Consideration of the nonlinear behavior of environmental material and a three-dimensional internal heat sources in mathematical modeling of heat conduction

Zhuravchak L. M., Kruk O. S.
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A numerical-analytical method of determining the heat field in a finite solid with taking into account the dependence of the coefficients of heat conductivity and of heat release on the temperature and the intensity of internal heat sources is suggested. The effectiveness of the combination of indirect methods of boundary and near-boundary elements with Kirchhoff transformation for partial linearization of nonlinear 3D problems of heat conduction, by which the process is modelled, is substantiated.
  1. Pidstryhach Y. S., Lomakin V. A., Kolyano Y. M. The bodies thermoelasticity in homogeneous structure. M.: Nauka, 368 (1984).
  2. Kolyano Y. M. The methods of heat conduction and thermoelasticity inhomogeneous body. K.: Naukova dumka, 280 (1992).
  3. Kushnir R. M., Popovich V. S. Simulation and optimization of heterogeneous termomehanics conductive bodies. Under gen. vers. Burak Ya. Y., Kushnir R. M. The thermoelasticity thermosensitive bodies Lviv, SPOLOM 3, 412 (2009).
  4. Kushnir R., Protsiuk B. A Method of the Green’s Functions for Quasistatic Thermoelasticity Problems in Layered Thermosensitive Bodies under Complex Heat Exchange. Operator Theory Advances and Applications 191, 143–154 (2009).
  5. Fedasyuk D., ˙V. The methods and tools for thermal design of microelectronic devices L. Pub. DU “Lviv Polytechnic”, 228 (1999).
  6. Zhuravchak L. M., Grytsko Y. G. Near-boundary element technique in applied problems of mathematical physics. Carpathian Branch of Subbotin Institute of Geophysics, NAS of Ukraine, Lviv, Ukraine, 220 (1996).
  7. Zhuravchak L. M. Solution of spatial nonstationary heat conduction problem for zonal-homogeneous thermosensitive body. Mathematical methods and physical-mechanical fields. 45, 137–142 (2002).
  8. Zhuravchak L. M. Solution of spatial thermal conductivity problem for zonal-homogeneous thermosensitive body with arbitrary form. Reports of National Academy of Sciences of Ukraine. 8, 37–41 (2002).
  9. Zhuravchak L. M. Zabrodska N. V. Nonstationary thermal fields in inhomogeneous materials with nonlinear behaviour of the components. Materials Science. 46-1, 33–41 (2010).
  10. Brebbia C. A., Telles J. C. F. Wrobel L. C. Boundary element methods. Theory and Application in Engineering, Springer-Verlag (1984).
  11. Zhuravchak L. M. Kruk O. S. Mathematical modeling of thermal field distribution in the parallelepiped with the severe heat on its borders and internal sources. Visnyk NU “Lviv Polytechnic” Computer Science and Information Technology. 771, 291–302 (2013).
Math. Model. Comput. Vol.2, No.1, pp.107-1133 (2015)