GAVRYSH V.I.
ABSTRACT
A heat equation with discontinuous and singular coefficients for an isotropic multi-layer plate with thermally insulated surfaces which contains a heat-generating foreign through inclusion has been deduced with the use of generalized functions. A numerical-analytical solution for the heat equation with boundary conditions of the second kind has been constructed using a piecewise linear approximation of the temperature on the boundary surfaces of the inclusion and Fourier integral transform. The numerical analysis of a single-layer infinite plate with a through heat-generating inclusion has been made.
KEYWORDS
temperature, conductivity, stationary boundary value problems, isotropic plate, foreign inclusions, perfect thermal contact.
REFERENCES
1. Belyaev, N.V. and Ryadno, A.A. (1982), Metody teorii teploprovodnosti. Ch. I [Methods of the theory of heat conduction. Part I], Vysshaya shkola, Moscow, Russia.
2. Nemirovskiy, Yu.V. and Yankovskiy, A.P. (2008), “The solution of the stationary problem of heat conduction of layered anisotropic inhomogeneous plates by the method of initial functions”, Mat. metody ta fiz.-mekh. polya, Vol. 51, no. 2, pp. 222-238.
3. Nemirovskiy, Yu.V. and Yankovskiy, A.P. (2007), “Asymptotic analysis of the problem of non-stationary heat conduction of layered anisotropic inhomogeneous plates under boundary conditions of the first and the third kind on the front surface”, Ibid., Vol. 50, no. 2, pp. 160-175.
4. Havrysh, V.I. and Kosach, A.I. (2012), “Boundary-value problem of heat conduction for a piecewise homogeneous with foreign inclusion”, Materials Science, Vol. 47, no. 6, pp. 773-782.
5. Havrysh, V.I., Fedasyuk, D.V. and Kosach, A.I. (2011), “Boundary-value problem of heat conduction for a layer with foreign cylindrical inclusion”, Ibid., Vol. 46, no. 5, pp. 702-708.
6. Gavrysh, V.I. (2012), “Thermal state modelling in thermo sensitive elements of microelectronic devices with reach-through foreign inclusions”, Semiconductor Physics, Quantum Electronics & Optoelectronics, Vol. 15, no. 3, pp. 247-251.
7. Gavrysh, V. (2011), “Modelling the temperature conditions in the three-dimensional piecewise homogeneous elements of microelectronic devices”, Ibid., Vol. 14, no. 4, pp. 478-482.
8. Gavrysh, V.I. (2012), “Modelling of temperature modes in heat sensitive microelectronic devices with through foreign inclusions”, Elektronnoe modelirovanie, Vol. 34, no. 4, pp. 99-107.
9. Gavrysh, V.I. and Kosach, A.I. (2011), “Modelling of temperature in the microelectronic devices elements”, Tekhnologiya i konstruirovanie v elektronnoy apparature, Vol. 90, no. 1-2, pp. 27-30.
10. Fedasyuk, D. and Gavrysh, V. (2012), “Modelling of temperature conditions in electrical devices of inhomogeneous structure”, Computational Problems of Electrical Engineering, Vol. 2, no. 1, pp. 25-28.
11. Podstrigach, Ya.S., Lomakin, V.A. and Kolyano, Yu.M. (1984), Termouprugost tel neodnorodnoy struktury [Thermoelasticity of bodies of inhomogeneous structure], Nauka, Moscow, Russia.
12. Kolyano, Yu.M. (1992), Metody teploprovodnosti i termouprugosti neodnorodnogo tela [Methods of thermal conductivity and thermo elasticity inhomogeneous body], Naukova dumka, Kiev, Ukraine.
13. Korn, G. and Korn, T. (1977), Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov [Handbook of mathematics for scientists and engineers], Nauka, Moscow, Russia.