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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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References

Murthy, J. Y., and Mathur, S. R., 1998, “Radiative Heat Transfer in Axisymmetric Geometries Using an Unstructured Finite-Volume Method,” Numer. Heat Transfer, Part B, 33, pp. 397–416. [CrossRef]
Kim, M. Y., and Baek, S. W., 2005, “Modeling of Radiative Heat Transfer in Axisymmetric Cylindrical Enclosures With Participating Medium,” J. Quant. Spectrosc. Radiat. Transfer, 90, pp. 377–388. [CrossRef]
Sanchez, A., Smith, T. F., and Krajewski, W. F., 1994, “Dimensionality Issues in Modeling With the Discrete-Ordinates Method,” ASME J. Heat Transfer, 116, pp. 257–260. [CrossRef]
Kumar, P., and Eswaran, V., 2007, “A Hybrid Scheme for Spatial Differencing in the Finite Volume Method for Radiative Heat Transfer in Complex Geometries,” The Fifth International Symposium on Radiative Transfer, Bodrum-Turkey.
Eswaran, V., and Prakash, S., 1998, “A Finite Volume Method for Navier-Stokes Equation,” Proceedings of the Third Asian Computational Fluid Dynamics Conference, Vol. 1, pp. 127–136.
Chai, J. C., ParthasarathyG., Lee, H. S., and Patankar, S. V., 1995, “Finite Volume Radiative Heat Transfer Procedure for Irregular Geometries,” J. Thermophys. Heat Transfer, 9(3), pp. 410–415. [CrossRef]

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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