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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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Figures

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Fig. 1

Description of the studied system

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Fig. 2

Schematic representation of the used spatial grid for the equations discretization

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Fig. 3

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

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