A simple necessary condition of optimality for a finned heat exchanger duct in laminar flow is derived. The criterion of optimality is maximum heat transfer from the fin per unit cost of the finned duct. The heat transfer is determined by the conjugate convection-conduction process rather than by the assumption of a given heat transfer coefficient on the fin surface. Both forced and natural convection are considered. Expressions comparing the performance of optimal assemblies of different materials are given. Approximate dimensions of optimal fins are derived. The relations between the present and earlier results are discussed.

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