Flame radiation:

In fuel fired furnaces and other furnaces like reverberatory furnace, the principle mechanism of heat transfer is from the flame to the charge. The flame consists of the products of combustion. By considering sink as the surface area of the charge  and source as the flame of area  and assigning to the flame an equivalent body of gray emissivity , the rate of heat flow from the flame to the charge can be written as:

(17)

Note   is gas emissivity without solid particles whereas  is emissivity of gas with solid particles. Also  .

Heat flow from flame to charge for a given area of source and sink, and temperatures of the source and sink depends on emissivity of the flame. In a non-luminous flame such as pale blue or visually transparent flames obtained by burning hydrogen and other gaseous fuels, the radiation and convection are the principle mechanisms of heat transfer. In combustion of oil and pulverized coal, the flame contains clouds of fine particles of ash and carbon in addition to the products of combustion. These particles increases the emissivity of the flame and as a result heat transfer is enhanced. The furnace operator tries to make the flame luminous over as much length of the furnace as possible. For large pulverized coal flames, the emissivity could approach to unity which results in maximum rate of heat flow from the flame to the charge. By putting  in the equation 17, we get the expression for maximum heat flow:

(18)

According to equation 18, the maximum heat transfer from the flame requires a knowledge of actual flame temperature in the furnaces.

References:

• D.R. Poirier and G.H. Geiger: transport phenomena in material; processing.
• R. Schumann: Metallurgical Engineering, volume 1 engineering Principles