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Nonlinear mathematical models of heat transfer in the presence of strong energy fluxes

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Literature cited

  1. 1.

    A. A. Uglov, “Thermophysical and hydrodynamic phenomena in laser working of metals,” Fiz.-Khim. Obrab. Mater., No. 3, 3–13 (1974).

  2. 2.

    A. A. Uglov, “Strong heat sources in working of inorganic materials,” Fiz.-Khim. Obrab. Mater., No. 3, 3–15 (1976).

  3. 3.

    N. N. Rykalin and A. A. Uglov, “Action of strong energy fluxes (SEF) on materials, problems, and prospects,” Fiz.-Khim. Obrab. Mater., No. 5, 3–18 (1983).

  4. 4.

    N. N. Rykalin and A. A. Uglov, “Heat and mass transfer in electron-beam and laser welding and heat treatment,” Prom. Teplotekhnika, No. 5, 3–16 (1981).

  5. 5.

    N. N. Rykalin and A. A. Uglov, “Development of the thermophysical foundations of technological processes,” Fiz.-Khim. Obrab. Mater., No. 1, 7–18 (1981).

  6. 6.

    A. A. Uglov, “Lasers in the technology of inorganic materials and metallurgy,” Kvantovaya Élektron., No. 5, 1037–1055 (1974).

  7. 7.

    K. I. Zaitsev and V. F. Lyashenko, “Investigation of thermal processes in butt welding of pipes consisting of thermal softening plastics,” Avtomat. Svarka, No. 1, 37–39 (1968).

  8. 8.

    A. A. Kazimirov, A. Ya. Nedoseka, and V. A. Sanchenko, “Calculation of the heat distribution in butt welding of plates taking into account the effect of the temperature on their physical properties,” Avtomat. Svarka, No. 11, 28–30 (1973).

  9. 9.

    A. Ya. Nedoseka, V. A. Sanchenko, and G. A. Vorona, “Temperature distribution on the surface of a plate exposed to a strong heat source,” Avtomat. Svarka, No. 6, 1–4 (1977).

  10. 10.

    A. Ya. Nedoseka and O. I. Chernova, “Temperature distribution in plates with the welding heat source at different depths,” Avtomat. Svarka, No. 7, 1–4 (1977).

  11. 11.

    V. I. Gol'din and V. A. Mogutov, “Investigation of the nonstationary temperature field in the region of the weld seam in polyethylene pipes,” Énerget. Str-vo.,89, No. 11, 47–50 (1968).

  12. 12.

    B. M. Budak, A. A. Golubeva, S. D. Dubrovkin, and A. V. Sladkov, “Investigation of thermal processes in contact butt welding of polyethylene pipes,” Svaroch. Pr-vo., No. 1, 3–6 (1970).

  13. 13.

    L. Paley and P. D. Hibbert, “Computation of temperatures in actual weld designs,” Weld J.,54, No. 11, 385–392 (1975).

  14. 14.

    V. Pavelic, R. Tanbakuchi, O. A. Uychara, and P. S. Myers, “Experimental and computed temperature histories in gas tungsten are welding in thin plates,” Weld J.,48, No.7, 295–305 (1969).

  15. 15.

    A. A. Uglov and G. V. Smol'skii, “Calculation of the heating of thin plates on a heatremoving backing by a normally distributed source taking into account the temperature dependence of the thermophysical coefficients,” Fiz.-Khim. Obrab. Mater., No. 2, 3–11 (1981).

  16. 16.

    A. A. Uglov, V. V. Ivanov, and A. I. Tuzhikov, “Calculation of the temperature field of moving heat sources taking into account the temperature dependence of the coefficients,” Fiz.-Khim. Obrab. Mater., No. 4, 7–11 (1980).

  17. 17.

    N. M. Fialko, “Solution of the problem of the thermal state of butt welded rods in the linear and nonlinear formulations,” Heat Transfer in Pipes and Channels [in Russian], Naukova Dumka, Kiev (1978), pp. 79–84.

  18. 18.

