- Rocha, L.A.O. and Lorente, S. and Bejan, A., Constructal design for cooling a disc-shaped area by conduction,
International Journal of Heat and Mass Transfer, vol. 45 no. 8
pp. 1643 - 1652 [S0017-9310(01)00269-1] .
(last updated on 2007/04/06)
This paper describes a hierarchical strategy to developing the optimal internal structure of a round heat-generating body cooled at its center with the help of optimally distributed inserts of high-conductivity material. The sequence begins with optimizing the geometry of the smallest heat generating entity - a sector-shaped elemental volume with the smallest dimension, and a single high-conductivity insert. Many such elements are assembled into disc-shaped constructs, or into sector-shaped constructs in which the elemental volumes are grouped into a formation shaped as a fan. When several sector-shaped constructs are assembled into a disc, they constitute a quasi-radial heat-flow structure in which each high-conductivity insert exhibits one branching. Every geometric detail of the optimized two-material conductive structures is determined based on principle - the minimization of global resistance subject to global constraints (total volume, total volume of high-conductivity material). The inserts of high-conductivity material form structures shape as trees. The global thermal resistance of each tree-shaped construct is reported. The minimization of global thermal resistance is the criterion for choosing between a design with radial inserts and one with branched inserts. © 2002 Elsevier Science Ltd. All rights reserved.
Heat conduction;Cooling;Heat resistance;Trees (mathematics);Structural optimization;