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Heat Transfer Research
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Heat Transfer Research

DOI: 10.1615/HeatTransRes.2013005856
pages 399-407

FRACTAL HEAT TRANSFER IN WOOL FIBER HIERARCHY

Jie Fan
National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123, Key Laboratory of Advanced Textile Composites, Ministry of Education of China, 399 West Binshui Road, Tianjin 300387
XiaoMei Shang
College of Textile and Apparel, Soochow University, 178 East Ganjiang Road, Suzhou, 215021, China

ABSTRACT

As a natural keratin fiber, wool possesses an optimal tree-like hierarchical structure which endows the fiber with a special thermal property. A possible mechanism for the wool fiber's hierarchy is illustrated, and a modified Fourier's law is introduced using the recently proposed fractal derivative. The theoretical analysis shows that the wool fiber is of extraordinarily good property for unilateral heat conduction. The thermal conduction of the hierarchy is about three orders of magnitude more efficient than would be predicted from the conventional thermal theory for continuous fibers without hierarchical structure. A better understanding of the mechanism could help the further design of biomimetic artificial fibers or clothes for special applications.


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