We perform a survey of the state of investigations in the radiation thermomechanics of bodies of different transparency with respect to thermal radiation. By using the procedure proposed for the solution of the nonlinear problems of heat transfer and thermoelasticity based on the finite-element method, we study the influence of the heat sensitivity of thermal, mechanical, and radiation characteristics on the stresses acting in semitransparent and opaque bodies for the model problem for irradiated heat-sensitive layers.
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References
A. G. Blokh, Yu. A. Zhuravlev, and L. N. Ryzhkov, Radiation Heat Transfer: A Handbook [in Russian], Énergoatomizdat, Moscow (1991).
A. R. Gachkevich, Thermoelasticity of Electroconducting Bodies Subjected to the Action of Electromagnetic Radiation of the Infrared Frequency Range [in Russian], Preprint No. 10-93, Podstrigach Institute for Applied Problems of Mechanics and Mathematics, Lviv (1993).
A. R. Gachkevich and V. Ya. Boichuk, “Thermomechanical behavior of nonmetallic electrical conductors during high-temperature treatment,” Mat. Metody Fiz.-Mekh. Polya, 39, No. 1, 74–79 (1996); English translation : J. Math. Sci., 86, No. 2, 2585–2589 (1997).
A. R. Gachkevich and V. Ya. Boichuk, “Thermal stress of a long cylinder heated by thermal radiation,” Prikl. Mekh., 23, No. 4, 18–23 (1987); English translation : Int. Appl. Mech., 23, No. 4, 328–332 (1987).
A. R. Gachkevich, B. S. Malkiel’, Yu. R. Sosnovyi, and R. F. Terletskii, “Mathematical modeling and the study of the heat exchange process in color kinescopes,” in: Mathematical Methods and Physicomechanical Fields [in Russian], Issue 30 (1989), pp. 57–63; English translation : J. Sov. Math., 63, No. 3, 358–363 (1993).
A. R. Hachkevych, R. F. Terletskii, and M. B. Brukhal’, “Some problems of mathematical modeling in thermomechanics of bodies of various transparencies subjected to thermal irradiation,” Mat. Metody Fiz.-Mekh. Polya, 51, No. 3, 202–219 (2008); English translation : J. Math. Sci., 165, No. 3, 403–425 (2010).
O. R. Hachkevych, R. F. Terlets’kyi, and T. L. Kurnyts’kyi, Mechanothermodiffusion in Partially Transparent Bodies, in: Ya. I. Burak and R. M. Kushnir (editors), Modeling and Optimization in the Thermomechanics of Electroconducting Inhomogeneous Bodies [in Ukrainian], Vol. 2, SPOLOM, Lviv (2007).
O. R. Hachkevych, R. F. Terlets’kyi, Yu. R. Sosnovyi, and M. B. Brukhal’, “Mechanical behavior of cooled bodies with regard for the emission of heat energy,” Fiz.-Khim. Mekh. Mater, 46, No. 1, 42–50 (2010); English translation : Mater. Sci., 46, No. 1, 47–55 (2010).
B. A. Grigor’ev, Pulse Heating by Radiation [in Russian], Vol. 2, Nauka, Moscow (1974).
O. B. Humenchuk, Thermal stress State of Partially Transparent Bodies with Cavities under Thermal Radiation [in Ukrainian], Candidate-Degree Thesis (Phys., Math.), Lviv (2008).
Y. Jaluria, Natural Convection: Heat and Mass Transfer, Pergamon, New York (1980).
R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer, McGraw-Hill, New York (1972).
A. E. Sheindlin (editor), Radiation Properties of Solid Materials: Handbook [in Russian], Énergiya, Moscow (1974).
A. D. Kovalenko, Foundations of Thermoelasticity [in Russian], Naukova Dumka, Kiev (1970).
F. Kreit and W. Z. Black, Basic Heat Transfer, Harper and Row, New York (1980).
L. N. Lavrikov and Yu. F. Yurchenko, Thermal Properties of Metals and Alloys [in Russian], Naukova Dumka, Kiev (1985).
A. V. Lykov, Theory of Heat Conduction [in Russian], Vysshaya Shkola, Moscow (1967).
S. B. Maslenkov and E. A. Maslenkova, Steels and Alloys for High Temperatures: Handbook [in Russian], Part 1, Metallurgiya, Moscow (1991).
