THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Ji-Huan He

WHEN MATHEMATICS MEETS THERMAL SCIENCE: THE SIMPLER IS THE BETTER

ABSTRACT
Mathematics is an important tool to dealing with a complex problem, but it might be too abstract and elusive to be directly applied by engineers. This paper shows mathematics should be simple but effective for thermodynamic problems, the simpler is the better. The two-scale fractal is used as an example to show the im-portance of application of mathematics to practical problems, and a fast-slow law is suggested to deal with many discontinuous problems by fractal calculus.
KEYWORDS
fractal geometry, porous medium, fractal derivative, two-scale fractal dimension, slow-fast law, Brachistochrone curve
PAPER SUBMITTED: 2020-07-15
PAPER ACCEPTED: 2020-07-15
PUBLISHED ONLINE: 2021-04-03
DOI REFERENCE: https://doi.org/10.2298/TSCI200715132H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 3, PAGES [2039 - 2042]
REFERENCES
  1. Wang, Y., et al., A Fractal Derivative Model for Snow's Thermal Insulation Property, Thermal Science, 23 (2019), 4, pp. 2351-2354
  2. Zhou, C. J., et al., Highly Selective Penetration of Red Ink in a Saline Water, Thermal Science, 23 (2019), 4, pp. 2265-2270
  3. Ain, Q. T., He, J.-H., On Two-Scale Dimension and its Application, Thermal Science, 23 (2019), 3B, pp. 1707-1712
  4. He, J.-H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Therm. Science, 23 (2019), 4, pp. 2131-2133
  5. He, J.-H., Ain, Q. T., New Promises and Future Challenges of Fractal Calculus: From Two-Scale Thermodynamics to Fractal Variational Principle, Thermal Science, 24 (2020), 2A, pp. 659-681
  6. He J.-H., Thermal Science for the Real World: Reality and Challenge, Thermal Science, 24 (2020), 4, pp. 2289-2294
  7. He, J.-H., Fractal calculus and its geometrical explanation, Results Phys., 10 (2018), Sept., pp. 272-276
  8. Wang, Q. L., et al., Fractal Calculus and its Application to Explanation of Biomechanism of Polar Hairs (Vol. 26, 1850086, 2018), Fractals, 27 (2019), 5, 1992001
  9. Wang, Q. L., et al., Fractal Calculus and its Application to Explanation of Biomechanism of Polar Hairs, Fractals, 26 (2018), 6, 1850086
  10. Fan, J., et al., Fractal Calculus for Analysis of Wool Fiber: Mathematical Insight of its Biomechanism, Journal of Engineered Fibers and Fabrics, 14 On-line first, doi.org/10.1177/1558925019872200, 2014
  11. Liu, F. J., et al., Silkworm (Bombyx Mori) Cocoon vs. Wild Cocoon: Multi-Layer Structure and Performance Characterization, Thermal Science, 23 (2019), 4, pp. 2135-2142
  12. Xu, L. Y., et al., Detection of Cigarette Smoke Using a Fiber Membrane Filmed with Carbon Nanoparticles and a Fractal Current Law, Thermal Science, 24 (2020), 4, pp. 2469-2474
  13. Zuo, Y. T., Effect of SiC Particles on Viscosity of 3-D Print Paste: A Fractal Rheological Model and Experimental Verification, Thermal Science, 25 (2021), 3B, pp. 2405-2409
  14. He, J. H., A Simple Approach to One-Dimensional Convection-Diffusion Equation and its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), 113565
PDF VERSION [DOWNLOAD]
When mathematics meets thermal science: The simpler is the better

© 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