THERMAL SCIENCE

International Scientific Journal

ONE MATHEMATICAL MODEL OF THERMAL CONDUCTIVITY FOR MATERIALS WITH A GRANULAR STRUCTURE

ABSTRACT
The creation of new materials based on nanotechnology is an important direction of modern materials science development. Materials obtained by using nanotechnology can possess unique physicomechanical and thermophysical properties, al-lowing to use them effectively in structures exposed to high-intensity thermomechanical effects. An important step of the creation and usage of new materials is the construction of mathematical models to describe the behavior of these materials in a wide range of changes in external influences. One of the possible models for describing the process of thermal conductivity in structurally sensitive materials is proposed in this paper. The model is based on the laws of rational thermodynamics of irreversible processes and models of a continuous medium with internal state parameters. A qualitative study of the constructed model is carried out. A difference scheme is constructed in order to find the solution of the non-stationary heat conduction problem with allowance for the spatial non-locality effect. The analysis of the solutions is carried out.
KEYWORDS
PAPER SUBMITTED: 2019-01-18
PAPER REVISED: 2019-02-02
PAPER ACCEPTED: 2019-04-11
PUBLISHED ONLINE: 2019-09-22
DOI REFERENCE: https://doi.org/10.2298/TSCI19S4273K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 4, PAGES [S1273 - S1280]
REFERENCES
  1. Andrievskiy, R. A., Nanomaterials: The Concept and Modern Problems, G. Ros. chem. J. Society for them. D.I. Mendeleyev, XLVI (2002), 5, pp. 50-56
  2. Roduner, E., Size Matters: Why Nanomaterials are Different. J. Chem Soc Rev., 35 (2006), 7, pp. 83-92
  3. Andrievskii, R. A., Ragulya, A. V., Nanostructural Materials, Akademiya, Moscow, 2005
  4. Gusev, A. N., Nanomaterials, Nanostructures and Nanotechnologies, Fizmatlit, Moscow, 2005
  5. Gusev, A. N., Rempel, A. A., Nanocrystalline Materials, Fizmatlit, Moscow, Russia, 2001
  6. Rusanov, A. I., A Wonderful World of Nanostructures, Journal of General Chemistry, 72 (2002), 4, pp. 532-549
  7. Suzdalev, I. P., Nanotechnology Physics and Chemistry of Nanoclusters, Komkniga, Moscow, 2005
  8. Kunin, I. A., Elastic Media with Microstructure I, Springer, Berlin, Germany,1982
  9. Golovin, N. N., Kuvyrkin, G. N., Mathematical Models of Carbon-Carbon Composite Deformation, Mechanics of Solids, 51 (2016), 5, pp. 596-605
  10. Zarubin, V. S., et al., Mathematical Model of a Nonlocal Medium with Internal State Parameters, Journal of Engineering Physics and Thermophysics, 86 (2013), 4, pp. 768-773
  11. Kuvyrkin, G. N. , Savelieva, I. Yu., Thermomechanical Model of of Nonlocal Deformation of a Solid, Mechanics of Solids, 51 (2016), 3, pp. 256-262
  12. Savelieva, I. Yu., Influence of Medium Nonlocality on Distribution of Temperature and Stresses in Elastic Body under Pulsed Heating, Mechanics of Solids, 53 (2018), 3, pp. 277-283
  13. Zarubin, V. S ., et al, Mathematical Model of Thermostatic Coating with Thermoelectric Modules, Journal of Engineering Physics and Thermophysics, 88 (2015), 6, pp. 1328-1335
  14. Kuvyrkin, G. N. et al., Mathematical Model of the Heat Transfer Process Taking into Account the Consequences of Nonlocality in Structurally Sensitive Materials, Journal of Physics: Conference Series, 991 (2018), 1, 012050
  15. Eringen, A. C., Nonlocal Continuum Field Theories, New York-Berlin-Heidelberg, Springer-Verlag, Germany, 2002
  16. Zarubin, V. S., Kuvyrkin, G. N., Mathematical Models of Continuum Mechanics and Electrodynamics, Izdat. MGTU im. Baumana, Moscow, 2008
  17. Pisano, A. A., Fuschi, P., Closed Form Solution for a Nonlocal Elastic Bar in Tension, International Journal of Solids and Structures, 40 (2013), 1, pp. 13-23
  18. Polizzotto, C., Nonlocal Elasticity and Related Variational Principles, International Journal of Solids and Structures, 38 (2001), 42-43, pp. 7359-7380
  19. Kalitkin, N. N., Numerical Methods, Nauka, Moscow, 1978
  20. Galanin, M. P., Savenkov, E. B., Metody Chislennogo Analiza Matematicheskikh Modeley. (Numerical Analysis of Mathematical Models - in Russian), MGTU im. N. E. Baumana., Moscow, 2010
  21. Samarskiy, A. A., Teoriya Raznostnykh Skhem (Difference scheme theory - in Russian), Nauka, Moscow, 1977

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence