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Photon path length analysis of radiative heat transfer in planar layers with arbitrary temperature distributions
Institution:1. Department of Mechanical Engineering, Masdar Institute, Khalifa University of Science and Technology, Masdar Institute Solar Platform, PO Box 127788, Abu Dhabi, United Arab Emirates;2. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, United States;3. Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, United States;4. Shiley-Marcos School of Engineering, University of San Diego, 5998 Alcala Park, San Diego, CA 92110, United States;1. Functional Nanosystems, Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy;2. Dipartimento di Chimica e Chimica Industriale, Università Degli Studi di Genova, Via Dodecaneso 31, 16146 Genova, Italy;3. Dipartimento di Fisica, Università Degli Studi di Genova, Via Dodecaneso 33, 16146, Genova, Italy;1. Department of Mechanical Engineering, 10-367 Donadeo Innovation Center for Engineering, Advanced Water Research Lab (AWRL), University of Alberta, Edmonton, AB T6G 1H9, Canada;2. School of Industrial Engineering, Purdue University, 315 N. Grant Street, West Lafayette, IN 47907, USA;1. Department of Nuclear Science and Engineering. Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA;2. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139 USA;1. Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI 53706, USA;2. Department of Nuclear Engineering, University of California, Berkeley, CA 94720, USA;3. Pyrochemistry and Molten Salt Systems Department, Idaho National Laboratory, Idaho Falls, ID 83415, USA;4. Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA;5. Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA;6. Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA;7. Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
Abstract:The internal source analytical technique is extended to predict the radiative heat transfer for a layer having an arbitrary temperature distribution. By combining a number of internal sources distributed at various optical depths in the layer and weighting them appropriately, a nonisothermal layer is modeled. Heat flux and intensity distributions within layers having a single internal source are presented. The distributions are found to present trends unique to the internal source problem. Isothermal layers are modeled and compare very well with published results. Increased accuracy is attained for all cases and particularly for larger optical depths and smaller albedos by increasing the number of internal sources. The technique is applied to a nonisothermal layer having a temperature distribution similar to that for a hot medium with a cold boundary region. The effect of the boundary region on the normalized heat flux leaving the layer is seen to collapse to a single line for small layer optical thicknesses and large albedos, the slope of which is governed by the temperature ratio Tmax/Tmin.
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