Combustion consists of chemical reactions in series and in parallel and involving various intermediate species. The composition and concentration of these species cannot be predicted very well unless knowledge is available of the flame reaction kinetics; this detailed knowledge is not usually available or convenient to obtain. Because the flame radiation properties depend on the distributions of temperature and species within the flame, a detailed prediction of radiation from flames is not often possible from knowledge of only the combustible constituents and the flame geometry. It is usually necessary to resort to empirical methods for predicting radiative transfer in systems involving combustion.

Under certain conditions the constituents in a flame emit much more radiation in the visible region than would be expected from their gaseous absorption coefficients. For example, the typical almost transparent blue flame of a Bunsen burner can become a more highly emitting yellow-orange flame by changing the fuel-air ratio. Such luminous emission is usually ascribed to incandescent soot (hot carbon) particles formed because of incomplete combustion in hydrocarbon flames. Alternatively, Echigo et al. (1967)  and others have advanced the hypothesis, supported by some experimental facts, that luminous emission from some flames is by emission from vibration-rotation bands of chemical species that appear during the combustion process prior to the formation of soot particles. However, since soot formation is the most widely accepted view, soot radiation will be emphasized in this discussion of luminous flames.

D-1 Radiation from Nonluminous Flames

Radiation from the nonluminous portion of the combustion products is fairly well understood. For this the complexities of the chemical reaction are not as important, since it is the gaseous end products above the active burning region that are considered. Most instances are for hydrocarbon combustion, and radiation is from the CO2 and H2O absorption bands in the infrared. For flames a meter or more thick, as in commercial furnaces, the emission leaving the flame within the CO2 and H2O vibration-rotation bands can approach blackbody emission in the band spectral regions. The gas radiation properties in Chap. 9, and the methods in this chapter, can be used to compute the radiative transfer. The analysis is greatly simplified if the medium is well mixed and can be assumed isothermal. A nonisothermal medium can be divided into approximately isothermal zones, and convection can be included if the circulation pattern in the combustion chamber is known. A nonisothermal analysis with convection was carried out in Hottel and Sarofim (1965) for cylindrical flames. In Dayan and Tien (1974), Edwards and Balakrishnan (1973), Modak (1975, 1977), Taylor and Foster (1974), and Lefebvre (1984), radiation from various types of nonluminous flames (laminar or turbulent, mixed or diffusion) is treated. The flame shape for an open diffusion flame is considered in Annamali and Durbetaki (1975). The local absorption coefficient in nonluminous flames is calculated in Grosshandler and Thurlow (1992) as a function of mixture fraction and fuel composition. Modest (2005) reviews models for radiative transfer in combustion gases.

When considering the radiation from flames, a characteristic parameter is the average temperature of a well-mixed flame as a result of the addition of chemical energy. Well-developed methods exist [Gaydon and Wolfhard (1979)] for computing the theoretical flame temperature from thermodynamic data. The effect of preheating the fuel and/or oxidizer can be included. An ideal theoretical flame temperature T is computed using energy conservation assuming complete combustion, no dissociation of combustion products, and no heat losses. The energy in the constituents supplied to the combustion process, plus the energy of combustion, is equated to the energy of the combustion products to give,




Energy losses by radiation and other means, that would lower the flame temperature, are not included. Methods for including these effects are in Gaydon and Wolfhard (1979); extinction of a flame by radiative energy loss is analyzed in Ju et al. (2000). A list of ideal theoretical flame temperatures (no radiation or other losses included) is in Table 12-5 for various hydrocarbon flames, using data from Gaydon and Wolfhard and from Barnett and Hibbard (1957). Results for complete combustion with dry air are shown, followed by calculated results modified to allow for product dissociation and ionization. The latter are compared with experimental results. The heats of combustion of the substances are also given. Extensive tabulations of similar data for more than 200 hydrocarbons are in Barnett and Hibbard and in Perry et al. (2007). After its average temperature has been estimated, the radiation emitted by a nonluminous flame can be considered, as illustrated by an example.

EXAMPLE D-1 As a result of combustion of ethane in 100% excess air, the combustion products are 4 mol of CO2, 6 mol of H2O vapor, 33.3 mol of air, and 26.3 mol of N2. Assume these products are in a cylindrical region 4 m high and 2 m in diameter, are uniformly mixed at a theoretical flame temperature of 1853 K, and are at 1 atm pressure. Compute the radiation from the gaseous region.

The partial pressure of each constituent is equal to its mole fraction: , and . The gas mean beam length for negligible self-absorption is, from (12-66), . To include self-absorption, a correction factor of 0.9 is applied to give Le = 0.9(1.6) = 1.44 m. Then pCO2Le = 0.0575 × 1.44 = 0.0828 atm · m = 8.54 bar-cm, and pH2OLe = 0.0862 × 1.44 = 0.124 atm · m = 12.8 bar-cm.. Using the Leckner correlations [Eq. (9-62)] at 1853 K gives εCO2 = 0.070 and εH2O = 0.096 × 1.03 = 0.099. The 1.03 factor in εH2O is a correction for the partial pressure of the water vapor being nonzero [Eq. (9-64)]. There is also a negative correction from spectral overlap of the CO2 and H2O radiation bands. This is obtained from Eq. (9-67) at the values of the parameters:


= 20.9 bar-cm.


The correction is Δε = 0.031. Then the gas emittance is . The radiation from the gas region at the theoretical flame temperature is,



TABLE 12-5 Heat of combustion and flame temperature for hydrocarbon fuels [Gaydon and Wolfhard (1979); Barnett and Hibbard (1957); Lide (2008)]


Heat of combustion kJ/kg

Maximum flame temperature, K (combustion with dry air at 298 K)

Theoretical (complete combustion)

Theoretical (with dissociation and ionization)


Carbon monoxide (CO)

10.1 × 104




Hydrogen (H2)

14.1 × 104




Methane (CH4)

5.53 × 104




Ethane (C2H6)

5.19 × 104




Propane (C4H8)

5.03 × 104




n-Butane (C4H10)

4.95 × 104




n-Pentane (C5H12)

4.53 × 104




Ethylene (C2H4)

5.03 × 104




Propylene (C3H6)

4.89 × 104




Butylene (C4H8)

4.53 × 104




Amylene (C5H10)

4.50 × 104




Acetylene (C2H2)

5.00 × 104




Benzene (C6H6)

4.18 × 104




Toluene (C6H5CH3)

4.24 × 104