THERMAL SCIENCE

International Scientific Journal

Fu-Juan Liu

,

Ping Wang

,

Yan Zhang

,

Hong-Yan Liu

,

Ji-Huan He

A FRACTIONAL MODEL FOR INSULATION CLOTHINGS WITH COCOON-LIKE POROUS STRUCTURE

ABSTRACT
Both silkworm cocoons and wild silkworm cocoons have excellent mechanical properties, as a protective barrier against environmental damage and attack by natural predators. In particular, this multilayer porous structure can be exceptionally tough to enhance the chance of survival for pupas while supporting their metabolic activity. Here, a fractional derivative is defined through the variational iteration method, and its application to explaining the outstanding thermal protection of insulation clothings with cocoon-like porous structure is elucidated. The fractal hierarchic structure of insulation clothings makes human body mathematically adapted for extreme temperature environment.
KEYWORDS
fractional model, insulation clothings, variational iteration method
PAPER SUBMITTED: 2015-10-15
PAPER REVISED: 2015-11-10
PAPER ACCEPTED: 2015-12-20
PUBLISHED ONLINE: 2016-08-13
DOI REFERENCE: https://doi.org/10.2298/TSCI1603779L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 3, PAGES [779 - 784]
REFERENCES
  1. Zhang, Y., et al., Mechanical Properties and Structure of Silkworm Cocoons: A Comparative Study of Bombyx Mori, Antheraea Assamensis, Antheraea Pernyi and Antheraea Mylitta Silkworm Cocoons, Ma - terials Science and Engineering C, 33 (2013), 6, pp. 3206-3213
  2. Danks, H. V., The Roles of Insect Cocoons in Cold Conditions, European Journal of Entomology, 101 (2004), 3, pp. 433-437
  3. Chen, F. J., et al., Silkworm Cocoons Inspire Models for Random Fiber and Particulate Composites, Physical Review E, 82 (2010), 4, pp. 041911-041917
  4. Blossman-Myer, B., et al., The Silk Cocoon of the Silkworm, Bombyx Mori: Macrostructure and its Influence on Transmural Diffusion of Oxygen and Water Vapor, Comparative Biochemistry and Physiology, 155 (2010), 2, pp. 259-263
  5. Chen, R. X., et al., Waterproof and Dustproof of Wild Silk: A Theoretical Explanation, Journal of Nano Research, 22 (2013), 1, pp. 61-63
  6. He, J.-H., et al., Local Fractional Variational Iterati on Method for Fractal Heat Transfer in Silk Coco on Hierarchy, Nonlinear Science Letters A, 4 (2013), 1, pp. 15-20
  7. Fei, D. D., et al., Fractal Approachto Heat Transfer in Silkworm Coco on Hierarchy, Thermal Science, 17 (2013), 5, pp. 1546-1548
  8. Liu, F. J., et al., He's Fractional Derivative for Heat Conduction in a Fractal Medium Arising in Silkworm Coco on Hierarchy, Thermal Science, 19 (2015), 4, pp. 1155-1159
  9. He, J.-H., Approximate Analytical Solution for Seepage Flow with Fractional Derivatives in Porous Media, Computer Methods in Applied Mechanics and Engineering, 167 (1998), 1-2, pp. 57-68
  10. He, J.-H., A Short Remark on Fractional Variational Iteration Method, Physics Letters A, 375 (2011), 38, pp. 3362-3364
  11. He, J.-H., A New Fractal Derivation, Thermal Science, 15 (2011), Suppl. 1, pp. S145-S147
  12. He, J.-H., Asymptotic Methods for Solitary Solutions and Compactons, Abstract and Applied Analysis, 2012 (2012), ID916793
  13. Wu, G. C., et al., Discrete Fractional Diffusion Equation, Nonlinear Dynamics, 80 (2015), 1, pp. 281-286
  14. Huang, L. L., Matrix Lagrange Multiplier of the VIM, Journal of Computational Complexity and Applica - tions, 2 (2016), 3, pp. 86-88
  15. Hu, Y., et al., On Fractal Space-Time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 773-777
  16. Sayevand, K., et al., Analysis of Nonlinear Fractionl KdV Equation Based on He's Fractional Derivative, Nonlinear Science Letters A., 7 (2016), 3, pp. 77-85
  17. He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
  18. Li, Z. B., et al., Fractional Complex Transform for Fractional Differential Equations, Mathematical & Computational Applications, 15 (2010), 5, pp. 970-973
  19. He, J.-H., et al., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
  20. Li, Z. B., et al., Exact Solutions of Time-Fractional Heat Conduction Equation by the Fractional Complex Transform, Thermal Science, 16 (2012), 2, pp. 335-338
  21. Liu, Z., et al., Tunable Surface Morphology of Electrospun PMMA Fiber Using Binary Solvent, Applied Surface Science, 364 (2016), Feb., pp. 516-521
  22. He, J.-H., An Alternative Approach to Establishment of a Variational Principle for the Torsional Problem of Piezoelastic Beams, Applied Mathematics Letters, 52 (2016), Feb., pp. 1-3
  23. Chen, R. X., et al., Series Solution of the Autocatalytic Hydrolysis of Cellulose, Cellulose, 18 (2015), 5, pp. 3099-3104
  24. He, C. H., et al., Bubbfil Spinning for Fabrication of PVA Nanofibers, Thermal Science, 19 (2015), 2, pp. 743-746
PDF VERSION [DOWNLOAD]
A fractional model for insulation clothings with cocoon-like porous structure

© 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