Three-dimensional tree constructs of “constant” thermal resistance

This article extends to three-dimensional heat flow the constructal method of minimizing geometrically the thermal resistance between a heat-generating volume and one point. Optimized is the geometry of each volume element, and the shape and distribution of high-conductivity inserts. The new feature is the maximization of the amount of heat-generating material that operates at temperatures close to the hot-spot level (Tmax). Volume elements and subsequent constructs acquire optimal shapes where all the external surfaces are isothermal at Tmax. The same, constant thermal resistance separates each surface point (Tmax) and the common heat-sink point (Tmin). The optimized architecture is pine-cone-like, with high-conductivity nerves and low-conductivity filling (and heat-generating) material. The similarities between the constant-resistance structures and the three-dimensional tree networks found in nature are discussed. The analogy between evolutionary flow systems and evolutionary mechanical support systems is reasoned based on the same (constructal) principle of pursuing objective (purpose) subject to global and local constraints.