THERMAL SCIENCE

International Scientific Journal

Xiao-Jun YangORCID

,

Pei-Tao Qiu

,

Gang-Lin Liu

A NEW INSIGHT ON ANALYTICAL THEORY OF THE SCALING LAW HEAT CONDUCTION ASSOCIATED WITH THE RICHARDSON SCALING LAW

ABSTRACT
In this article, we propose a new model for the scaling law heat conduction equation associated with the Richardson scaling law. To find the analytical solution for it, we present a scaling law series associated with the Kohlrausch-Williams-Watts function analogous to the Fourier series. The proposed technology is efficient to handle the Richardson scaling law problems in mathematical physics.
KEYWORDS
scaling law heat conduction equation, scaling law series, Kohlrausch-Williams-Watts function, Richardson scaling law
PAPER SUBMITTED: 2021-06-01
PAPER REVISED: 2021-07-20
PAPER ACCEPTED: 2021-07-29
PUBLISHED ONLINE: 2022-04-09
DOI REFERENCE: https://doi.org/10.2298/TSCI2202025Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE No. 2, PAGES [1025 - 1035]
REFERENCES
[1] Fourier, J. B. J., Théorie Analytique de la Chaleur (The Analytical Theory of Heat), Cambridge University Press, Cambridge, London, UK, 1822
[2] Richardson, L., F., Atmospheric Diffusion Shown on a Distance-Neighbour Graph, Proceedings of the Royal Society A, 110 (1926), 756, pp.709-737, 10.1098/rspa.1926.0043
[3] Yang, X.-J., New Insight into the Fourier-like and Darcy-like Models in Porous Medium, Thermal Science, 24 (2020), 6A, pp. 3847-58, 10.2298/tsci2006847y
[4] Kohlrausch, R., Theorie des Elektrischen Rckstandes in der Leidener Flasche, Annalen der Physik, 167 (1854), 2, pp. 179-214, 10.1002/andp.18541670203
[5] Williams, G., Watts, D. C., Non-Symmetrical Dielectric Relaxation Behaviour Arising from a Simple Empirical Decay Function, Transactions of the Faraday society, 66 (1970), June, pp. 80-85, 10.1039/tf9706600080
[6] Rognon, P., et al., A Scaling law for Heat Conductivity in Sheared Granular Materials, EPL (Europhys-ics Letters), 89 (2010), 5, ID 58006, 10.1209/0295-5075/89/58006
[7] Volkov, A. N., Zhigilei, L. V., Scaling Laws and Mesoscopic Modeling of Thermal Conductivity in Carbon Nanotube Materials, Physical Review Letters, 104 (2010), 21, ID 215902, 10.1103/physrevlett.104.215902
[8] Wu, M. C., Hsu, J. Y., Thermal Conductivity of Carbon Nanotubes with Quantum Correction via Heat Capacity, Nanotechnology, 20 (2009), 14, ID 145401, 10.1088/0957-4484/20/14/145401
[9] Yang, X. J., New Non-Conventional Methods for Quantitative Concepts of Anomalous Rheolo-gy, Thermal Science, 23 (2019), 6B, pp. 4117-4127, 10.2298/tsci191028427y
[10] Yang, X. J., Theory and Applications of Special Functions for Scientists and Engineers, Springer Singa-pore, New York, USA, 2021, 10.1007/978-981-33-6334-2
PDF VERSION [DOWNLOAD]
A new insight on analytical theory of the scaling law heat conduction associated with the Richardson scaling law

© 2026 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