Nature Inspired Optimal Design of Heat Conveying Networks for Advanced Fiber-Reinforced Composites

A concept of composite materials reinforced by branching
micro or nanotubes optimized for both heat transfer and
strength of the material is presented. Numerous examples of
reinforcement by branched fibers in cells, tissues and organs of
plants and animals are studied. It is shown orientation of the
fibers according to principals of the stress tensor at given
external load is the main principle of optimal reinforcement in
nature. The measurement data obtained on venations of the
plant leaves revealed clear dependencies between the
diameters, lengths and branching angles that correspond to
delivery of the plant sap to live cells of the leaf with minimal
energy expenses. The mathematical problem on geometry of
asymmetrical loaded branched fibers experienced minimal
maximal stress is solved. Heat propagation in the fibers is
described by generalized Guyer-Krumhansl equation. It is
shown the optimality for the heat propagation, fluid delivery
and structural reinforcement are based on the same relations
between the diameters, lengths and branching angles. The
principle of optimal reinforcement is proposed for technical
constructions, advanced composite materials and MEMS
devices.