V. A. Petrov and N. V. Marchenko, Energy Transfer in Partially Transparent Solid Materials [in Russian], Nauka, Moscow (1985).
V. S. Popovych and O. M. Vovk, “A procedure for the solution of the problem of conductive-radiation heat transfer between a cylindrical and an N-angular prismatic shells,” Mat. Metody Fiz.-Mekh. Polya, 47, No. 1, 158–168 (2004).
Yu. S. Postol’nyk and A. P. Ohurtsov, Nonlinear Applied Thermomechanics [in Ukrainian], NMTs VO MONU, Kyiv (2000).
N. A. Rubtsov, Radiation Heat Transfer in Continua [in Russian], Nauka, Novosibirsk (1984).
N. A. Rubtsov, A. M. Timofeev, and N. A. Savvinova, Combined Heat Transfer in Semitransparent Media [in Russian], Izd. SO RAN, Novosibirsk (2003).
R. F. Terletskii, Thermal stress State of Low-Electroconducting Bodies under the Action of Electromagnetic Radiation [in Russian], Candidate-Degree Thesis (Phys., Math., 01.02.04), Lviv (1988).
R. F. Terletskii, O. P. Turii, and M. B. Brukhal’, “Problems of thermomechanics for irradiated bodies,” in: Theoretical and Applied Mechanics [in Russian], Issue 4(50) (2012), pp. 30–37.
R. F. Terlets’kyi and O. P. Turii, “Thermomechanical behavior of a plate composed of layers with different transparencies under the action of thermal radiation,” Fiz.-Khim. Mekh. Mater., 43, No. 6, 17–26 (2007); English translation : Mater. Sci., 43, No. 6, 769–779 (2007).
O. P. Turii, Thermal stress State of Layered Plates under Thermal Radiation [in Ukrainian], Candidate-Degree Thesis (Phys., Math.), Lviv (2010).
C. A. Wert and R. M. Thomson, Physics of Solids, McGraw-Hill, New York (1964).
W. Espe, Technology of Electric Vacuum Devices [Russian translation], Vol. 2, Énergiya, Moscow (1968).
E. E. Anderson and R. Viskanta, “Effective thermal conductivity for heat transfer through semitransparent solids,” J. Am. Ceram. Soc., 56, No. 10, 541–546 (1973).
F. Asllanaj, G. Jeandel, and J. R. Roche, “Numerical solution of radiation transfer equation coupled with nonlinear heat conduction equation,” Int. J. Numer. Method Heat Fluid Flow, 11, No. 5, 449–472 (2001).
A. L. Burka and P. M. Likhanskii, “Transient radiation-conductive heating of plexiglas,” Prikl. Mekh. Tekh. Fiz., 42, No. 3, 101–106 (2001); English translation : J. Appl. Mech. Tech. Phys., 42, No. 3, 469–474 (2001).
Chang Yan-Po and R. S. Smith (Jr.), ”Steady and transient heat transfer by radiation and conduction in a medium bounded by two coaxial cylindrical surfaces,” Int. J. Heat Mass Transfer, 13, No. 1, 69–80 (1970).
H.-S. Chu and L.-C. Weng, “Transient combined conduction and radiation in anisotropically scattering spherical media,” J. Thermophys. Heat Transfer, 6, No. 3, 553–556 (1992).
R. Coquard, D. Rochais, and D. Baillis, “Experimental investigations of the coupled conductive and radiation heat transfer in metallic/ceramic foams,” Int. J. Heat Mass Transfer, 52, No. 21-22, 4907–4918 (2009).
Fan Tai-His and A. G. Fedorov, “Radiation transfer in a semitransparent hemispherical shell,” J. Quant. Spectroscopy RA, 73, No. 2-5, 285–296 (2002).
R. Fernandes and J. Francis, “Combined conductive and radiation heat transfer in an absorbing, emitting, and scattering cylindrical medium,” Trans. ASME, J. Heat Transfer, 104, No. 4, 594–601 (1982).
Kong Hoon Lee and R. Viskanta, “Two-dimensional combined conduction and radiation heat transfer: comparison of the discrete ordinates method and the diffusion approximation methods,” Numer. Heat Transfer, Part A, 39, No. 3, 205–225 (2001).
