## THERMAL SCIENCE

International Scientific Journal

### A FRACTAL DERIVATIVE MODEL FOR SNOW'S THERMAL INSULATION PROPERTY

**ABSTRACT**

Snow is of porous structure and good thermal insulation property. A fractal derivative model is established to reveal its thermal property, it is extremely high thermal-stable, the whole snow will not be affected much by the sudden environmental temperature change. A simple experiment is carried out to verify the theoretical finding, and the result is helpful to design advanced materials mimicking the snow structure.

**KEYWORDS**

PAPER SUBMITTED: 2017-08-01

PAPER REVISED: 2018-11-23

PAPER ACCEPTED: 2018-11-23

PUBLISHED ONLINE: 2019-09-14

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**4**, PAGES [2351 - 2354]

- Liu, F. J., et al., A fractional Model for Insulation Clothings with Cocoon-Like Porous Structure, Ther-mal Science, 20 (2016), 3, pp. 779-784
- He, J.-H., A New Fractal Derivation, Thermal Science, 15 (2011), Suppl. 1, pp. S145-S147
- Liu, F. J., et al., A Delayed Fractional Model for Cocoon Heat-Proof Property, Thermal Science, 21 (2017), 4, pp. 1867-1871
- Shen, J., et al., Effect of Pore Size on Gas Resistance of Nanofiber Membrane by the Bubble Electro-spinning, Thermal Science, 19 (2015), 4, pp. 1349-1351
- Liu, Y. Q., et al. Air Permeability of Nanofiber Membrane with Hierarchical Structure, Thermal Science, 22 (2018), 4, pp.1637-1643
- Wang, F. Y., et al., Improvement of Air Permeability of Bubbfil Nanofiber Membrane, Thermal Science, 22 (2018), 1A, pp. 17-21
- Tian, D., et al., Self-Assembly of Macromolecules in a Long and Narrow Tube, Thermal Science, 22 (2018), 4, pp. 1659-1664
- Tian, D., et al., Macromolecule Orientation in Nanofibers, Nanomaterials, 8 (2018), 11, ID 918
- Tian, D., et al., Macromolecular Electrospinning: Basic Concept & Preliminary Experiment, Results in Physics, 11 (2018), Dec., pp. 740-742
- He, J.-H., Fractal Calculus and Its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
- He, J.-H., Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
- He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, Int J Theor Phys, 53 (2014), 11, pp. 3698-3718
- Li, X. X., et al., A Fractal Modification of the Surface Coverage Model for an Electrochemical Arsenic Sensor, Electrochimica Acta, 296 (2019), Feb., pp. 491-493
- Wang, Q. L., et al., Fractal Calculus and Its Application to Explanation of Biomechanism of Polar Bear Hairs, Fractals, 26 (2018), 6, ID 1850086
- Wang, Y., An, J. Y., Amplitude-Frequency Relationship to A fractional Duffing Oscillator Arising in Microphysics and Tsunami Motion, Journal of Low Frequency Noise, Vibration & Active Control, On-line first, doi.org/10.1177/1461348418795813
- Wang, Y., Deng, Q., Fractal Derivative Model for Tsunami Travelling, Fractals, On-line first, doi.org/10.1142/S0218348X19500178
- Ain, Q. T., He, J.-H., On Two-Scale Dimension and Its Applications, Thermal Science 23 (2019), 3B, pp. 1707-1712
- He, J.-H., Ji, F.Y., Taylor Series Solution for Lane-Emden Equation, Journal of Mathematical Chemistry (2019), On-line first, doi.org/10.1007/s10910-019-01048-7