    V. I. Mazhukin and D. I. Cherednichenko, “Effect of the nonlinearity of thermophysical characteristics on the temperature state of a semiconductor under the action of an impulsive heat source,” Fiz.-Khim. Obrab. Mater., No. 6, 16–19 (1976).

  19. 19.

    A. V. Temnikov and N. A. Klopkova, “Electric modeling of temperature fields in materials treatment processes taking into account the temperature dependence of the thermophysical properties,” Fiz.-Khim. Obrab. Mater., No. 5, 3–7 (1972).

  20. 20.

    A. E. Dyudin, I. S. Znatdinov, L. A. Kozdoba, and N. M. Fialko, “Taking into account nonlinearities in numerical modeling of the thermal states of elements in power plants,” in: Power Machine Building [in Russian], Vishcha shkola, Khar'k. Otd-nie, Kharkov (1979), pp. 101–107.

  21. 21.

    N. N. Rykalin, A. A. Uglov, and M. M. Nizametdinov, “Calculation of the heating of materials by laser radiation taking into account the temperature dependence of the thermo physical coefficients,” Kvantovaya Elektron., No. 7, 1509–1516 (1977).

  22. 22.

    A. A. Uglov, V. V. Ivanov, and A. I. Tuzhikov, “Heating of metals by a group of mobile heat sources,” Fiz.-Khim. Obrab. Mater., No. 5, 3–6 (1981).

  23. 23.

    A. P. Amosov and A. N. Gryadunov, “Heating of a solid accompanying rapid motion of a surface heat source whose intensity is temperature dependent,” Fiz.-Khim. Obrab. Mater., No. 2, 12–15 (1981).

  24. 24.

    L. M. Anishchenko and S. Yu. Lavrenyuk, “Application of the methods of systems analysis to the solution of heat-conduction problems,” Fiz.-Khim. Obrab. Mater., No. 4, 27–31 (1979).

  25. 25.

    L. M. Anishchenko and S. Yu. Lavrenyuk, “Calculation of heat fluxes from a source on a substrate during thermal evaporation,” Fiz.-Khim. Obrab. Mater., No. 1, 158–162 (1981).

  26. 26.

    L. M. Anishchenko and S. Yu. Lavrenyuk, “Thermal regimes of a substrate accompanying deposition of film coatings,” Fiz.-Khim. Obrab. Mater., No. 2, 21–25 (1981).

  27. 27.

    A. V. Kozlov, T. M. Popova, Yu. I. Rybin, and V. M. Fastovskii, “Temperature distribution accompanying local heating of a structure for welding,” Fiz.-Khim. Obrab. Mater., No. 6, 24–28 (1983).

  28. 28.

    E. M. Ivanov, “Thermophysics of plasma deposition of protective coatings,” Fiz.-Khim. Obrab. Mater., No. 4, 60–64 (1982).

  29. 29.

    V. F. Brekhovskikh, M. M. Nikitin, and M. Kh. Shorshorov, “Effect of the optical properties of the substrate material and the geometry of the substrate-evaporator system on the magnitude of the heat flux on the surface of the deposited film,” Fiz.-Khim. Obrab. Mater., No. 2, 88–90 (1975).

  30. 28.

    M. Ivanov, “Approximate calculation of the process of crystallization of a layer of melt on the substrate,” Fiz.-Khim. Obrab. Mater., No. 2, 79–84 (1981).

  31. 31.

    M. N. Libenson, G. S. Romanov, and Ya. A. Imas, “Taking into account the effect of the temperature dependence of the optical constants of a metal on the nature of its heating by laser radiation,” Zh. Tekh. Fiz.,38, No. 7, 1116–1119 (1968).

  32. 32.

    I. P. Dobrovol'skii and A. A. Uglov, “Heating of solids by laser radiation taking into account the temperature dependence of the absorptivity,” Kvantovaya Élektron., No. 6, 1423–1427 (1974).

  33. 33.

    F. V. Bunkin, N. A. Kirichenko, and B. S. Luk'yanchuk, “Possibility of reducing energy consumption in laser heating of metals,” Fiz.-Khim. Obrab. Mater., No. 5, 7–14 (1980).

