A theoretical study is undertaken to determine the optimal geometry of a composite heat spreader subjected to cooling by a single phase fluid. Optimal geometry is obtained when heat transfer from the spreader is maximized. Constructal theory is employed, where the fundamental construct for the composite consists of a thin high-thermal conductivity blade in contact with a matrix of lesser conductivity. Following a systematic procedure, a tree-like geometry is built up from this fundamental unit, which increases in surface area with each successive construct and possesses optimal geometry at each construct level. Numerical results are calculated for a carbon-fiber composite in an epoxy matrix. We find the optimal aspect ratio for all constructs to be of the order of 1 for a wide range of prescribed surface area for the fundamental unit.

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