Accurate Three-Term Approximation of the Angular Distribution of the Radiation Intensity

Abstract

A very accurate approximation for the exponential integral £2 ( K ) was achieved by approximating the thermal radiation intensity by the first six terms of Legendre polynomial. The six constants in the three- 3 term expression for £2 ( K) = 2: Q; e- b; K through algebraic manipu- i = I lations were found. Unlike curve fitting approximations for £2 ( K ), the present three-term approximation gives accurate values for all optical thicknesses. For the sake of testing the new developed approximation, radiative equilibrium for planar participating gray media is considered. The radiative heat flux and the temperature distribution are compared with P-l and P-3 method results. Using the developed approximation for attacking radiative heat transfer in nongray medium is illustrated.