北极熊毛的微观结构对其热传导性能影响的分数阶模型研究

Nature gives birth to a wide variety of species in the evolution process of billions of years. Every living thing has magical properties and capabilities. Mankind replicates and re-creates certain biological features and functionality through researching, learning and imitating the properties. Polar bears have a special ability to survive in the cold areas of the Arctic. Studies have found that the polar bear hair plays an important role in protection against the bitter cold. The structure of polar bear hair is completely different from the structure of other mammals' hair, which has a unique membrane - pore structure. The unique membrane -pore structure makes polar bear hair not only can maintain body temperature, but also can absorb energy from surrounding environment. This is the real reason that the polar bears can perennially live in the environment of -45℃ to -50℃ and to maintain body temperature at around 37℃. This project is based on the membrane-pore structure of polar bear. We approximately consider the structure of the polar bear hair as fractal space and establish the one-dimensional, two-dimensional and three-dimensional unsteady fractional heat conduction equation to quantitatively investigate thermal protection and diffusion process of polar bear hair, and uncover the mechanism of the effect of membrane-pore structure on the heat transfer, to provide a theoretical basis for the bio-mimetic designs of materials, and to supply an experimental basis and scientific guidance for development of high thermal bionic functional fibers.

自然界在亿万年的演化过程中孕育了各种各样的生物, 每种生物都拥有神奇的特性和功能。人类通过研究、学习、模仿来复制和再造某些生物的特性和功能。北极熊具有在寒冷的北极地区生存下去的特殊能力。研究发现：北极熊的毛对其抵御严寒起了重要作用, 北极熊毛的结构与其他哺乳动物毛的结构完全不一样，北极熊毛具有独特的膜孔结构。独特的膜孔结构使得北极熊毛不但能保持体温，而且能从周围环境吸收能量。这就是北极熊能够常年生活在零下45℃-50℃的环境中，并保持体温在37℃左右的真正原因。 本课题基于北极熊毛的膜孔结构，通过把北极熊毛的内部结构近似看成分形空间, 建立一维、二维和三维的非定常分数阶热传导方程来定量研究北极熊毛的热保护和扩散过程，揭示膜孔结构对传热性能的影响机理，为仿生材料设计提供理论依据，为开发高保暖的仿生功能纤维提供实验基础和科学指导。

本项目采用数学模型法、实验法研究了北极熊毛的热传递问题，通过测定北极熊毛的物性参数、建立模型、数值计算、图形展示、统计分析、实验验证等手段，探索了北极熊毛的热传递机理。研究结果表明：（一）北极熊毛的内部是中空的膜-孔结构，而且这种结构可以近似看作分形空间。（二）北极熊具有“脂肪－皮肤－毛发”保温系统。（三）北极熊毛的膜-孔结构（表征参数为分形维数、孔隙率）对传热性能有重要影响。北极熊毛的总导热系数与分形维数呈负相关，随着分形维数的增加，总导热系数呈非线性递减趋势，北极熊毛的热传导能力减弱。北极熊毛的孔隙率与导热系数亦呈负相关，随着孔隙率的増大，北极熊毛的固相比例减小，流体相比例逐渐増大，热阻也就相应的増大，北极熊毛的导热系数逐渐减小，从而削弱了北极熊毛的热传导能力。（四）北极熊毛的中空膜-孔结构限制了热对流，减少了热传导，增强了体内热辐射的反射。. 上述研究结果提高了人们对北极熊毛传热现象的认识，为设计仿生多孔材料提供了理论依据和基础数据。另外，本项目所采用的研究手段，可为人们研究蚕茧、动物骨骼等天然多孔材料提供借鉴。