Chapter 5.3.6 - Relative Humidity And The Absorption Coefficient

Air as a transparent gas is normally considered a radiatively nonparticipating gas
except when its temperature is extremely high. However, water vapor certainly
absorbs and/or emits radiative energy. This indicates an effect of the moisture content
of the ambient air on the radiative heat exchange of a system containing ambient
air.A quantity that is often used to express the amount of water vapor content
in the ambient air is the relative humidity. Therefore, to incorporate the effect of
moisture content in the air into the radiative heat exchange analysis, a correlation
between the relative humidity and the absorption coefficient of the water vapor may
be desirable.The absorption coefficient is a parameter that appears in the radiative
transfer equation (Sec. 2, Chap. 3 of this Handbook) and determines the attenuation
of the radiative energy by the medium, which in this case is humid air. It is known
that water vapor is an important participant of radiative heat exchange at high temperature
as for radiation of combustion product.The following sections present the
fundamental ideas to establish the relationship between relative humidity and the
absorption coefficient for humid air.

3.6.1 Absorption in Gas Layers

As shown in Fig. 3.10, for a beam of radiation that penetrates a gas layer in a coordinate
system, the spectral intensity along this beam can be written as (Özişik, 1977)

In Eq. (3.27), dI_λ is the spectral absorption coefficient of the gas layer.The solution
to this differential equation with an appropriate boundary condition gives

where I_λ0 is the spectral intensity evaluated at S = 0. When the thickness of the
medium that the beam penetrates is a length L, the spectral intensity at the location
L is evaluated as

The decrease in the intensity between S = 0 and S = L is the spectral radiation
attenuated by the gas layer of its thickness L. This can be written as (Özişik, 1977)

Equation (3.30) leads to obtain the spectral absorptivity, α_λ, of the gas layer that
forms the following relation (Özişik, 1977):

Equation (3.31) shows a direct relationship between the absorptivity and the
absorption coefficient of the gas layer for a known beam length of radiation. This
beam length can be determined by the notion of mean beam length for any desired
geometry. To solve Eq. (3.31) for the absorption coefficient, the absorptivity of the
gas must be found.

Air as a transparent gas is normally considered a radiatively nonparticipating gas
except when its temperature is extremely high. However, water vapor certainly
absorbs and/or emits radiative energy. This indicates an effect of the moisture content
of the ambient air on the radiative heat exchange of a system containing ambient
air.A quantity that is often used to express the amount of water vapor content
in the ambient air is the relative humidity. Therefore, to incorporate the effect of
moisture content in the air into the radiative heat exchange analysis, a correlation
between the relative humidity and the absorption coefficient of the water vapor may
be desirable.The absorption coefficient is a parameter that appears in the radiative
transfer equation (Sec. 2, Chap. 3 of this Handbook) and determines the attenuation
of the radiative energy by the medium, which in this case is humid air. It is known
that water vapor is an important participant of radiative heat exchange at high temperature
as for radiation of combustion product.The following sections present the
fundamental...