Three-dimensional tree constructs of “constant” thermal resistance

Abstract

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.

Constructal design for a steam generator based on entransy dissipation extremum principle

“…This theory can be expressed, for simplicity, as the structure derived from the optimal performance. Since constructal theory was applied to optimization problems involving heat conduction [3], constructal theory has been developing rapidly [4][5][6][7][8][9][10][11][12][13][14][15][16] and has provided new research impetus into heat transfer problems [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Constructal optimization of discrete and continuous-variable cross-section conducting path based on entransy dissipation rate minimization

“…Neagu and Bejan [10] optimized the external boundary of the element and pointed out that the maximum temperature difference could be decreased by 33% when the external boundary of the element was an arc. By assembling the arc shape elements, a treeshaped construct was proposed and the rationality of tree-like network constructal method was illuminated further [11]. Almogbel and Bejan [12] proposed that when the uniform distribution of conducting paths through assembling was released the best conducting paths distribution of first order assembly was nonuniform and that there existed some offsets, the maximum temperature difference was decreased by 5.7% when the element number of first order assembly was 6.…”

The area-point constructal optimization for discrete variable cross-section conducting path

“…The first aspect is to consider a heat conduction model which is more close to the reality, such as the case that conduction trees with spacing at the tips [8], the case that heat flux is not linear in high conductive link [10] and the three-dimensional model [23]. The second aspect is to relax the constraints of the model, such as adding degrees of freedom to minimize heat resistance [9,17,18,[24][25][26].…”