THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Lei Zhao

,

Ya Li

,

Ji-Huan He

PROMISES AND CHALLENGES OF FRACTAL THERMODYNAMICS

ABSTRACT
The fractal thermodynamics deals with thermodynamical phenomena to find na-ture laws in a fractal space. Here is introduced a new concept of fractal entropy, and the traditional principle of entropy increase should be revised as the fractal entropy equilibrium. Additionally, the law of brachistofractality, or the minimal fractional dimensions law, is also introduced, it implies that an object remains its fractal dimensions unchanged without an external action, and it minimizes its fractal dimensions under an external perturbation. An example is given to meas-ure the fractal dimensions of a fabric, so that a swimming vest with minimal fric-tion can be optimally designed. This article offers a new angle for observing a thermodynamical phenomenon.
KEYWORDS
fractal entropy, minimal energy consumption, fractal harmonic law, fractal diffusion, minimal fractal dimensions change
PAPER SUBMITTED: 2022-12-01
PAPER REVISED: 2023-03-15
PAPER ACCEPTED: 2023-03-15
PUBLISHED ONLINE: 2023-06-11
DOI REFERENCE: https://doi.org/10.2298/TSCI233A735Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 3, PAGES [1735 - 1740]
REFERENCES
  1. Qian, M. Y., He, J.-H., Two-Scale Thermal Science for Modern Life - Making the Impossible Possible, Thermal Science, 26 (2022), 3B, pp. 2409-2412
  2. He, J.-H., Frontier of Modern Textile Engineering and Short Remarks on Some Topics in Physics, International Journal of Nonlinear Sciences and Numerical Simulation, 11 (2010), 11, pp. 555-563
  3. Majumder, M., et al., Nanoscale Hydrodynamics - Enhanced Flow in Carbon Nanotubes, Nature, 438 (2005), Nov., p. 44
  4. El Naschie, M. S., From Nikolay Umov E = kmc2 via Albert Einstein's E = gmc2 to the Dark Energy Density of the Cosmos E = (21/22)mc2，World Journal of Mechanics, 8 (2018), Apr., pp. 73-81
  5. El Naschie, M. S. A Review of E Infinity Theory and the Mass Spectrum of High Energy Particle Physics, Chaos Solitons & Fractals, 19 (2004), 1, pp. 209-236
  6. Mikheev, S. A., et al., Fractal Thermodynamics of the States of Instantaneous Heart Rhythm, Russian Journal of Mathematical Physics, 28 (2021), Apr., pp. 251-256
  7. He, C.-H., Liu, C., Fractal Dimensions of a Porous Concrete and its Effect on the Concrete's Strength, Facta Universitatis Series: Mechanical Engineering, 228 (2023), 116986
  8. He, C.-H., et al., A Fractal Model for the Internal Temperature Response of a Porous Concrete, Applied and Computational Mathematics, 21 (2022), 1, pp. 71-77
  9. Liu, F. J., et al., Thermal Oscillation Arising in a Heat Shock of a Porous Hierarchy and its Application, Facta Universitatis Series: Mechanical Engineering, 20 (2022), 3, pp. 633-645
  10. He, C.-H., et al., A Novel Bond Stress-Slip Model for 3-D Printed Concretes, Discrete and Continuous Dynamical Systems, 15 (2022), 7, pp. 1669-1683
  11. Elias-Zuniga, A., et al., Recent Strategy to Study Fractal-Order Viscoelastic Polymer Materials Using an Ancient Chinese Algorithm and He's Formulation, Journal of Low Frequency Noise, Vibration and Active Control. 41 (2022), 3, pp. 842-851
  12. Feng, G. Q., Niu, J. Y., An Analytical Solution of the Fractal Toda Oscillator, Results in Physics, 44 (2023), 106208
  13. Wang ,Y., Deng, Q. G., Fractal Derivative Model for Tsunami Travelling, Fractals, 27 (2019), 2, 1950017
  14. Wang, Y., et al., A Variational Formulation for Anisotropic Wave Travelling in a Porous Medium, Fractals, 27 (2019), 4, 1950047
  15. Li, X. J., A Fractal-Fractional Model for Complex Fluid Flow with Nanoparticles, Thermal Science, 27 (2023), 3B, pp.
  16. Sun, J. S., Fractal Modification of Schrodinger Equation and its Fractal Variational Principle, Thermal Science, 27 (2023), 3B, pp.
  17. He, C.-H. A Variational Principle for a Fractal Nano/Microelectromechanical (N/MEMS) System, International Journal of Numerical Methods for Heat & Fluid Flow, 33 (2023) , 1, pp. 351-359
  18. He, C.-H., Liu, C., A Modified Frequency-Amplitude Formulation for Fractal Vibration Systems, Fractals, 30 (2022), 3, 2250046
  19. Wang, K. L., He, C.-H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, 1950134
  20. Ma, H. J., Fractal Variational Principle for an Optimal Control Problem, Journal of Low Frequency Noise, Vibration and Active Control, 41 (2022), 4, pp. 1523-1531
  21. Kumbhakar, M., Tsai, C. W., Analytical Modeling of Vertical Distribution of Streamwise Velocity in Open Channels Using Fractional Entropy, Chaos, Solitons & Fractals, 169 (2023), Apr., 113285
  22. Cvetic, M., et al., Black Hole Thermodynamics and Negative Entropy in de Sitter and Anti-de Sitter Einstein-Gauss-Bonnet Gravity, Nuclear Physics B, 628 (2002), Apr., pp. 295-330
  23. Cerf, N. J., Adami, C., Negative Entropy and Information in Quantum Mechanics, Physical Review Letters, 79 (1997), 26, pp. 5194-5197
  24. Marmur, A., The Lotus Effect: Superhydrophobicity and Metastability, Langmuir, 20 (2004), 9, pp. 3517-3519
  25. Zhuang, Y. L., Study on Photostability and Quantitative Structure-Activity Relationship of Hemicyanine Fluorescent Dye (in Chinese), M. Sc. Thesis, Soochow University, Soochow, China, 2015
  26. Wang, Q. L., Shi, X. Y., Nonlinear Oscillator of an Artificial Bone, Journal of Low Frequency Noise, Vibration and Active Control, 38 (2019), Dec., pp. 1184-1187
  27. Milić, P., et al., Reissner-Mindlin Based Isogeometric Finite Element Formulation for Piezoelectric Active Laminated Shells, Tehnicki Vjesnik, 30 (2023), 2, pp. 416-425
  28. Faghidian, S. A., Tounsi, A., Dynamic Characteristics of Mixture Unified Gradient Elastic Nanobeams, Facta Universitatis-Series Mechanical Engineering, 20 (2022), 3, pp. 539-552
PDF VERSION [DOWNLOAD]
Promises and Challenges of Fractal Thermodynamics

© 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