Constructal multi-scale structures with asymmetric heat sources of finite thickness A.K. da Silva a , S. Lorente b , A. Bejan a, * a Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300, USA b Laboratory for Materials and Durability of Constructions, National Institute of Applied Sciences (INSA), 135 Avenue de Rangueil, Toulouse 31077, France Received 20 December 2004; received in revised form 31 January 2005 Available online 29 March 2005 Abstract This paper details the generation of multi-scale flow structure in a package with heat sources. The model is based on abandoning two common assumptions (1) the assumption that there are many channels (components) in the package, which is traditionally made to exploit simplifications due to symmetry, and (2) the assumption that the heat-generating components have negligible thickness. Numerical simulations document the flow stagnation and separation generated by blunt heat sources, and the effect of these flow phenomena on the optimized internal flow structure. The effect of asymmetric thermal boundary conditions on the optimal spacing between heat-generating plates is significant. If the package has some channels with symmetric boundary conditions, and some with asymmetric boundary conditions, then the optimal structure has multiple spacings. The effect of freedom on design performance is documented by optimizing competing configurations that have different numbers of degrees of freedom. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Constructal; Multi-scale; Optimal spacings; Discrete heat sources; Forced convection; Heatlines 1. Introduction An emerging body of work [1–13] draws attention to the link between the maximization of the heat transfer rate packed into a fixed volume and the development of the internal structure of the package through which the coolant flows. This link represents a most fundamen- tal optimization opportunity, which is applicable not only to the cooling of heat-generating packages but to flow structures in general. Spacings between solid parts must be sized in an optimal way, which is tailored to the intensity of the flow regime—tighter spacings where flows are faster. Spacings must be distributed in a certain way (non-uniformly) through a given volume—tighter spacings near the frontal region of the package. These features continue to hold as the size of the package de- creases to dimensions so small that slender channels and boundary layers disappear, and the flow structure becomes a Ôdesigned porous mediumÕ [1,14]. In summary, the link between the maximization of heat transfer density and geometry is an invitation to the discovery of flow architecture. The generation of flow configuration is the mechanism through which the heat transfer device achieves its global objective. This 0017-9310/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2005.01.028 * Corresponding author. Tel.: +1 919 660 5309; fax: +1 919 660 8963. E-mail address: dalford@duke.edu (A. Bejan). International Journal of Heat and Mass Transfer 48 (2005) 2662–2672 www.elsevier.com/locate/ijhmt