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Technical Brief

On the Boundary Intensities in a Plane Parallel Slab With Linearly Varying Refractive Index

[+] Author and Article Information
Vital Le Dez, Hamou Sadat

Institut PPRIMME,
UPR CNRS 3346,
Université de Poitiers,
40 Avenue du Recteur Pineau,
Poitiers 86022, France

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 11, 2015; final manuscript received February 29, 2016; published online April 5, 2016. Assoc. Editor: Laurent Pilon.

J. Heat Transfer 138(7), 074501 (Apr 05, 2016) (8 pages) Paper No: HT-15-1111; doi: 10.1115/1.4032982 History: Received February 11, 2015; Revised February 29, 2016

An exact expression of the outgoing boundary intensities in the case of a gray nonscattering semitransparent medium (STM) confined in a plane parallel slab with a refractive index linearly depending on the position is proposed. It is shown that directly using the diffuse reflection law gives in a much easier way exactly the same result as the one obtained with the pseudosource method.

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References

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Xia, X.-L. , Huang, Y. , Tan, H.-P. , and Zhang, X.-B. , 2002, “ Simultaneous Radiation and Conduction Heat Transfer in a Graded Index Semi-Transparent Slab With Gray Boundaries,” Int. J. Heat Mass Transfer, 45(13), pp. 2673–2688. [CrossRef]
Ma, J. , Sun, Y.-S. , and Li, B.-W. , 2013, “ Completely Spectral Collocation Solution of Radiative Heat Transfer in an Anisotropic Scattering Slab With a Graded Index Medium,” ASME J. Heat Transfer, 136(1), p. 012701. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Description of the studied system

Grahic Jump Location
Fig. 2

Schematic representation of the used spatial grid for the equations discretization

Grahic Jump Location
Fig. 3

Temperature fields in the slab for two optical depths: (a) τ0=0.1 and (b) τ0=1

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