International Scientific Journal

Authors of this Paper

External Links


This paper addresses a non-traditional approach for the scaling-law fluid-flows described by fractal scaling-law vector calculus associated with the Mandelbrot scaling law. Their quantum equations were proposed to control the fluid-flows associated with the Mandelbrot scaling law. This gives a new insight into the descriptions for the scaling-law behaviors of the fluid-flows in the Mandelbrot scaling-law phenomena.
PAPER REVISED: 2021-02-20
PAPER ACCEPTED: 2021-04-06
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 6, PAGES [4561 - 4568]
  1. Bourgoin, M., et al., The Role of Pair Dispersion in Turbulent Flow, Science, 311 (2006), 5762, pp. 835-838
  2. Collins, R. T., et al., Electrohydrodynamic Tip Streaming and Emission of Charged Drops from Liquid Cones, Nature Physics, 4 (2008), 2, pp. 149-154
  3. Philip, J., et al., Scaling Law for a Subcritical Transition in Plane Poiseuille Flow, Physical Review Letters, 98 (2007), 15, pp. 154502
  4. Chesler, P. M., et al., Holographic Vortex Liquids and Superfluid Turbulence, Science, 341 (2013), 6144, pp. 368-372
  5. Carbone, V., et al., Experimental Evidence for Differences in the Extended Self-Similarity Scaling Laws between Fluid and Magnetohydrodynamic Turbulent Flows, Physical Review Letters, 75 (1995), 17, 3110
  6. Yakhot, V., et al., Scaling of Global Properties of Turbulence and Skin Friction in Pipe and Channel Flows, Journal of Fluid Mechanics, 652 (2010), May, pp. 65-73
  7. Brodu, N., et al., New Patterns in High-Speed Granular Flows, Journal of Fluid Mechanics, 769 (2015), Mar., pp. 218-228
  8. Yao, J., Lundgren, T. S., Experimental Investigation of Microbursts, Experiments in Fluids, 21 (1996), 1, pp. 17-25
  9. Reeves, M. T., et al., Inverse Energy Cascade in Forced 2-D Quantum Turbulence, Physical Review Letters, 110 (2013), 10, 104501
  10. Mandelbrot, B., How Long is the Coast of Britain, Statistical Self-Similarity and Fractional Dimension, Science, 156 (1967), 3775, pp. 636-638
  11. Tarasov, V. E., Fractional Hydrodynamic Equations for Fractal Media, Annals of Physics, 318 (2005), 2, pp. 286-307
  12. Ostoja-Starzewski, From Fractal Media to Continuum Mechanics, ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 94 (2014), 5, pp. 373-401
  13. Balankin, A. S., Elizarraraz, B. E., Map of Fluid-Flow in Fractal Porous Medium into Fractal Continuum Flow, Physical Review E, 85 (2012), 5, 056314
  14. Yang, X. J., et al., On the Theory of the Fractal Scaling-Law Elasticity, Meccanica, (2021), July, pp. 1-13
  15. Yang, X. J., On Traveling-Wave Solutions for the Scaling-Law Telegraph Equations, Thermal Science, 24 (2020), 6B, pp. 3861-3868
  16. Stokes, G. G., On the Theories of the Internal Friction of Fluids in Motion, and of the Equilibrium and Motion of Elastic Solids, Transactions of the Cambridge Philosophical Society, 8 (1845), 2, pp. 287-305
  17. Stockes, G. G., On the Effect of the Internal Friction of Fluids on the Motion of Pendulums, Transactions of the Cambridge Philosophical Society, 9 (1851), 2, pp. 8-106
  18. Reynolds, O., The Sub-Mechanics of the Universe, Cambridge University Press, Cambridge, UK, 1903
  19. Euler, L., Principes Généraux du Mouvement des Fluides (in French), Mémoires de l'académie des sciences de Berlin, 11 (1757), 1757, pp. 274-315
  20. Cauchy, A. L., Recherches sur l'équilibre et le mouvement intérieur des corps solides ou fluides, élastiques ou non-élastiques (in French), Bulletin de la Société Philomathique, Paris, France, 1823, pp. 9-13
  21. Stokes, G. G., A Smith's Prize Paper, Cambridge University, Calendar, Cambridge, UK, 1854
  22. Navier, C. L., Mémoire sur les lois du mouvement des fluides (in French), Mémoires de l'Académie Royale des Sciences de l'Institut de France, 6 (1822), 1822, pp. 375-394

© 2024 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