Abstract
The equivalent beam length for the radiation from gas masses to their boundary surfaces as given by Hottel and Eckert results in good approximation when the gas bodies are small in size. However, the error is inevitable whem the gas body is as large as some furnaces including modern boiler furnaces. An exact calculation was practically impossible because the calculation was so tedious. In this paper is presented a simple method of calculation under the usual assumptions that the gas is homogeneous in its temperature and composition and that the radiation follows Beer's law, i.e.,
εg=1-e-Al
where
εg=gas emissivity,
A=coefficient of absorption,
l=path length,
e=base of hyperbolic logarithms.
Then, the emissivity of the wedge-shaped gas mass, as shown in Fig. 2, with height h and cross section 1/2 r2Δψ-an element of a cylindrical volume-to the infinitesimal a rea df can be obtained by the following equation given by E. Schmidt:
where
By integration, the emissivity at the corners of the surface bc in the rectangular parallelepiped b×c×h is given by the following equation:
The integration can be performed by transforming Φ(Z) into the following equation:
Φ(Z)=K0-K1Z+K2Z2-K3Z3
The results of the integration are summarized in Fig. 5 for various shapes and sizes of rectangular parallelepipeds. To find the emissivity at any point on the base surface of any rectangular parallelepiped, divide the parallelepiped into four parallelepipeds by two planes passing through the point. Then the emissivity for the four parallelepipeds to the point can readily be obtained from Fig. 5. The sum of the four emissivities is the emissivity in question.
