THERMAL SCIENCE

International Scientific Journal

A NEW SCALING LAW HEAT CONDUCTION PROBLEM ASSOCIATED WITH THE KORCAK SCALING LAW

ABSTRACT
In this article, we address a new model for the scaling law heat conduction problem by using the scaling law vector calculus associated with the Korcak scaling law. The scaling law heat conduction equations are discussed in detail. The scaling law vector calculus formulas are proposed as an efficiently mathematical tool to describe the Korcak scaling -law phenomena in heat transport system.
KEYWORDS
PAPER SUBMITTED: 2021-06-04
PAPER REVISED: 2021-07-21
PAPER ACCEPTED: 2021-07-25
PUBLISHED ONLINE: 2022-04-09
DOI REFERENCE: https://doi.org/10.2298/TSCI2202047Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 2, PAGES [1047 - 1059]
REFERENCES
  1. Marsden, J. E., Tromba, A., Vector Calculus, Macmillan, London, UK, 2003
  2. Green, G., An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, Notingham, London, UK, 1828
  3. Gauss, C. F., Theoria Attractionis Corporum Sphaeroidicorum Ellipticorum Homogeneorum Methodo novo Tractata, Commentationes Societatis Regiae Scientiarum Gottingensis Recentiores, 2 (1813), pp. 2-5
  4. Ostrogradsky, M. V., Note sur la Théorie de la Chaleur, Mémoires présentés à l'Académie impériale des Sciences de St. Petersbourg, 6 (1831), 1, pp. 123-138 (Presented in 1828)
  5. Ostrogradsky, M. V., Mémoire sur L'equilibre et le Mouvement des Corps Elastiques, Mémoires présen-tés à l'Académie impériale des Sciences de St. Petersbourg, 6 (1831), 1, pp. 39-53 (Presented in 1828)
  6. Stokes, G. G., A Smith's Prize Paper, The Cambridge University Press, Cambridge, UK, 1854
  7. Hankel, H., Zur allgemeinen Theorie der Bewegung der Flussigkeiten, Dieterische University, Buch-druckerei, 1861
  8. Maxwell, J. C., A Treatise on Electricity and Magnetism, Clarendon Press, Oxford, UK, 1873
  9. Eddington, A. S., The Mathematical Theory of Relativity, The Cambridge University Press, Cambridge, UK, 1923
  10. Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, The Cambridge University Press, Cambridge, UK, 1906
  11. Carslaw, H. S., Introduction to the Mathematical Theory of the Conduction of Heat in Solids, Dover Publication, Mineola, N. Y., USA, 1906
  12. Navier, C. L., Mémoire sur les lois du mouvement des fluides, Mémoires de l'Académie Royale des Sci-ences de l'Institut de France, 6 (1822), 1822, pp. 375-394
  13. Stockes, G. G., On the Effect of the Internal Friction of Fluids on the Motion of Pendulums, Transac-tions of the Cambridge Philosophical Society, 9 (1851), 2, pp. 8-106
  14. Reynolds, O., The Sub-Mechanics of the Universe, Cambridge University Press, Cambridge, UK, 1903
  15. Frisch, U., Turbulence, Cambridge University Press, New York, NY, 1995
  16. Mandelbrot, B., How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimen-sion, Science, 156 (1967), 3775, pp. 636-638
  17. Richardson, L., F., Atmospheric Diffusion Shown on a Distance-Neighbour Graph, Proceedings of the Royal Society A, 110 (1926), 756, pp. 709-737
  18. Korcak, J., Geopolitické základy Československa. Jeho kmenové oblasti (The Geopolitic Foundations of Czechoslovakia. Its Tribal Areas), Prague, Orbis, 1938
  19. Yang, X.-J., New Insight into the Fourier-like and Darcy-Like Models in Porous Medium, Thermal Sci-ence, 24 (2020), 6A, pp. 3847-58
  20. Yang, X. J., On Traveling-Wave Solutions for the Scaling law Telegraph Equations, Thermal Sci-ence, 24 (2020), 6B, pp. 3861-3868
  21. Yang, X. J., et al., On the Theory of the Fractal Scaling law Elasticity, Meccanica (2021), July, pp. 1-13
  22. Yang, X. J., Theory and Applications of Special Functions for Scientists and Engineers, Springer Singa-pore, New York, USA, 2021
  23. Rognon, P., et al., A Scaling Law for Heat Conductivity in Sheared Granular Materials, EPL (Europhys-ics Letters), 89 (2010), 5, ID 58006
  24. Volkov, A. N., Zhigilei, L. V., Scaling Laws and Mesoscopic Modeling of Thermal Conductivity in Carbon Nanotube Materials, Physical Review Letters, 104 (2010), 21, ID 215902

© 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