The work presented in this thesis is organized in four parts. The first part describes a proposal to design flow structures with maximal heat transfer rate per unit volume, by shaping each duct so that it fits optimally on the body of the convective flow. Two examples are given. In the first, a heat-generating strip is cooled inside a duct of rectangular cross-section. In the second example, the duct is a tube with isothermal internal surface, and the flow is sufficiently slow so that boundary layers do not form inside the duct. In both cases the duct geometry was selected so that the fixed duct volume packs a maximal heat transfer rate density.;The second part completes the description of geometry optimization in stacks of parallel plates that generate heat. The spacing between plates, or the number of plates in a fixed volume, has been maximized in two limits: pure natural convection, and pure forced convection. The second part constructs a correlation that bridges the gap between the two limits, and provides a single formula for optimal spacings covering the entire domain, from natural convection to forced convection.;The third part shows that in a space filled with heat generating parallel plates and laminar forced convection, the heat transfer density can be increased beyond the level known for parallel plates with optimal spacing. The technique consists of inserting in every entrance region new generations of smaller plates because smaller plates have thin boundary layers that fit in the unused (isothermal) entrance flow. The complete optimized architecture and performance of structures with one, two and three plate length scales are reported.;The fourth part extends the multi-scale concept of part three to cylinders in cross-flow: the use of cylinders of several sizes, and the optimal placement of each cylinder in the assembly. The thesis reports the optimized flow architectures and performance for structures with 1, 2 and 3 cylinder sizes, which correspond to structures with 1, 2 and 4 degrees of freedom. The heat transfer rate density increases (with diminishing returns) as the optimized structure becomes more complex. The optimized cylinder diameters are relatively robust, i.e., insensitive to changes in complexity and flow regime (pressure difference). The resulting flow structure has multiple scales that are distributed non-uniformly through the available volume.
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