Heat Transfer in a Parallel-Plate Enclosure with Graded-Index Coatings on its Walls

Authors: Jiun-Wei Chen, Chih-Yang Wu, Ming-Feng Hou

Abstract:

A numerical study on the heat transfer in the thermal barrier coatings and the substrates of a parallel-plate enclosure is carried out. Some of the thermal barrier coatings, such as ceramics, are semitransparent and are of interest for high-temperature applications where radiation effects are significant. The radiative transfer equations and the energy equations are solved by using the discrete ordinates method and the finite difference method. Illustrative results are presented for temperature distributions in the coatings and the opaque walls under various heating conditions. The results show that the temperature distribution is more uniform in the interior portion of each coating away from its boundary for the case with a larger average of varying refractive index and a positive gradient of refractive index enhances radiative transfer to the substrates.

Keywords: Radiative transfer, parallel-plate enclosure, coatings, varying refractive index

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330311

References:

[1] M. F. Modest, Radiative Heat Transfer, 2nd ed., New York: Academic, 2003, Ch.6.
[2] R. Siegel, "Temperature Distributions in Channel Walls with Translucent Thermal Barrier Coatings," J. Thermophys. Heat Transf., vol. 12, pp. 289-296, 1998.
[3] R. Siegel, "Radiative exchange in a parallel-plate enclosure with translucent protective coatings on its walls," Int. J. Heat Mass Transf., vol. 42, pp. 73-84, 1999.
[4] R. Siegel, C.M. Sp├╝ckler, "Variable refractive index effects on radiation in semitransparent scattering multilayered regions," J. Thermophys. Heat Transf., vol. 7, pp. 624-630, 1993.
[5] P. Ben Abdallah and V. Le Dez, "Temperature field inside an absorbing-emitting semi-transparent slab at radiative equilibrium with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transf., vol. 65, pp. 595-608, 2000.
[6] D. Lemonnier and V. Le Dez, "Discrete ordinate solution of radiative transfer across a slab with variable refractive index," J. Quant. Spectrosc. Radiat. Transf., vol. 73, pp. 195-204, 2002.
[7] C.-Y. Wu, Discrete ordinates solution of transient radiative transfer in refractive planar media with pulse irradiation, in: G. de Vahl Davis (Ed.), The Annals of the Assembly for International Heat Transfer, vol. 13, Begell House Inc., Published online, 2006.
[8] R.F. Gong, X.-L. Cheng, W. Han, "Bioluminescence tomography for media with spatially varying refractive index," Inverse Probl. Sci. Eng., vol. 18, pp. 295-312,2010.
[9] P. Ben Abdallah and V. Le Dez,, "Radiative flux field inside an absorbing-emitting semi-transparent slab with variable spatial refractive index at radiative conductive coupling," J. Quant. Spectrosc. Radiat. Transf., vol. 67, pp. 125-137, 2000.
[10] X.L. Xia, Y. Huang, H.P. Tan and X.B. Zhang, "Simultaneous radiation and conduction heat transfer in a graded index semitransparent slab with gray boundaries," Int. J. Heat Mass Transf., vol. 45, pp. 2673-2688, 2002.
[11] L.H. Liu, J.Y. Tan, B. X. Li, "Meshless approach for coupled radiative and conductive heat transfer in one-dimensional graded index medium," J. Quant. Spectrosc. Radiat. Transf., vol. 101, pp. 237-248, 2006.
[12] J. R. Howell, R. Siegel,M. P. Menguc, Thermal Radiation Heat Transfer, 5th ed., Boca Raton, FL: CRC, 2010, Ch. 3.