- Nelson, Ralph A. Jr. and Bejan, Adrian, Self-organization of the internal flow geometry in convective heat transfer,
American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD, vol. 357-3
pp. 149 - 161 .
(last updated on 2007/04/06)
In this paper, 'constructal theory' is used to predict the formation of geometric shape and structure in finite-size fluid systems subjected to heating from below. Two classes of systems are considered: (1) single-phase fluid layers and (2) fully developed saturated pool nucleate boiling. In the first system, the minimization of thermal resistance across the layer accounts for the appearance of organized macroscopic motion (streams) on the background of disorganized motion (diffusion). By optimizing the shape of the flow, it is possible to predict analytically the main structural and heat-transfer characteristics of the system. The convective regime emerges as the result of a process of geometric optimization of heat flow path in which diffusion is assigned to length scales smaller than the smallest macroscopic flow element. When the system is constrained (e.g., by the distribution of nucleation sites in nucleate boiling), the optimization of flow geometry may not lead to a steady or steady-periodic flow. Nevertheless, the principle of geometric optimization of paths for imposed currents constitutes a deterministic approach to the self-organization of the macroscopic state of the finite-size system: the mechanism and the structure, with streams and diffusion combined.
Steady flow;Nucleate boiling;Heat resistance;Optimization;Thermal diffusion in liquids;Geometry;