The $SKN$ method is proposed for solving radiative transfer problems in solid spherical participating medium. The method relies on approximating the integral transfer kernels by a sum of synthetic kernels. Then the transfer equation is reducible to a set of N-coupled second-order differential equations. The method is benchmarked against the exact and the discrete-ordinates method solutions for various optical radius and scattering albedos. Spatially varying scattering albedos are used to test the performance of the method in inhomogeneous media. Three quadrature sets are proposed for use with this method, and their convergence to the exact solution is investigated. It is demonstrated that the $SKN$ method possess the capability of solving radiative transfer problems yielding excellent solutions in solid spherical media.

1.
Lewis, E. E., and Miller, W. F., 1984, Computational Methods of Neutron Transport, John Wiley & Sons, Inc.
2.
,
B. I.
, and
Sterbentz
,
J. S.
,
1985
, “
Approximations to Neutron Transport Problems in Complex Geometries: I
,”
Nucl. Sci. Eng.
,
90
, pp.
431
440
.
3.
Altac¸
,
Z.
, and
,
B. I.
,
1990
, “
The SKN Method I: A High Order Transport Approximation to Neutron Transport Problems
,”
Nucl. Sci. Eng.
,
106
, pp.
471
479
.
4.
,
B. I.
, and
Altac¸
,
Z.
,
1990
, “
The SKN Method II: Heterogeneous Problems
,”
Nucl. Sci. Eng.
,
106
, pp.
480
488
.
5.
Altac¸, Z., 1989, “The SKN approximation: A New Method for Solving the Integral Transport Equations,” Ph.D. thesis, Iowa State University, Ames, IA.
6.
Altac¸
,
Z.
,
1997
, “
The SKN approximation for solving Radiation Transport Problems In Absorbing, Emitting, and Scattering Media
,”
DOGA Turk. Eng. Environ. Sci.
,
21
, pp.
51
58
.
7.
Altac¸
,
Z.
, and
Tekkalmaz
,
M.
,
2002
, “
The SKN approximation for Solving Radiation Transport Problems in Absorbing, Emitting, and Scattering Rectangular Geometries
,”
,
73
, pp.
219
230
.
8.
Altac¸
,
Z.
,
2002
, “
The SKN approximation for Solving Radiative Transfer Problems In Absorbing, Emitting, and Isotropically Scattering Plane-Parallel Medium: Part 1
,”
ASME J. Heat Transfer
,
124
(
4
), pp.
674
684
.
9.
Altac¸
,
Z.
,
2002
, “
The SKN approximation for Solving Radiative Transfer Problems In Absorbing, Emitting, and Linearly Anisotropically Scattering Plane-Parallel Medium: Part 2
,”
ASME J. Heat Transfer
,
124
(
4
), pp.
685
695
.
10.
Viskanta
,
R.
, and
Crosbie
,
A. L.
,
1967
, “
Radiative Transfer Through a Spherical Shell of an Absorbing-Emitting Gas Medium
,”
,
7
, pp.
871
889
.
11.
Abramowitz, M., and Stegun, I. A., 1964, Handbook of Mathematical Functions, Dover Publications Inc.
12.
Tsai
,
J. R.
,
O¨zis¸ik
,
M. N.
, and
Santarelli
,
F.
,
1989
, “
Radiation in Spherical Symmetry With Anisotropic Scattering and Variable Properties
,”