Note about problem 13

11 Abril 2012, 13:35 Pedro Jorge Martins Coelho

There is a mistake in the statement of problem 13 (which has been taken from the book "Radiation Heat Transfer" by H.R.N. Jones, apart from minor changes in the data). Here is the correct formulation:

"Pulverized coal with density 1200 kg/m3is burned under stoichiometric conditions in air at 1600 ºC and 1 bar in a laboratory cylindrical combustion chamber with diameter 0.5 m and length 2 m. Calculate the emissivity of the combustion gases, assuming that the particles are black and their mean diameter is 50micron. What would be the emissivity of the combustion gases if the length and the diameter of the combustion chamber were 10 times larger?"

The solution is identical to that presented during the lecture, with the extinction coefficient being evaluated as 3*fv/2d. For large  black  particles, the absorption efficiency is equal to one, and the scattering efficiency is equal to zero, which yields an absorption coefficient equal to the extinction coefficient. Assuming that the gases are transparent to radiation, and only the particles contribute to the emissivity of the combustion gases, then we have emisivity=1-exp(-k*Lm).

Comment: in problems where both the radiation from the gases and the radiation from the particles are needed, the emissivity of gases+particles is given by 1-transmissvity(gases+particles), which is equal to 1 - transmissivity(gases)*transmissivity(particles).