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A NEW VIEWPOINT ON THEORY OF THE SCALING-LAW HEAT CONDUCTION PROCESS

ABSTRACT
In this article, we suggest a new model for the heat-conduction problem by us­ing the scaling-law vector calculus with Mandelbrot scaling law. The linear and non-linear scaling-law heat conduction equations are considered as analogues to the work of Fourier, Laplace, and Burgers. The obtained results are considered as typical examples to deal with the Mandelbrots scaling-law phenomena in heat transport system.
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PAPER SUBMITTED: 2020-06-01
PAPER REVISED: 2020-07-20
PAPER ACCEPTED: 2020-07-29
PUBLISHED ONLINE: 2021-12-24
DOI REFERENCE: https://doi.org/10.2298/TSCI2106505Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 6, PAGES [4505 - 4513]
REFERENCES
  1. Fourier, J. B. J., The Analytical Theory of Heat (in French), Cambridge University Press, Cambridge, London, UK, 1882
  2. Rognon, P., et al., A Scaling Law for Heat Conductivity in Sheared Granular Materials, EPL, 89 (2010), 5, 58006
  3. Dubessy, R., et al., Electric Field Noise above Surfaces: A Model for Heating-Rate Scaling Law in Ion Traps, Physical Review A, 80 (2009), 3, 031402
  4. Volkov, A. N., Zhigilei, L. V., Scaling Laws and Mesoscopic Modelling of Thermal Conductivity in Carbon Nanotube Materials, Physical Review Letters, 104 (2010), 21, 215902
  5. Zhou, X. W., et al., Analytical Law for Size Effects on Thermal Conductivity of Nanostructures, Physical Review B, 81 (2010),7, 073304
  6. Wu, M. C., Hsu, J. Y., Thermal Conductivity of Carbon Nanotubes with Quantum Correction Via Heat Capacity, Nanotechnology, 20 (2009), 14, 145401
  7. Su, Y. Q., et al., Stability of Heterogeneous Single-Atom Catalysts: A Scaling Law Mapping Thermodynamics to Kinetics, NPJ Computational Materials, 6 (2020), 1, pp. 1-7
  8. Barenblatt, G. I., et al., The Thermal Explosion Revisited, Proceedings of the National Academy of Sciences, 95 (1998), 23, pp. 13384-13386
  9. Li, L., Yu, B., Fractal Analysis of the Effective Thermal Conductivity of Biological Media Embedded with Randomly Distributed Vascular Trees, International Journal of Heat and Mass Transfer, 67 (2013), Dec., pp. 74-80
  10. Yang, X. J., On Traveling-Wave Solutions for the Scaling-Law Telegraph Equations, Thermal Science, 24 (2020), 6B, pp. 3861-3868
  11. Yang, X. J., et al., On the Theory of the Fractal Scaling-Law Elasticity, Meccanica, (2021), pp. 1-13
  12. Yang, X. J., Theory and Applications of Special Functions for Scientists and Engineers, Springer Nature, New York, USA, 2021
  13. Laplace, P. S., Mémoire sur les suites (in French), Histoire de l'Academie Royale des Sciences, Paris, France, 1782
  14. Burgers, J. M., Mathematical Examples Illustrating Relations Occuring in the Theory of Turbulent Fluid Motion, Transactions of the Royal Dutch Academy of Sciences in Amsterdam, 17 (1939), 2, pp. 1-53

© 2023 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, 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