radiationparticipatingmedium

7/29/2019 Radiationparticipatingmedium

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RADIATION EXCHANGE WITH EMITTING AND ABSORBING GASES

So far, radiation heat transfer between surfaces separated by a medium that does

not emit, absorb, or scatter radiation a non-participating medium that is

completely transparent to thermal radiation - A PERFECT VACUUM or air at ordinary

temperaturesand pressures comes very closeGases that consist of monatomic molecules such Ar and He and symmetric diatomic

molecules such as N2 and 02 are essentially transparent to radiation, except at

extremely high temperaturesat which ionisation occurs.

Hence, atmospheric air can be considered to be a non-participating medium in

radiation calculations

Gases with asymmetric molecules such as H20, CO2, CO, SO2 and hydrocarbons HnCmmay participate in the radiation process by absorption at moderate temperatures,

and by absorption and emission at high temperatures such as those encountered in

combustion chambers.

Therefore, air or any other medium that contains such gases with asymmetric

molecules at sufficient concentration must be treated as a participating medium inradiation calculations

Combustion gases in a furnace or a combustion chamber, for example, contain

sufficient amounts of H20 and CO2 and thus the emission and absorption of gases in

furnaces must be taken intoconsideration


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The presence of a participating medium complicates the radiation analysis

considerably for several reasons:

a participating medium emits and absorbs radiation throughout its entire volume.

That is, gaseous radiation is volumetric phenomena, thus it depends on the

size and the shape of the body. This is the case even if the temperature is

uniform throughoutthe medium

Gases emit and absorb radiation at a number ofnarrow wavelength bands. This is

in contrast to solids, which emit and absorb radiation over the entire

spectrum. Therefore, the gray assumption may not always be appropriate

for a gas even when the surrounding surfaces are gray

The emission and absorption characteristics of the constituents of a gas mixturealso depends on the temperature, pressure and composition of the gas

mixture. Therefore, the presence of other participating gases affects the

radiation characteristicsof a particulargas.

We will consider the emission and absorption of radiation by H2O and

CO2 only since they are the participating gases most commonlyencountered in practice (combution products in furnaces and

combustion chambers burning hydrocarbon fuels contain both gases at

high concentrations), and they are sufficient to demonstrate the basic

principles involved


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Radiation properties of a participating medium

Consider a participating medium of thickness L . A spectral radiation beam of

intensity I ,0 is incident on the medium, which is attenuated as it propagates due toabsorption. The decrease in the intensity of radiation as it passes through a layer of

thickness dx is proportional to the intensity itself and the thickness dx. This isknown as Beers law.

k Spectral absorption coefficient of the medium (m-1)

L

0x

L

0x

dxxI

xdI

dxxIxdI

Absorptivity of the medium is assumed to be

independent of x

L

0,

L,e

I

I

Radiation intensity decays exponentially according to Beers law


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Spectral transmissivity of a medium is defined as the ratio of the intensity of

radiation leaving the medium to that entering the medium

L

0,

L,e

I

I

=1 when no radiation is absorbed and thus the radiation intensityremains constantSpectral transmissivity of a medium represents the fraction of radiation transmitted

by the medium at a given wavelength.

Radiation passing through a non-scattering (and thus non-reflecting)

medium is either absorbed or transmitted. Therefore, + =1, andthe spectral absorptivity of a medium of thickness L is

Le111

From Kirchoffs law, the spectral emissivity of the medium is

Le1

Note that the spectral absorptivity, transmissivity and emissivity of a medium are

dimensionless quantities, with values less than or equal to 1. The spectral

absorption coefficient of a medium (, , ), in general, vary with wavelength,temperature,pressure and composition.


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For an optically thick medium ( a medium with large value ofL)0ee

L 11

1e1L

9933.01073795.6e;5L35

An optically thick medium emits like a blackbody at the given

wavelength

An optically thick absorbing-emitting medium with no significant

scattering at a given temperature Tg can be viewed as a black surface

at Tg since it will absorb essentially all the radiation passing through it

and it will emit the maximum possible radiation that can be emitted

by a surface at Tg, which is Eb(Tg)


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Emissivity of gases and gas mixtures

Spectral absorptivity of CO2 at 830 K and 10 atm

for a path length of 38.8 cm

Shape and width of absorption

bands vary with temperature and

pressure, but the magnitude of

absorptivity also varies with the

thickness of the gas layer

Hence, absorptivity values without

specified thickness and pressure

are meaningless

The non-gray nature of properties should be considered in radiation calculations for

high accuracy. This can be done using a band model, and thus performing

calculations for each absorption band. However, satisfactory results can be obtained

by assuming the gas to be gray, and using an effective total absorptivity and

emissivity determined by some averaging process.


