A method is presented for finding plate fin geometries for maximizing dissipated heat flux. The method is based on approximate analytical solutions of conjugated heat transfer which are utilized in optimization. As a result non-dimensional variables have been found that contain thermal and geometrical properties of the fin and the flow. These variables have a fixed value at the optimal point. The values are given for rectangular, convex parabolic, triangular, and concave parabolic fin shapes for natural and forced convection including laminar and turbulent boundary layers. An essential fact is that there is no need to evaluate convection heat transfer coefficients because they are already included in these variables. Easy-to-use design rules are presented for finding the geometry of fixed volume fins that gives the maximum heat transfer.

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