Optimum Anisotropic Coating Thickness for a Wall Separating Two Different Media and Subjected to Local Heating

The article states and solves the problem of determining a steady-state temperature field in an isotropic wall separating media with different thermal and physical properties. The wall features an anisotropic coating displaying general anisotropy of its properties. The uncovered coating boundary is subjected to a steady-state heat flow with a Gaussian intensity profile. We obtained the solution in an analytically closed form and used it to validate the possibility that an optimum thickness of the anisotropic coating exists in terms of minimising the steady-state temperature at the hottest point

References

[1] Carslaw H., Jaeger J. Conduction of heat in solids. Oxford University Press, 1986. 520 p.

[2] Lykov A.V. Teoriya teploprovodnosti [Theory of thermal conduction]. Moscow, Vysshaya shkola Publ., 1967. 600 p.

[3] Kartashov E.M. Analiticheskie metody v teorii teploprovodnosti tverdykh tel [Analytical methods in heat conduction theory of solid bodies]. Moscow, Vysshaya shkola Publ., 2001. 550 p.

[4] Formalev V.F. Teploprovodnost anizotropnykh tel. Ch. 1. Analiticheskie metody resheniya zadach [Thermal conduction of anisotropic bodies. P. 1. Analytical problem solving methods]. Moscow, Fizmatlit Publ., 2014. 312 p.

[5] Zarubin V.S. Optimum thickness of cooled wall exposed to the external heating. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [Proceedings of Higher Educational Institutions. Маchine Building], 1970, no. 10, pp. 18–21 (in Russ.).

[6] Zarubin V.S., Kotovich A.V., Kuvyrkin G.N. Optimal thickness of the anisotropic surface on the cooling plate with applied local external heating. Izvestiya RAN. Energetika [Proceedings of RAS. Power Engineering], 2014, no. 5, pp. 45–50 (in Russ.).

[7] Pekhovich A.I., Zhidkikh V.M. Raschet teplovogo rezhima tverdykh tel [Calculating thermal regimes of solid body]. Leningrad, Energiya Publ., 1968. 304 p.

[8] Koshlyakov N.S., Gliner E.B., Smirnov M.M. Uravneniya v chastnykh proizvodnykh matematicheskoy fiziki [Partial differential equations of mathematical physics]. Moscow, Vysshaya shkola Publ., 1970. 712 p.

[9] Sneddon I.N. Fourier transforms. McGraw-Hill, 1951. 542 p.

[10] Elsgolts L.E. Differentsialnye uravneniya i variatsionnoe ischislenie [Differential equations and variational calculus]. Moscow, Nauka Publ., 1969. 424 p.

[11] Bateman H., Erdelyi A. Tables of integral transforms. Vol. 1. McGraw Hill, 1954. 411 p.

[12] Bellman R. Introduction to matrix analysis. McGraw-Hill, 1960. 328 p.