M. Lazard, S. André, and D. Maillet, “Diffusivity measurement of semi-transparent media: model of the coupled transient heat transfer and experiments on glass, silica glass and zinc selenide,” Int. J. Heat Mass Transfer, 47, 477–487 (2004).
B. J. van der Linden and R. M. M. Mattheij, “A new method for solving radiation heat problems in glass,” Int. J. Forming Processes, 2, No. 1-2, 41–61 (1999).
M. F. Modest, Radiation Heat Transfer, Academic, New York (2003).
C. Muresan, R. Vaillon, C. Menezo, and R. Morlot, “Discrete ordinates solution of coupled conductive radiation heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation,” J. Quant. Spectroscopy, RA, 84, No. 4, 551–562 (2004).
T. H. Ping and M. Lallemand, “Transient radiation-conductive heat transfer in flat glasses submitted to temperature, flux and mixed boundary conditions,” Int. J. Heat Mass Transfer, 32, No. 5, 795–810 (1989).
D. Schwander, G. Flamant, and G. Olalde, “Effects of boundary properties on transient temperature distributions in condensed semitransparent media,” Int. J. Heat Mass Transfer, 33, No. 8, 1685–1695 (1990).
E. Sharbati, B. Safavisohi, and C. Aghanajafi, “Transient heat transfer analysis of a layer by considering the effect of radiation,” J. Fusion Energy, 23, No. 3, 207–215 (2004).
N. Siedow, T. Grosan, D. Lochegnies, and E. Romero, “Application of a new method for radiation heat transfer to flat glass tempering,” J. Am. Ceram. Soc., 88, No. 8, 2181–2187 (2005).
R. Siegel, “Transient effects of radiation transfer in semitransparent materials,” Int. J. Eng. Sci., 36, No. 12-14, 1701–1739 (1998).
R. Siegel, “Transient heat transfer in a semitransparent radiating layer with boundary convection and surface reflections,” Int. J. Heat Mass Transfer, 39, No. 1, 69–79 (1996).
R. Siegel, “Two-flux method for transient radiation transfer in a semitransparent layer,” Int. J. Heat Mass Transfer, 39, No. 5, 1111–1115 (1996).
M.-H. Su and W. H. Sutton, “Transient conductive and radiation heat transfer in a silica window,” J. Thermophys. Heat Transfer, 9, No. 2, 370–373 (1995).
W. H. Sutton, “A short time solution for coupled conduction and radiation in a participating slab geometry,” Trans. ASME, J. Heat Transfer, 108, No. 2, 465–466 (1986).
G. Thömmes, “A linear iterative scheme for the fast solution of the radiation heat transfer equations for glass,” J. Comput. Phys., 193, No. 2, 544–562 (2004).
C.-F. Tsai and G. Nixon, “Transient temperature distribution of a multilayer composite wall with effects of internal thermal radiation and conduction,” Numer. Heat Transfer, 10, No. 1, 95–101 (1986).
J. R. Tsai and M. N. Özişik, “Transient, combined conduction and radiation in an absorbing, emitting, and isotropically scattering solid sphere,” J. Quant. Spectroscopy, RA, 38, No. 4, 243–251 (1987).
P.-Y. Wang, H.-E. Cheng, and H.-P. Tan, “Transient thermal analysis of semitransparent composite layer with an opaque boundary,” Int. J. Heat Mass Transfer, 45, No. 2, 425–440 (2002).
K. C. Weston and J. L. Hauth, “Unsteady, combined radiation and conduction in an absorbing, scattering, and emitting medium,” Trans. ASME, J. Heat Transfer, 95, No. 3, 357–364 (1973).
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Published in Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 2, pp. 212–224, April–June, 2013.
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Terlets’kyi, R.F., Brukhal’, M.B. & Nemirovskii, Y.V. Моdeling and Investigation of the Thermomechanical Behavior of Heat-Sensitive Bodies with Regard for the Influence of Thermal Radiation. J Math Sci 203, 265–278 (2014). https://doi.org/10.1007/s10958-014-2106-6
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DOI: https://doi.org/10.1007/s10958-014-2106-6