Chebyshev collocation spectral method for one-dimensional radiative heat transfer in graded index media |
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| Authors: | Ya-Song Sun Ben-Wen Li |
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| Affiliation: | 1. US Army Research, Development, and Engineering Command, Building 5400, Redstone Arsenal, AL 35898-5000, USA;2. Department of Math & Computer Sciences, Oakwood University, Huntsville, AL 35896, USA;1. NASA Langley Research Center, MS 475, Hampton, VA 23681, United States;2. University of California at Los Angeles, Joint Institute for Regional Earth System Science and Engineering, 607 Charles E Young Drive East, Young Hall, Room 4242, Los Angeles 90095-7228, United States;3. Stevens Institute of Technology, 1 Castle Point on Hudson, Physics and Engineering Physics, Hoboken, NJ 07030, United States;4. NASA Goddard Space Flight Center, Code 613, Greenbelt, MD 20771, United States;1. School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, PR China;2. Department of Mathematics, School of Science, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, PR China |
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| Abstract: | Chebyshev spectral collocation method based on discrete ordinates equation is developed to solve radiative transfer problems in a one-dimensional absorbing, emitting and scattering semitransparent slab with spatially variable refractive index. For radiative transfer equation, the angular domain is discretized by discrete ordinates method, and the spatial domain is discretized by Chebyshev collocation spectral method. Due to the exponential convergence of spectral methods, a very high accuracy can be obtained even using few nodes for present problems. Numerical results by the Chebyshev collocation spectral-discrete ordinates method (SP-DOM) are compared with those available data in references. Effects of refractive index gradient on radiative intensity are studied for space dependent scattering media. The results show that SP-DOM has a good accuracy and efficiency for solving radiative heat transfer problems in even spatially varying absorbing, emitting, scattering, and graded index media. |
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