The Differential-Discrete-Ordinate Method for Solutions of the Equation of Radiative Transfer

[+] Author and Article Information
S. Kumar, A. Majumdar, C. L. Tien

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

J. Heat Transfer 112(2), 424-429 (May 01, 1990) (6 pages) doi:10.1115/1.2910395 History: Received November 29, 1988; Revised July 26, 1989; Online May 23, 2008


This paper introduces a powerful but simple methodology for solving the general equation of radiative transfer for scattering and/or absorbing one-dimensional systems. Existing methods, usually designed to handle specific boundary and energy equilibrium conditions, either provide crude estimates or involve intricate mathematical analysis coupled with numerical techniques. In contrast, the present scheme, which uses a discrete-ordinate technique to reduce the integro-differential equation to a system of ordinary differential equations, utilizes readily available software routines to solve the resulting set of coupled first-order ordinary differential equations as a two-point boundary value problem. The advantage of this approach is that the user is freed from having to understand complicated mathematical analysis and perform extensive computer programming. Additionally, the software used is state of the art, which is less prone to numerical instabilities and inaccuracies. Any degree of scattering anisotropy and albedo can be incorporated along with different conditions of energy equilibrium or specified temperature distributions and boundary conditions. Examples are presented where the radiative transfer is computed by using different quadratures such as Gaussian, Lobatto, Fiveland, Chebyshev, and Newton-Cotes. Comparison with benchmark cases shows that in a highly forward scattering medium Gaussian quadrature provides the most accurate and stable solutions.

Copyright © 1990 by The American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.






Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In