The S-N discrete ordinates (DO) method is developed for the first time to solve transient radiative heat transfer in a two-dimensional rectangular enclosure with absorbing, emitting, and anisotropically scattering medium subject to diffuse and/or collimated laser irradiation. The transient DO method is used to solve several example problems and compared with the existing results and the Monte C...

A discussion of a modern version of the discrete-ordinates method is given, and in order to demonstrate well some aspects of the method, a very basic transport model is used to solve the elementary critical problem for a bare slab and for a bare cylinder. In addition to numerical results for these basic applications, various extensions of the method made to more challenging problems are noted.

In his classic work on radiative transfer, Chandrasekhar introduced the discrete ordinates method for solving the integro-di erential equation of radiative transfer; the spherical harmonics method is a spectral analog of this method. Not surprisingly, there is a close connection between the spherical harmonics and discrete ordinates methods. The spherical harmonics method raises some interestin...

A version of the discrete-ordinates method is used to solve, for the case of flow in a cylindrical tube, the classical Poiseuille and thermal-creep problems based on the Bhatnagar, Gross, and Krook model in the theory of rarefied-gas dynamics. In addition to the development of a discrete-ordinates solution that is valid for a wide range of the Knudsen number, the solution is evaluated numerical...

An e$cient method is used to compute the eigenvalues required in a discrete-ordinates solution to a special class of radiative-transfer problems. The basis for this computation is an algorithm for "nding eigenvalues of a matrix that consists of the sum of a diagonal matrix and a rank-one matrix, a form that can arise in a discrete-ordinates solution of some basic transport problems. To illustra...

In this work, we demonstrate the validity of the simplified spherical harmonics equations to approximate the more complicated equation of radiative transfer for modeling light propagation in biological tissue. We derive the simplified spherical harmonics equations up to order N = 7 for anisotropic scattering and partially reflective boundary conditions. We compare numerical results with diffusi...

The Discrete Ordinates Method (DOM) for solving transient radiation transfer equation in cylindrical coordinates is developed for radiation heat transfer in participating turbid media in pico-scale time domain. The application problems addressed here are laser tissue welding and soldering. The novelty of this study lies with the use of ultrashort laser pulses as the irradiation source. The char...