Advertisement

Materials Science

, Volume 51, Issue 3, pp 331–339 | Cite as

Nonlinear Boundary-Value Problem of Heat Conduction for a Layered Plate with Inclusion

  • V. І. Havrysh
Article

We consider a nonlinear boundary-value problem of heat conduction for an isotropic infinite heat-sensitive layered plate with heat-insulated faces containing a foreign through thermally active inclusion. By using the proposed transformation, we perform partial linearization of the initial heat-conduction equation. As a result of a piecewise-linear approximation of temperatures on the boundary surfaces of the foreign layers and the inclusion, the equation is completely linearized. We find an analytic-numerical solution of this equation with boundary conditions of the second kind in order to determine the introduced function with the use of the Fourier integral transformation. The computational formulas for the unknown values of temperature are presented in the case of a linear temperature dependence of the heat-conduction coefficients of structural materials for the two-layer plates. The numerical analysis is performed for a single-layer plate containing a through thermally active inclusion (the material of the plate is VK94-I ceramic and the material of the inclusion is silver).

Keywords

isotropic layered infinite heat-sensitive plate with heat-insulated faces perfect thermal contact temperature field heat conduction foreign through thermally active inclusion 

References

  1. 1.
    A. F. Barvins’kyi and V. I. Havrysh, “Nonlinear problem of heat conduction for an inhomogeneous layer with internal heat sources,” Probl. Mashinostroen., 12, No. 1, 47–53 (2009).Google Scholar
  2. 2.
    V. I. Havrysh and D. V. Fedasyuk, “Method for the determination of temperature fields in a heat-sensitive piecewise-homogeneous strip with foreign inclusion,” Promyshl. Teplotekh., 32, No. 5, 18–25 (2010).Google Scholar
  3. 3.
    V. I. Gavrysh, “Modeling of temperature modes in heat-sensitive microelectronic devices with through foreign inclusions,” Élektron. Modelir., 34, No. 4, 99–107 (2012).Google Scholar
  4. 4.
    E. V. Golitsyna and Yu. R. Osipov, “Quasistationary three-dimensional problem of heat conduction in a rotating solid cylinder made of a composite material with nonlinear boundary conditions,” Konstruk. Kompoz. Mater., No. 4, 47–58 (2007).Google Scholar
  5. 5.
    Ya. S. Podstrigach, V. A. Lomakin, and Yu. M. Kolyano, Thermoelasticity of Bodies with Inhomogeneous Structure [in Russian], Nauka, Moscow (1984).Google Scholar
  6. 6.
    Yu. M. Kolyano, Methods of Heat Conduction and Thermoelasticity for Inhomogeneous Bodies [in Russian], Naukova Dumka, Kiev (1992).Google Scholar
  7. 7.
    G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1968).Google Scholar
  8. 8.
    V. A. Lomakin, Theory of Elasticity for Inhomogeneous Bodies [in Russian], Moscow University, Moscow (1976).Google Scholar
  9. 9.
    R. Berman, Thermal Conduction in Solids, Clarendon Press, Oxford (1976).Google Scholar
  10. 10.
    V. N. Yurenev and P. D. Lebedev, Thermotechnical Handbook [in Russian], Vol. 2, Énergiya, Moscow (1976).Google Scholar
  11. 11.
    V. Havrysh and O. Nytrebych, “Modeling of the thermal state in elements of microelectronic devices with through foreign inclusions,” Visn. Nats. Univ. “L’viv. Politekh.:” Komp’yut. Nauky Inform. Tekhnol., No. 719, 144–148 (2011).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.“L’vivs’ka Politekhnika” National UniversityLvivUkraine

Personalised recommendations