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Condition for the Existence of the Optimal Wall Thickness Dividing Two Different Environments with Local Heat Exposure

  • HEAT AND MASS TRANSFER AND PHYSICAL GASDYNAMICS
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Abstract

The sufficient conditions for the existence of an optimal thickness of an orthotropic dividing wall are determined with the zero-order Hankel integral transform. Both wall surfaces participate in a heat transfer with external media with constant temperatures, and one of them is also affected by a stationary axisymmetric heat flux with a Gaussian-type intensity. The need to minimize the temperature of the most heated point of the object of study is used as an optimality criterion. A sufficient condition is obtained in the form of an inequality that establishes a connection between the thermophysical characteristics of the orthotropic material of the wall and the parameters of the external thermal effects. The accuracy of the obtained condition was established by a computational experiment.

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REFERENCES

  1. Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, Oxford: Clarendon, 1959, 2nd ed.

    MATH  Google Scholar 

  2. Lykov, A.V., Teoriya teploprovodnosti (Theory of Heat Conduction), Moscow: Vysshaya Shkola, 1967.

  3. Kartashov, E.M., Analiticheskie metody v teorii teploprovodnosti tverdykh tel (Analytical Methods in the Theory of Heat Conduction of Solids), Moscow: Vysshaya Shkola, 2001.

  4. Kartashov, E.M. and Kudinov, V.A., Analiticheskaya teoriya teploprovodnosti i prikladnoi termouprugosti (Analytical Theory of Heat Conduction and Applied Thermoelasticity), Moscow: URSS, 2012.

  5. Formalev, V.F., Teploprovodnost’ anizotropnykh tel. Analiticheskie metody resheniya zadach (Heat Conduction of Anisotropic Bodies: Analytical Methods for Solving Problems), Moscow: Fizmatlit, 2014.

  6. Butkovskii, A.G., Malyi, S.A., and Andreev, Yu.N., Optimal’noe upravlenie nagrevom metallov (Optimal Control of Metal Heating), Moscow: Metallurgiya, 1972.

  7. Egorov, A.I., Optimal’noe upravlenie nestatsionarnymi teplovymi i diffuzionnymi protsessami (Optimal Control of Nonstationary Heat and Diffusion Processes), Moscow: Nauka, 1978.

  8. Zarubin, V.S., Raschet i optimizatsiya teploizolyatsii (Calculation and Optimization of Thermal Insulation), Moscow: Energoatomizdat, 1991.

  9. Zarubin, V.S., Izv. Vyssh. Uchebn. Zaved., Mashinostr., 1970, no. 10, p. 18.

  10. Zarubin, V.S., Kotovich, A.V., and Kuvyrkin, G.N., Izv. Ross. Akad. Nauk, Energ., 2014, no. 5, p. 45.

  11. Attetkov, A.V., Vlasov, P.A., and Volkov, I.K., High Temp., 2018, vol. 56, no. 3, p. 389.

    Article  Google Scholar 

  12. Attetkov, A.V., Volkov, I.K., and Tverskaya, E.S., J. Eng. Phys. Thermophys., 2001, vol. 74, no. 6, p. 1467.

    Article  Google Scholar 

  13. Attetkov, A.V., Volkov, I.K., and Tverskaya, E.S., High Temp., 2005, vol. 43, no. 3, p. 467.

    Article  Google Scholar 

  14. Attetkov, A.V., Volkov, I.K., and Tverskaya, E.S., J. Eng. Phys. Thermophys., 2005, vol. 78, no. 2, p. 216.

    Article  Google Scholar 

  15. El’sgol’ts, L.E., Differentsial’nye uravneniya i variatsionnoe ischislenie (Differential Equations and Calculus of Variations), Moscow: Nauka, 1969.

  16. Volkov, I.K. and Kanatnikov, A.N., Integral’nye preobrazovaniya i operatsionnoe ischislenie (Integral Transformations and Operational Calculus), Moscow: Mosk. Gos. Tekh. Univ. im. N.E. Baumana, 1996.

  17. Bateman, H. and Erdélyi, A., Tables of Integral Transforms, 2 vols., New York: McGraw-Hill, 1954.

  18. Bronshtein, I.N. and Semendyaev, K.A., Spravochnik po matematike dlya inzhenerov i uchashchikhsya vtuzov (Handbook of Mathematics for Engineers and Students of Technical Colleges), Moscow: Nauka, 1998.

  19. Gradshtein, I.S. and Ryzhik, I.M., Tablitsy integralov, summ, ryadov i proizvedenii (Tables of Integrals, Sums, Series, and Products), Moscow: Nauka, 1971.

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  1. Bauman Moscow State Technical University, 105005, Moscow, Russia

    P. A. Vlasov

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  1. P. A. Vlasov
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Correspondence to P. A. Vlasov.

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Vlasov, P.A. Condition for the Existence of the Optimal Wall Thickness Dividing Two Different Environments with Local Heat Exposure. High Temp 57, 694–699 (2019). https://doi.org/10.1134/S0018151X19040242

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  • DOI: https://doi.org/10.1134/S0018151X19040242

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