Transient Radiation and Conduction Heat Transfer in Glass Sheets by the Thin Layer Approximation

[+] Author and Article Information
Georges El Hitti1

 Mines ParisTech, Center for Energy and Process Studies (CEP), CNRS FRE 2861, 60 Boulevard Saint-Michel, F-75272 Paris Cedex 06, Francegeorges.el_hitti@mines-paristech.fr

Maroun Nemer, Khalil El Khoury

 Mines ParisTech, Center for Energy and Process Studies (CEP), CNRS FRE 2861, 60 Boulevard Saint-Michel, F-75272 Paris Cedex 06, France


Corresponding author.

J. Heat Transfer 132(2), 023506 (Dec 03, 2009) (8 pages) doi:10.1115/1.4000228 History: Received October 31, 2008; Revised March 20, 2009; Published December 03, 2009; Online December 03, 2009

This paper is devoted to the simulation of 3D transient radiation and conduction heat transfer occurring inside thin glass sheets undergoing high temperature processing. The glass is considered as an absorbing, emitting, and nonscattering medium. The zonal method is used to establish the governing radiation transfer model. Direct exchange areas are calculated by the flux planes approximation. The thin layer approximation (TLA) is then introduced for increasing CPU efficiency. Three different numerical integration schemes made possible by the TLA are presented. Comparisons are made, with calculations performed using the finite volume method (FVM). The transient coupled energy equation is solved by a full implicit control volume method using the incomplete Cholesky conjugate gradient method. The heat transfer analysis of a glass sheet residing inside a hot rectangular enclosure is studied. Results obtained by the zonal method, with or without the TLA, are in close agreement with those obtained by the FVM. CPU requirements for radiative heat transfer analysis of the zonal method with TLA are, depending on the numerical integration scheme used, between 8 and 23 times smaller than those of the zonal method without TLA. The difference between the results of the different models never exceeds 4%. The zonal method with the TLA offered significant improvements in CPU time when compared with the original zonal method with similar or acceptable accuracy.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Simple schematic 2D representation of a standard processing furnace: processing enclosure (left), and discrete physical model of glass (right)

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Figure 2

Radiative exchange between two surfaces

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Figure 3

Absorption, reflection, refraction, and transmission of incident radiation on a glass sheet

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Figure 4

Geometric example of a flux plane projection onto a quarter of a plane

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Figure 5

DEA calculation between Sk and Vj: (a) regular meshing, and (b) ITL meshing

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Figure 6

Glass processing furnace analysis model

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Figure 7

Comparisons for steady state calculation: (a) glass dimensionless temperature along centerline x, (b) glass dimensionless temperature along centerline y, (c) heat flux divergence along centerline x, and (d) heat flux divergence along centerline y

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Figure 8

Dimensionless glass temperature as a function of dimensionless time: (a) x/Wglass=0.5, y/Hglass=0, and z/Lglass=0; (b) x/Wglass=0, y/Hglass=0, and z/Lglass=0




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