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Technical Briefs

# Definition and Evaluation of Mean Beam Lengths for Applications in Multidimensional Radiative Heat Transfer: A Mathematically Self-Consistent Approach

[+] Author and Article Information
Walter W. Yuen

Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106

J. Heat Transfer 130(11), 114507 (Sep 05, 2008) (5 pages) doi:10.1115/1.2969752 History: Received June 19, 2007; Revised June 04, 2008; Published September 05, 2008

## Abstract

A set of mathematically self-consistent definitions of mean beam length is introduced to account for surface-surface, surface-volume, and volume-volume radiative exchanges in general three-dimensional inhomogeneous medium. Based on these definitions, the generic exchange factor (GEF) formulated by the recently introduced multiple-absorption-coefficient-zonal-method (MACZM) can be written in an equivalent one-dimensional form. The functional behavior of the proposed mean beam lengths is shown to be readily correlated by either simple algebraic relations or neural network based correlations. They can be implemented directly with MACZM in general computational code to account for the radiation effect in complex three-dimensional systems. In addition, these definitions of mean beam length can also be used to assess the accuracy of the conventional mean beam length concept currently used by the practicing engineering community.

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## Figures

Figure 1

Geometry of the emitting volume (area) and receiving volume (element) used in the definition of the two components of the GEF and the associated coordinate system

Figure 2

Comparison of the emission MBL and the conventional MBL and the corresponding exchange factor for the g1g2,pp exchange factor with (nx,ny,nz)=(0,0,0)

Figure 3

Schematic of a two-layer neural network used in generating the correlation for the emission MBL

Figure 4

Comparison between the neural network prediction of the emission MBL, Lem,pp, for different geometric configurations with nz=1

Figure 5

Comparison between the neural network prediction of the emission MBL, Lem,pd, for different geometric configurations with nz=1

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