V.I. Havrysh, R.B. Tushnytskyy, V.Ya. Krayovskyy, Ye.V. Levus
Èlektron. model. 2017, 39(2):91-102
The paper deals with an axially symmetric boundary value problem of heat conduction for isotropic piecewise-homogeneous layer with a through cylinder-shaped inclusion heated at one of its boundary surfaces by concentrated heat flow. Having expressed the heat conductivity factor for the whole system as an indivisible entity with a help of a unit function, we obtained the heat conduction equation with discontinuous and singular coefficients for the considered structure. Having made piecewise-linear approximation of temperature at the lateral surface of the inclusion and at the surfaces of conjugation of the layer’s elements, and then having applied Hankel’s transformation, and analytical-numerical solution of the problem is obtained. The temperature field in a “layer-inclusion” (the material of layer is silicon, the material of the inclusion is silver) structure has been calculated and analyzed.
temperature, isotropic piecewise-homogeneous layer, heat conduction, through foreign inclusion, perfect thermal contact, heat flow.
1. Carpinteri, A. and Paggi, M. (2008), “Thermoelastic mismatch in nonhomogeneous beams”, J. Eng. Math, Vol. 61, no. 2-4, pp. 371-384.
2. Noda, N. (1991), “Thermal stresses in materials with temperature-dependent properties”, Appl. Mech. Rev., Vol. 44, pp. 383-397.
3. Otao, Y., Tanigawa, O. and Ishimaru, O. (2000), “Optimization of material composition of functionality graded plate for thermal stress relaxation using a genetic algorithm”, J. Therm. Stresses, Vol. 23, pp. 257-271.
4. Tanigawa, Y., Akai, T. and Kawamura, R. (1996), “Transient heat conduction and thermal stress problems of a nonhomogeneous plate with temperature-dependent material properties”, J. Therm. Stresses, Vol. 19, no. 1, pp. 77-102.
5. Tanigawa, Y. and Otao, Y. (2002), “Transient thermoelastic analysis of functionally graded plate with temperature-dependent material properties taking into account the thermal radiation”, Nihon Kikai Gakkai Nenji Taikai Koen Ronbunshu, Vol. 2, pp. 133-134.
6. Yangian, Xu and Daihui, Tu. (2009), “Analysis of steady thermal stress in a ZrO2/FGM/Ti-6Al-4V composite ECBF plate with temperature-dependent material properties by NFEM”, 2009-WASE Int. Conf. on Informa. Eng., Vol. 2, no. 2, pp. 433-436.
7. Byelyayev, M.M. and Ryadno, O.A. (1992), Matematychni metody teploprovidnosti [Mathematical methods of heat conduction], Vyshcha shkola, Kyiv, Ukraine.
8. Nazarov, S.A., Svyrs, H.Kh. and Slutskiy, A.S. (2009), “A heat conduction problem for thin plate with contrast road-shaped inclusions”, Vestnik Sankt-Peterburgskogo universiteta, Ser. 1: Matematika, mekhanika, astronomiya, no. 4, pp. 44-54.
9. Nemyrovskyy, Yu.V. and Yankovskyy, A.P. (2008), “Solution of steady-state problem of heat conduction of layered anisotropic non-homogeneous plates by means of initial functional method”, Matematychni metody ta fizyko-mekhanichni polya, Vol. 51, no. 2, pp. 222- 238.
10. 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.
11. Havrysh, V.I. and Fedasyuk, D.V. (2012), Modelyuvannya temperaturnykh rezhymiv u kuskovo-odnoridnykh strukturakh [Modeling of temperature conditions in piecewise-homogeneous structures], Vydavnytstvo Natsionalnoho universytetu “Lvivska politekhnika”, Lviv, Ukraine.
12. Havrysh, V.I. (2015), “Nonlineare boundary-value problem of heat conduction for a layered plate with”, Materials Science, Vol. 51, no. 3, pp. 331-339.
13. Havrysh, V.I. (2015), “Modeling of temperature regimes in non-homogenious elements of electronic devices with through foreign inclusions”, Elektronnoe modelirovanie, Vol. 37, no. 4, pp. 109-118.
14. Havrysh, V.I. (2016), “Investigation of temperature fields in a thermosensitive layer with a through inclusion”, Fizyko-khimichna mekhanika materialiv, Vol. 52, no. 4, pp. 63-68.
15. Kolyano, Yu.M. (1992), Metody teploprovodnosti i termouprugosti neodnorodnogo tela [Methods of heat conduction and thermoelasticity of inhomogeneous body], Naukova dumka, Kiev, Ukraine.
16. Podstrigach, Ya.S. and Lomakin, V.A. and Kolyano, Yu.M. (1984), Termouprugost tel neodnorodnoi struktury [Thermoelasticity of bodies with inhomogeneous structure], Nauka, Moscow, Russia.
17. Korn, G. and Korn, T. (1977), Spravochnik po matematike dlja nauchnykh rabotnikov i inzhenerov [Reference book for scientific workers and engineers], Nauka, Moscow, Russia.