In this paper we develop an analytical and graphical formulation of the constructal law of maximization of flow access in systems with heat and fluid flow irreversibilities and freedom to change configuration. The flow system has global objective (e.g., minimization of global flow resistance) and global constraints (e.g., overall size, and total duct volume). The infinity of possible flow structures occupies a region of the two-dimensional domain of “global performance versus freedom to morph.” This region of “nonequilibrium” flow structures is bounded by a line representing the best flow structures that are possible when the freedom to morph is limited. The best of all such structures are the “equilibrium” structures: here the performance level is the highest, and it does not change even though the flow architecture continues to change with maximum freedom. The universality of this graphical and analytical presentation is illustrated with examples of flow structures from three classes: flow between two points, flow between a circle and its center, and flow between one point and an area. In sum, this paper presents an analytical and graphical formulation of the constructal principle of thermodynamic optimization of flow architecture under global constraints. The place of this new and self-standing principle in the greater framework of thermodynamics is outlined.

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