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Research Papers: Radiative Heat Transfer

Immersed Boundary Method for Radiative Heat Transfer Problems in Nongray Media With Complex Internal and External Boundaries

[+] Author and Article Information
Piotr Łapka

Institute of Heat Engineering,
Warsaw University of Technology,
Nowowiejska Street 21/25,
Warsaw 00-665, Poland
e-mail: plapka@itc.pw.edu.pl

Piotr Furmański

Institute of Heat Engineering,
Warsaw University of Technology,
Nowowiejska Street 21/25,
Warsaw 00-665, Poland
e-mail: pfurm@itc.pw.edu.pl

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 16, 2016; final manuscript received August 19, 2016; published online November 8, 2016. Assoc. Editor: Laurent Pilon.

J. Heat Transfer 139(2), 022702 (Nov 08, 2016) (13 pages) Paper No: HT-16-1140; doi: 10.1115/1.4034772 History: Received March 16, 2016; Revised August 19, 2016

The immersed boundary method (IBM) is gaining attention in the computational fluid dynamics but its applications in the field of a conjugated radiative–conductive or radiative–convective heat transfer seem limited. Therefore, the paper presents extension of this method to heat transfer problems dominated by thermal radiation in a nongray medium. The present model enables simulation of heat and fluid flows in a domain with complex stationary or moving internal and external boundaries on a fixed Cartesian grid (FCG) by applying the finite volume method. The special attention is paid to modeling thermal radiation and optical phenomena at highly curved, opaque, or transparent boundaries which confine the computational domain or separate zones of different thermophysical and optical properties, e.g., different values of a refractive index. The model is limited to a 2D planar or axisymmetric spaces. Detailed verification procedure proves accuracy and correctness of the developed model and shows its potential application field. The model may be used for simulations of a conjugated radiative–conductive or radiative–convective heat transfer in a nongray medium in a complex domain with opaque or transparent curved internal or external boundaries without unstructured or body fitted mesh generation.

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References

Figures

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Fig. 1

(a) Spectral intensities at the interface between the semitransparent media a and b of nν,a < nν,b, (b) transmission of the incident ray from a to b, and (c) transmission of the incident ray from b to a

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Fig. 2

(a) Representation of the SLI and normal temperature gradients reconstruction, (b) way for accounting for the radiative heat fluxes at marker i, and (c) general idea of the IBM

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Fig. 3

(a) View of the overlapping CSA, (b) view of the overlapping CSA for the case of the reflection and refraction, and (c) application of the PT during calculation of the intensities at the transparent interface

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Fig. 4

Distribution of the nondimensional radiative heat flux on the lateral wall of the 2D axisymmetric domain filled with the emitting and absorbing hot medium

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Fig. 5

Distribution of the nondimensional radiative heat flux on the lateral wall of the 2D axisymmetric domain filled with the absorbing and isotropically scattering cold medium

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Fig. 6

Distribution of the dimensionless incident radiation along the slab composed of two layers: (a) n1 = 1.25 and n2 = 1.5 and (b) n1 = 1.5 and n2 = 1.15

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Fig. 7

Distribution of the radiative heat flux along the bottom wall of the cavity filled with a nongray absorbing and emitting medium

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Fig. 8

Distribution of the divergence of the radiative heat flux along the line y = 1.0 m

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Fig. 9

Distribution of the radiative heat flux along boundaries of the notch in the cavity filled with a nongray mixture of gases

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Fig. 10

Distribution of the divergence of the radiative heat flux along the line y = 0.7 m

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Fig. 11

(a) Axisymmetric model of the Bridgman furnace with the temperature profile and (b) SLI locations in the ampoule for four values of Ka,s

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