  34. 34.

    G. L. Gurevich and V. A. Murav'ev, “Effect of the temperature dependence of the reflection coefficient on the laser heating of thin films,” Fiz.-Khim. Obrab. Mater., No. 4, 26–29 (1973).

  35. 35.

    B. M. Gavrilov and T. F. Nezvanova, “Modeling of heat transfer during welding taking into account the latent heat of crystallization,” Abstracts of Reports at a ScientificTechnical Conference on the Mathematical Modeling and Hybrid Computational Technology, Kuibyshev (1975), pp. 31–32.

  36. 36.

    T. F. Gavrilova, “Method for modeling heat transfer in welding by melting taking into account the liberation of the latent heat of crystallization,” in: Hybrid Computers and Computing Complexes [in Russian], Naukova Dumka, Kiev (1976), pp.142–143.

  37. 37.

    M. G. Kogan and V. N. Kryukovskii, “Temperature field in welding with a scanning energy source,” Fiz.-Khim. Obrab. Mater., No. 5, 24–30 (1975).

  38. 38.

    N. N. Rykalin, A. A. Uglov, and I. Yu. Smurov, “Three-dimensional nonlinear problems in laser heating of metals,” Fiz.-Khim. Obrab. Mater., No. 2, 3–13 (1979).

  39. 39.

    A.0 A. Uglov, V. V. Ivanov, A. I. Tuzhikov, and I. Yu. Smurov, “Calculation of the temperatures in the zone of interaction of strong energy fluxes with metals,” Prom. Teplotekhnika,2, No. 2, 68–72 (1980).

  40. 40.

    N. N. Rykalin, A. A. Uglov, and I. Yu. Smurov, “Nonlinearity of laser heating of metals,” Dokl. Akad. Nauk SSSR,267, No. 2, 377–381 (1982).

  41. 41.

    A. A. Uglov and V. V. Ivanov, “Effect of preheating of metals on the cutting rate,” Fiz.-Khim. Obrab. Mater., No. 6, 15–17 (1982).

  42. 42.

    A. A. Uglov and V. V. Ivanov, “Local comoving heating of metals as a means for increasing the rate of cutting,” Fiz.-Khim. Obrab. Mater., No. 5, 36–38 (1982).

  43. 43.

    N. N. Rykalin, A. I. Pugin, and N. A. Klopkova, “Mathematical description of thermal processes accompanying contact resistance welding,” Svaroch. Pr-vo., No. 3, 1–3 (1973).

  44. 44.

    A. A. Uglov and O. I. Isaeva, “Calculation of the rate of laser heating of metals,” Fiz.-Khim. Obrab. Mater., No. 2, 23–28 (1976).

  45. 45.

    N. M. Fialko, “Investigation of the temperature states of bodies in the presence of moving concentrated energy sources,” Author's Abstract of Candidate's Dissertation, Engineering Sciences, Kiev (1980).

  46. 46.

    L. A. Kozdoba, Solution of Nonlinear Heat-Conduction Problems [in Russian], Naukova Dumka, Kiev (1976).

  47. 47.

    T. Gudmen, “Application of integral methods in nonlinear, nonstationary heat-transfer problems,” Problems in Heat Transfer [in Russian], Atomizdat, Moscow (1967), pp. 41–95.

  48. 48.

    N. A. Klopkova, “Investigation of nonlinear processes in the propagation of heat from strong sources into metals by methods of electric modeling,” Author's Abstract of Candidate's Dissertation, Engineering Sciences, Kuibyshev (1974).

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Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 22, No. 6, pp. 34–38, November–December, 1986.

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Shvets, Y.I., Fialko, N.M., Sherenkovskaya, G.P. et al. Nonlinear mathematical models of heat transfer in the presence of strong energy fluxes. Soviet Materials Science 22, 571–575 (1987). https://doi.org/10.1007/BF00718104

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Keywords

  • Heat Transfer
  • Mathematical Model
  • Energy Flux
  • Strong Energy
  • Nonlinear Mathematical Model