Fractal Heat Transfer in Wool Fiber Hierarchy

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.