as valid as yours to use DTRM. DTRM is more expensive but it can handle transparent regions (absorption coefficient = 0) while P1 will just blow up in your face (divide by 0). If you are using a constant non-zero absorption coefficient, you are safe; however, if your absorption coefficient is a function of mixture composition be careful.

Summary: the vocabulary for emissivity should be kept to the boundaries only, and not to refer to the material within the fluid zone.

Hope the above helps,


Allan Walsh January 11, 2008 14:36

Re: how to define the emissivity
I'm curious why you think emissivity shouldn't be used for gases? The charts from Hottel et al. are probably the most widely used source for finding gas emissivities, and that's term they use.

I don't think that the DTRM model can be used when particulate participate in radiation. For this case, with optically thin (i.e. not 70% CO2) gas, the DO model would seem to be a better choice.

opaque January 11, 2008 15:21

Re: how to define the emissivity
Dear Allan,

I do not have neither Hottel's nor Sarofim's books with me, but I do recall that Siegel and Howell referred to their data by "emittance charts" and not emissivity. Perhaps, I am old school, but emittance was used for accounting for extensive quantities (that depend on the amount of material such as thickness) and emissivity was an intensive quantity.

On the other hand, I noticed that Modest has removed the distinction between emissivity and emittance and use them freely. However, I rather use more basic names as they are known in the radiation literature and to avoid confusion. In fact, FLUENT ask the user for Absorption Coefficient, Scattering Coefficient and Refractive index instead of a gas emissivity as I am suggesting. I had extracted data from Hottel's chart, but I never refer to them as emissivity (matter of taste, perhaps).

DTRM can be used with particulate participating radiation. CFX supports it, but FLUENT does not. Then, it is not a model limitation, but an implementation issue. If the user also include particles, sure it must P1 or DO in FLUENT. However, DO is way more computationally intensive than DTRM. Also, if the user wants to go for a higher fidelity model of radiation properties, DO becomes even demanding.

Except for the classical value of Hottel's chart, the use of "gas emissivity" will not provide as many as hits when searching for detailed properties of gases. See how M. Modest or B Webb refer to radiation properties in their high end models.

Have a nice weekend,


Rami January 14, 2008 07:07

Re: how to define the emissivity
Few comment on the discussion.

I mostly agree with opaque. As to the choice of a model in FLUENT, it much depends on their limitations (which I don't remember off hand) as related to the problem at hand. The DO model is definitely the most general, but may be an over-kill.

As to the required properties -

1. Eric, please note that the absorption coefficient is NOT limited to the range 0-1 (unlike the emissivity). The upper limit may be larger. The same is also true for the scattering coefficient.

2. As the medium is a particle suspension in gas, it is most likely that the absorption and scattering coefficients are dominated by the particles, and NOT due to the gas. The appropriate value may be quite difficult to estimate in general, but can be measured or used parametrically (again, the values may be larger than 1, e.g., ~10 1/m was measured in our lab for a dilute suspension of fine carbon particles in CH4+CO2 carrier gas).

3. If the particles and gas are in equilibrium (i.e. have the same temperature and velocity at each location) a single fluid may be used with the gas properties + the radiative properties of the suspension. On the other hand, if there is no thermal equilibrium, I very much suspect if FLUENT can deal with it (at least as far as I understood their support engineer after long-lasting correspondence). This is mainly so since the radiation model uses the fluid temperature (which is the only temperature in the model) to calculate the emission of the medium, possibly with some contribution from the particles, rather than the other way around. There is also no convection model between the fluid and solid temperatures at each location in the volume.

4. In many cases of particles in a fluid, scattering is important, which makes thinks more complicated. For a crude model, is may be sufficient to assume isotropic scattering and the albedo (the scattering to extinction coefficient ratio) or even to use non-scattering medium with the extinction coefficient (=absorption coef. + scattering coef.) replacing the absorption coefficient.

5. The pipe walls emissivity should also be prescribed as a boundary condition. THIS is the non-dimensional property in the range 0-1.

Eric Hasamann January 14, 2008 07:10

Re: how to define the emissivity
Dear Allan and Opaque, First of all, thanks for all your help. I am trying to get the books you mentioned, and i hope i can work it out. Regards, Eric

sauravs February 21, 2014 04:47

absorption coefficients
my thesis is on recuperator(radiation modelling in ansys). flue gas have 10% each steam and co2, for that i need absortion coefficient to put it into ansys software. can u give me the data or references of these data? how to calculate them?

Aviral April 7, 2015 02:41

You can specify emissivity in boundary conditions.

anand.jittanakatti August 26, 2016 05:40


Originally Posted by Eric Hasamann
Hey Allan, Do you meant absorptivity/emissivity=absorption coefficient* mean beam length ? Up to now, I tried use DTRM model for simulation, and changed the absorptivity coefficient from 0.1 to 1, actually 0.1,0.5 and 0.9 were empoyed in order to find some helpful hints. I will try P1 later. Thanks so much for your help. Eric

I thought to update few things on Absorption coefficient and absorptivity

As the thickness of object increases the absorptivity increases
Absorptivity \propto Thickness of object

Objects become opaque to radiation if they are sufficiently thick enough to observe all the radiation passing through it.
Absorption coefficient is material property, while Absorptivity is with respect to objects, which in turn will depend on its size dimension.

Consider a glass of thickness 5 mm = 0.005 m
and if the absorption coefficient of the glass is 60 m^-1
Then absorptivity of the glass is 0.005*60 = 0.3

and if you increase the thickness of the glass to 50 mm = 0.05 m
then absorptivity of the glass equals to = 0.05*60 = 3

Limit of thickness at which the object becomes opaque is when absorptivity equals to 1.

Above absorptivity value of 1 object is opaque, below absorptivity value of 1 object is transparent to radiation

I hope this triggers some more life to this thread.

Thanks & Regards,
Anand Jittanakatti

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