Radiative transfer in anisotropically scattering nonplanar media

Abstract

write a program (or proceed by hand calculation) to generate the array g. Running the commercial program with/and g as separate load cases would then give the strains to be used as input to an additional small, user written program for calculating the force Ff (and F«) of Eq. (5).Referencê allagher, R.H., Finite Element Analysis Fundamentals, Prentice-Hall, Englewood Cliffs, N.J., 1975, pp. 310-311. dimensional cylindrical and spherical geometries. To this effect, a linear phase function is used. Modest and Azad 3 showed that a slightly modified form of the linear model, used together with the differential P l approximation, yields quite accurate results in planar geometry. AnalysisConsider the equation of transfer ft.V/=o/,,-(a! + a)/+ -f /(IT) •/>(!),IT)dw-' 4TT J4* (1) Nomenclature B= emissive power, irl b I -radiation intensity I b = blackbody intensity t = direction cosine n = radius ratio, r 2 //*/ P = phase function Q = a constant r = dimensionless radial direction (a + a)r' r' = radial direction X = position vector a.= absorption coefficient j8 = polar angle e = emissivity X = scattering albedo, a/(a + a) % =cos0 a = scattering coefficient T = optical thickness, r 2 -r 1 <t > -azimuthal angle w = solid angle 0 = unit direction vector Subscripts 1,2 = inner and outer boundary, respectively

Radiative Heat Transfer in Absorbing, Emitting, and Anisotropically Scattering Boundary-Layer Flows

“…(9) or (10), together with the respective boundary conditions, constitute the system of differential equations to be solved simultaneously. After the temperature and radiative flux distributions are determined for a given set of values of the system parameters m, Pr, TV, d w , \, and a, the net heat flux at the wall can be evaluated by (12) In terms of the dimensionless quantities, Eq. (12) is expressed as…”