ARTICLE:

• NEW DISCRETE P₁ APPROXIMATION APPROACH TO SOLUTION OF RADIATIVE TRANSFER EQUATION IN MULTIDIMENSIONAL AND COMPLEX DOMAINS  download article

V. S. Yuferev
A. F. Ioffe Physical -Technical Institute of Russian Academy of Sciences, St. Petersburg, Russia

M. G. Vasil'ev
A. F. Ioffe Physical -Technical Institute of Russian Academy of Sciences, St. Petersburg, Russia

E. N. Kolesnikova
A. F. Ioffe Physical -Technical Institute of Russian Academy of Sciences, St. Petersburg, Russia

ABSTRACT

Advanced method for the solution of multi-dimensional radiative heat transfer problems is suggested. The basic idea of the method lies in construction of the special subdivision of the total solid angle surrounding an arbitrary point into a set of smaller solid angles (cells) and in representation of radiation intensity in each solid angle by P₁-approximation. Radiant transport equation is satisfied in the mean over each elementary cell and the system of the second order partial differential equations with respect to the local zeroth-moments of radiation intensity are derived in rectangular and cylindrical coordinates. It is demonstrated that the solid angle subdivision can be carried out by different ways with respect to specific features of the heat transfer problem under consideration. As a result even in using very rough partition one can get to satisfactory accuracy of the numerical solution. Special attention is given to the application of the proposed method to the calculation of radiative transfer in a non-participating media. One of the main advantages of this method consists in using the solid angle subdivisions which can be varied from point to point of a spatial domain. The latter gave possibility at the first time to calculate the radiative heat transfer in the optically dense circular cylinder of finite length with transparent specular side surface.

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