ARTICLE:

• TRANSIENT RADIATIVE TRANSFER IN PARTICIPATING MEDIA WITH SHORT-PULSE IRRADIATION - AN APPROXIMATE LAGUERRE-GALERKIN SOLUTION  download article

T. Okutucu
Middle East Technical University, Ankara, Turkey

Yaman Yener
Mechanical, Industrial and Manufacturing Engineering Department, Northeastern University, Boston, MA 02115

ABSTRACT

The Laguerre-Galerkin method previously developed by the authors for the solution of radiative transfer in a one-dimensional absorbing and isotropically scattering medium with short-pulse irradiation on one of its boundaries is further extended to include irradiation of Gaussian profile. In the application of the method, the time-dependent radiative intensity is first expanded in a series of Laguerre polynomials with time as the argument. Moments of the radiative transfer equation, as well as of the boundary conditions, then yield a set of coupled time-independent radiative transfer problems. This set, in turn, is reduced to a set of algebraic equations by the application of the Galerkin method. The transient transmittance and reflectance of the medium are evaluated for various values of the optical thickness, scattering albedo and pulse duration. When compared to the direct application of the Galerkin method, it is demonstrated that the Laguerre-Galerkin method is easier to implement and more efficient. The results are also in excellent agreement with those obtained by the Galerkin method.

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