THERMAL SCIENCE
International Scientific Journal
THERMAL PERFORMANCE OF FRACTAL METASURFACE AND ITS MATHEMATICAL MODEL
ABSTRACT
How can we explain the thermal phenomenon by a fractal metasurface? This has been puzzling scientists and engineers for at least ten years, and so far no answer has been found. Now, modern mathematics offers a completely new window to physically understand the magical phenomenon that lies far beyond the Fourier law for heat conduction. A fractal-fractional modification of the Fourier law is elucidated, and its extremely high thermal conductivity is mathematically revealed. This article shows that thermal science is the key to nanotechnology.
KEYWORDS
PAPER SUBMITTED: 2024-01-01
PAPER REVISED: 2024-03-23
PAPER ACCEPTED: 2024-03-24
PUBLISHED ONLINE: 2024-04-14
THERMAL SCIENCE YEAR
2024, VOLUME
28, ISSUE
Issue 3, PAGES [2379 - 2383]
- Song, Q. H., et al., Plasmonic Topological Metasurface by Encircling an Exceptional Point, Science, 373 (2021), 1133
- High, A. A., et al., Visible-Frequency Hyperbolic Metasurface, Nature, 522 (2015), June, pp. 192-196
- Xu, Z. H., et al., Chimera Metasurface for Multiterrain Invisibility, Proceedings of the National Academy of Sciences of the United States of America, 121 (2024), 6, Article Number: 2309096120
- Zhang, Y., et al., Fourier Metasurface Cloaking: Unidirectional Cloaking of Electrically Large Cylinder Under Oblique Incidence, Optics Express, 32 (2024) , 1, pp. 1047-1062
- Wood, J., New Metamaterial May Lead to a Magnetic Cloak: Magnetic Materials, Materials Today, 11 (2008), 4, p. 8
- Ji, Q., et al., Selective Thermal Emission and Infrared Camouflage Based on Layered Media, Chinese Journal of Aeronautics, 36 (2023), 3, pp. 212-219
- Omam, Z. R., et al., Adaptive Thermal Camouflage Using Sub-Wavelength Phase-Change Metasurfaces, Journal of Physics D, 56 (2023), 2, Article Number: 025104
- Duan, Y. P., et al., Layered Metamaterials with Sierpinski Triangular Fractal Metasurface: Compatible Stealth for S-Band Radar and Infrared, Materials Today Physics, 38 (2023), 101210
- Goyal, N., Panwar, R., Minkowski Inspired Circular Fractal Metamaterial Microwave Absorber for Multiband Applications, Applied Physics A, 129 (2023), 4, 293
- Zheludev, N. I., The Road Ahead for Metamaterials, Science, 328 (2010), Apr., pp. 582-583
- Dong, L., et al., Metasurface-Enhanced Multifunctional Flag Nanogenerator for Efficient Wind Energy Harvesting and Environmental Sensing, Nano Energy, 124 (2024), 109508
- Wang, Z. X., et al., Phase Change Plasmonic Metasurface for Dynamic Thermal Emission Modulation, APL Photonics, 9 (2024), 1, Article Number: 010801
- Kumar, N., et al., Thermally Switchable Metasurface for Controlling Transmission in the THz-Gap, Plasmonics, on-line first, doi.org/10.1007/s11468-023-02115-1, 2023
- Li, Y. H., et al., Broadband Absorbing Property of the Composite by Fractal Gap-Square-Ring Metasurface and Dielectric Layers, Applied Physics Express, 8 (2023), 8, Article Number: 084501
- Aziz, A. A. A., et al., Fractal Metasurface for THz Applications with Polarization and Incidence Angle Insensitivity, Journal of Instrumentation, 18 (2023), 3, Article Number: P03030
- Mandelbrot, B., The Fractal Geometry of Nature, Freeman, New York, USA, 1983
- Goncharova, L. V., Basic Surfaces and their Analysis, Morgan & Claypool Pub., Bristol, UK, 2018
- Roy, S ., et al., Comparison of Thermal and Athermal Dynamics of the Cell Membrane Slope Fluctuations in the Presence and Absence of Latrunculin-B, Physical Biology, 20 (2023), 4, Article Number: 046001
- Zhu, Z. J., et al., Modified Graphene Nanoplatelets/Cellulose Nanofibers-Based Wearable Sensors with Superior Thermal Management and Electromagnetic Interference Shielding, Advanced Functional Materials, on-line first, doi.org/10.1002/adfm.202315851, 2024
- Zhao, L., et al., Promises and Challenges of Fractal Thermodynamics, Thermal Science, 27 (2023), 3A, pp. 1735-1740
- 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
- He, C.-H., Liu, C., Fractal Dimensions of a Porous Concrete and Its Effect on the Concrete's Strength, Facta Universitatis Series: Mechanical Engineering, 21 (2023), 1, pp. 137-150
- He, J.-H., El-Dib, Y. O., A Tutorial Introduction to the Two-Scale Fractal Calculus and Its Application to the Fractal Zhiber-Shabat Oscillator, Fractals, 29 (2021), 8, Article Number: 2150268
- Wang, K. J., Shi, F., A New Fractal Model of the Convective-Radiative Fins with Temperature-Dependent Thermal Conductivity, Thermal Science, 27 (2023), 4A, pp. 2831-2837
- Fan, J., et al., Fractal Calculus for Analysis of Wool Fiber: Mathematical Insight of Its Biomechanism, Journal of Engineered Fibers and Fabrics, 14 (2019), 1, 1558925019872200
- Elias-Zuniga, A., et al., A Weighted Power-Form Formulation for the Fractal Warner-Gent Viscohyperlastic Model, Fractals, 31 (2023), 7, Article Number: 2350094
- Tian, D., He, C.-H., A Fractal Micro-Electromechanical System and Its Pull-In Stability, Journal of Low Frequency Noise and Active Control, 40 (2021), 3, pp. 1380-1386