0
Journal of Heat Transfer | Volume 127 | Issue 8 | Research Paper
RESEARCH PAPERS: Radiative Heat Transfer

Hybrid Method to Calculate Direct Exchange Areas Using the Finite Volume Method and Midpoint Intergration

[+] Author and Article Information
Weixue Tian

Department of Mechanical Engineering,  University of Connecticut, Storrs, CT 06269-3139

Wilson K. Chiu

Department of Mechanical Engineering,  University of Connecticut, Storrs, CT 06269-3139wchiu@engr.uconn.edu

J. Heat Transfer 127(8), 911-917 (Jan 27, 2005) (7 pages) doi:10.1115/1.1929786 History: Received March 29, 2004; Revised January 27, 2005
Article
References
Figures
Citing Articles

This paper presents a hybrid method to calculate direct exchange areas for an infinitely long black-walled rectangular enclosure. The hybrid method combines the finite volume method (FVM) with the midpoint integration scheme. Direct numerical integration of direct exchange areas for adjacent and overlapping zones is difficult because of singularities in the integrand. Therefore, direct exchange areas of adjacent and overlapping zones are calculated using the FVM. Direct exchange areas of nonadjacent zones are calculated by the efficient midpoint integration scheme. Thus, direct exchange areas in an infinitely long enclosure can be obtained with both efficiency and accuracy. Volume-volume direct exchange areas of zones with various aspect ratios and optical thickness have been calculated and compared to exact solutions, and satisfactory results are found.
FIGURES IN THIS ARTICLE
<>
Copyright © 2005 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
+Schematic of volume i and volume j zone in an infinite rectangular duct
View Large  |  Save Figure  |  Download Slide (.ppt)
Schematic of volume i and volume j zone in an infinite rectangular duct
Figure 1

Schematic of volume i and volume j zone in an infinite rectangular duct

Grahic Jump Location
+Schematic of an infinitely small volume i to volume j zone
View Large  |  Save Figure  |  Download Slide (.ppt)
Schematic of an infinitely small volume i to volume j zone
Figure 2

Schematic of an infinitely small volume i to volume j zone

Grahic Jump Location
+Change of η and Δτ with τij for 5% error
View Large  |  Save Figure  |  Download Slide (.ppt)
Change of η and Δτ with τij for 5% error
Figure 3

Change of η and Δτ with τij for 5% error

Grahic Jump Location
+Schematic of adjacent zones for direct exchange areas calculation using the FVM
View Large  |  Save Figure  |  Download Slide (.ppt)
Schematic of adjacent zones for direct exchange areas calculation using the FVM
Figure 4

Schematic of adjacent zones for direct exchange areas calculation using the FVM

Grahic Jump Location
+Enclosure with 10×10 zones to calculate direct exchange areas to zone 0
View Large  |  Save Figure  |  Download Slide (.ppt)
Enclosure with 10×10 zones to calculate direct exchange areas to zone 0
Figure 5

Enclosure with 10×10 zones to calculate direct exchange areas to zone 0

Grahic Jump Location
+Midpoint integration and its error for τL=τH=1 and Δτ=0.1: (a) comparison of direct exchange areas by midpoint integration and exact solution; and (b) relative error by midpoint integration
View Large  |  Save Figure  |  Download Slide (.ppt)
Midpoint integration and its error for τL=τH=1 and Δτ=0.1: (a) comparison of direct exchange areas by midpoint integration and exact solution; and (b) relative error by midpoint integration
Figure 6

Midpoint integration and its error for τL=τH=1 and Δτ=0.1: (a) comparison of direct exchange areas by midpoint integration and exact solution; and (b) relative error by midpoint integration

Grahic Jump Location
+Finite volume method and its error for τL=τH=1 and Δτ=0.1: (a) comparison of direct exchange areas by FVM and exact solution; and (bb) relative error by FVM
View Large  |  Save Figure  |  Download Slide (.ppt)
Finite volume method and its error for τL=τH=1 and Δτ=0.1: (a) comparison of direct exchange areas by FVM and exact solution; and (bb) relative error by FVM
Figure 7

Finite volume method and its error for τL=τH=1 and Δτ=0.1: (a) comparison of direct exchange areas by FVM and exact solution; and (bb) relative error by FVM

Grahic Jump Location
+Change in maximum error with optical thickness, 10×10 zones and τL=τH varying from 0.1 to 9: (a) maximum relative error of nonadjacent direct exchange areas by midpoint integration; and (b) maximum relative error of adjacent direct exchange areas by FVM
View Large  |  Save Figure  |  Download Slide (.ppt)
Change in maximum error with optical thickness, 10×10 zones and τL=τH varying from 0.1 to 9: (a) maximum relative error of nonadjacent direct exchange areas by midpoint integration; and (b) maximum relative error of adjacent direct exchange areas by FVM
Figure 8

Change in maximum error with optical thickness, 10×10 zones and τL=τH varying from 0.1 to 9: (a) maximum relative error of nonadjacent direct exchange areas by midpoint integration; and (b) maximum relative error of adjacent direct exchange areas by FVM

Grahic Jump Location
+Change of maximum error with varying aspect ratio, 10×10 zones, τL=0.5 and τH varying from 0.5 to 2.5: (a) maximum relative error of nonadjacent direct exchange areas by midpoint integration; and (b) maximum relative error of adjacent direct exchange areas by FVM
View Large  |  Save Figure  |  Download Slide (.ppt)
Change of maximum error with varying aspect ratio, 10×10 zones, τL=0.5 and τH varying from 0.5 to 2.5: (a) maximum relative error of nonadjacent direct exchange areas by midpoint integration; and (b) maximum relative error of adjacent direct exchange areas by FVM
Figure 9

Change of maximum error with varying aspect ratio, 10×10 zones, τL=0.5 and τH varying from 0.5 to 2.5: (a) maximum relative error of nonadjacent direct exchange areas by midpoint integration; and (b) maximum relative error of adjacent direct exchange areas by FVM

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Strategic Academic Mangment System
International Conference on Software Technology and Engineering, 3rd (ICSTE 2011)
Implementation of Selective Error Protection on SPIHT Coefficients for Wireless Visual Network
International Conference on Software Technology and Engineering, 3rd (ICSTE 2011)
A Study of the Influence of Facial Landmark Mislocalization on Automatic Age Estimation System
International Conference on Software Technology and Engineering, 3rd (ICSTE 2011)
Tales of the JEDEC Knight
More Hot Air> Chapter 5
Telecom: A Field with Myths and Mistakes All Its Own
More Hot Air> Chapter 7
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In