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Even with gray assumption, the total emissivity and absorptivity of a gas depends

on the geometry of the gas body as well as the temperature, pressure, and

composition.

Gases that participate in radiation exchange such as CO2 and H2O typically coexist

with non-participating gases such as N2 and O2, and thus radiation properties of an

absorbing and emitting gas are usually reported for a mixture of the gas with non-

participating gases rather than the pure gas.

The emissivity and absorptivity of a gas component in a mixture depends primarily

on its density, which is a function of temperature and partial pressure of the gas


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Emissivity at a total pressure P other than P = 1 atm is determined by multipllying

the emissivity value at 1 atm by a pressure correction factor Cw for water vapour

atm1,www C

Note that Cw = 1 for P = 1 atm and thus (Pw + P)/2 0.5 ( a very low concentration ofwater vapour is used in the preparation of the emissivity chart in the figure and thus

Pw is very low)


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If the CO2 and H2O gases exist together in a mixture with non-

participating gases

wcg

atm1,wwatm1,ccg CC is the emissivity correction factor which accounts for the overlap ofemission bands. For a gas mixture that contains both CO2 and H2O

gases, is plotted.


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The emissivity of a gas also depends on the mean length an emitted

radiation beam travels in the gas before reaching a bounding surface,

and thus the shape and the size of the gas body involved.

During their experiments in the 1930s, Hottel and his coworkers

considered the emission of radiation from a hemispherical gas body to

a small surface element located at the center of the base of the

hemisphere. Therefore, the given charts represent emissivity data for

the emission of radiation from a hemispherical gas body of radius L

toward the center of the base of the hemisphere.

It is certainly desirable to extend the reported emissivity data to gasbodies of other geometries, and this is done by introducing the

concept of mean beam length, which represents the radius of

equivalent hemisphere

CONCEPT OF MEAN BEAM LENGTH


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Concept of the mean beam length

Consider a hot, isothermal, non-scattering gas volume radiating toward a black area element

dA on its surface.

The spectral heat flux arriving at and absorbed by dA from a volume element is equal to thespectral emission by dV into all 4 directions the fraction intercepted by dA the fractiontransmitted along the path from dV to dA

Spectral heat flux arriving at dA from all volume elements may be written as

SV b eScosdA

dVIq

244


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b i i f d i ( l d )


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Absorptivity of gases and gas mixtures (Hottels procedure)

Absorptivity of a gas that contains CO2 and H2O gases for radiation emitted by a

source at temperature Ts can be determined similarly from

wcg = is determined from the emissivity correction figure at the sourcetemperature Ts. Absorptivity is assumed to be same as emissivity, hence same charts

may be used.

gscsw

45.0

s

g

wc2

gscsc

65.0

s

g

cc2

T/L TP,TT

TCOH

T/L TP,TT

TCCO

The notation indicates that the emissivities should be evaluated using Ts instead of

Tg, PcLTs/Tg instead of PcL and PwLTs/Tg instead of PwL.Note that the absorptivity of the gas depends on the source temperature Ts as well

as the gas temperature Tg. Also, = when Ts = Tg, as expected.The pressure correction factors Cc and Cw are evaluated using PcL and PwL, as in

emissivity calculations.

Wh th t t l i i it f t t t T i k th i i


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When the total emissivity of a gas g at temperature Tg is known, the emissive powerof the gas (radiationemittedby the gas per unit surface area) is given by

4

gsggTAE

If the bounding surface is black at temperature Ts, the surface will emit radiation to

the gas at a rate of AsTs4 without reflecting any, and the gas will absorb thisradiation at a rate ofgAsTs4,whereg is the absorptivityof the gas.Then the net rate of radiation heat transfer between the gas and a black surface

surrounding it becomes

If the surface is not black, the analysis becomes more complicated because of the

radiation reflected by the surface. But for surfaces that are nearly black with an

emissivity s > 0.7, Hottel recommends this modification

4sg4ggssblack,netsgray,net TTA2

1Q2

1Q

The emissivity of wall surfaces of furnaces and combustion chambers are typically

greater than 0.7, and thus the relation above provides great convenience for

preliminary radiationheat transfer calculations.

44 sgggsnet TTAQ Black enclosure


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Reconsider the cylindrical furnace in the above example. For a wall temperature of

600 K, determine the absorptivity of the combustion gases and the rate of radiation

heat transfer from the combustiongases to the furnace walls.


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