Geodesic
Application of the least squares method to the problem of radiation transfer in a spherical cavity
Matematičeskoe modelirovanie i čislennye metody (2015), pp. 53-65.

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A lot of heat-shielding materials used in engineering have porous structure. When there is an intensive thermal exposure, there occurs a necessity to consider thermal energy transfer by means of radiation in pores of such materials. We contructed a mathematical model describing heat exchange by radiation in a spherical cavity. Its form can be considered as an average statistical form in relation to forms of closed pores in solid bodies. For the quantitative analysis of this model we used the method of the least squares and introduced an equivalent coefficient of thermal conductivity in the conditional continuous environment filling a pore. This allows to regard the material with porous structure as a continuous non-uniform solid body.
Keywords: Spherical cavity, mathematical model of radiative transfer, least squares method. 
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V. S. Zarubin; O. V. Pugachev; I. Yu. Savelyeva. Application of the least squares method to the problem of radiation transfer in a spherical cavity. Matematičeskoe modelirovanie i čislennye metody (2015), pp. 53-65. http://geodesic.mathdoc.fr/item/MMCM_2015_a2/

[1] Eliseev V.N., Tovstonog V.A., Heat exchange and thermal tests of materials and designs of space equipment at radiation heating, BMSTU Publ., Moscow, 2014, 396 pp.

[2] Dimitrienko Yu.I., Mechanics of composite materials at high temperatures, Mashinostroenie Publ., Moscow, 1997, 368 pp.

[3] Dimitrienko Yu.I., Fedonyuk N.N., Gubareva E.A., Sborshchikov S.V., Prozorovskiy A.A., Science and Education: Electronic Scientific and Technical Edition, 2014, no. 7 <ext-link ext-link-type='doi' href='https://doi.org/10.7463/0714.0717805'>10.7463/0714.0717805</ext-link><ext-link ext-link-type='doi' href='https://doi.org/10.7463/0714.0717805'>10.7463/0714.0717805</ext-link>

[4] Dimitrienko Yu.I., Fedonyuk N.N., Gubareva E.A., Sborshchikov S.V., Prozorovskiy A.A., Erasov V.S., Yakovlev N.O., Herald of Bauman Moscow State Technical University. Ser. Natural Sciences, 2014, no. 5, 66–81

[5] Dimitrienko Yu.I., Gubareva E.A., Sborshchikov S.V., Mathematical Modeling and Computational Methods, 2014, no. 1, 36–56

[6] Dimitrienko Yu.I., Sborshchikov S.V., Sokolov A.P., Sadovnichiy D.N., Gafarov B.R., Composites and Nanostructures, 2013, no. 3, 35–51

[7] Dimitrienko Yu.I., Minin V.V., Syzdykov E.K., Computing Technologies, 17:2 (2012), 43–59

[8] Zarubin V.S., Mathematical modeling in engineering, BMSTU Publ., Moscow, 2010, 496 pp.

[9] Zarubin V.S., Kuvyrkin G.N., Mathematical Modeling and Computational Methods, 2014, no. 1, 5–17

[10] Dulnev G.N., Zarichnyak Yu.P., Heat conductivity of mixes and composite materials, Energiya Publ., Leningrad, 1974, 264 pp.

[11] Chudnovskiy A.F., Heat and physical characteristics of disperse materials, Fizmatgiz Publ., Moscow, 1962, 456 pp.

[12] Zarubin V.S., Kuvyrkin G.N., High Temperature, 41:2 (2003), 300–309

[13] Zarubin V.S., Kuvyrkin G.N., Saveleva I.Yu., High Temperature, 53:2 (2015), 243–249

[14] Zigel R., Hauell Dzh., Heat exchange by radiation, Mir Publ., Moscow, 1975, 936 pp.

[15] Isaev S.I., Kozhinov I.A., Kofanov V.I., Theory of a heat and mass exchange, BMSTU Publ., Moscow, 1997, 684 pp.

[16] Zarubin V.S., Engineering Journal: Science and Innovation, 2013, no. 8

[17] Zarubin V.S., Kuvyrkin G.N., Mathematical models of mechanics and electrodynamics of the continuous environment, BMSTU Publ., Moscow, 2008, 512 pp.

[18] Korn G., Korn T., The reference book on mathematics for scientists and engineers, Nauka Publ., Moscow, 1968, 720 pp.

[19] Zarubin V.S., Kuvyrkin G.N., Savelyeva I.Yu., Thermal Processes in Engineering, 2012, no. 10, 470–474