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Technical Briefs

A Methodology to Solve 2D and Axisymmetric Radiative Transfer Problems Using a General 3D Solver

[+] Author and Article Information
P. Kumar

e-mail: dpradeep@iitk.ac.in

V. Eswaran

Department of Mechanical Engineering,
Indian Institute of Technology Kanpur,
Kanpur 208 016, India

1Corresponding author.

2Currently at IIT Hyderbad, e-mail: eswar@iith.ac.in.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 26, 2008; final manuscript received October 3, 2008; published online September 27, 2013. Assoc. Editor: Ofodike A. Ezekoye.

J. Heat Transfer 135(12), 124501 (Sep 27, 2013) (3 pages) Paper No: HT-08-1030; doi: 10.1115/1.4024674 History: Received January 26, 2008; Revised October 03, 2008

A method to solve the radiative transfer equation (RTE) for absorbing-emitting and/or scattering media for 2-D and axisymmetric geometries using a general 3-D solver with a special treatment of the boundary condition in the third direction is presented. It allows a choice of first- or second- order schemes and can be used with non-orthogonal hexahedral grids for complex domains. Two-dimensional or axisymmetric problems are treated as different special cases of a three-dimensional problem. The method is tested on axisymmetric problems with absorbing-emitting and/or scattering media and on a 2D planar problem with a transparent medium and validated by comparisons with benchmark solutions.

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Figures

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Fig. 1

Angular discretization

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Fig. 2

Schematic diagram of an axisymmetric plane rotated from the y–z plane, showing the complementary ray sc of an incoming ray sm

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Fig. 3

Grid system involved for axisymmetric calculation. The grid is only one cell wide in the axisymmetric direction.

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Fig. 4

A schematic diagram of a 2D complex geometry, with the bottom wall at 1000 K and other walls at 0 K, filled with an absorbing–emitting medium

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Fig. 5

Heat flux on the top wall of the 2D complex geometry

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Fig. 6

Nondimensional wall heat flux distribution on the curved wall on the truncated conical enclosure for an isotropic scattering medium, for different scattering albedo

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