A plate fin is an extended surface made from a plate. Classical longitudinal and radial fins are particular cases of plate fins with very simple shapes and no curvature. In this paper, the problem of a flat plate fin of constant thickness, straight base, and symmetrical shape given by a proposed power law is considered. Particular attention is paid to some basic shapes: rectangular, triangular, convex parabolic, concave parabolic, convergent trapezoidal, and divergent trapezoidal. One- and two-dimensional analyses are conducted for every shape and comparison of results is carried through the usage of a proposed shape factor. Beyond shape, temperature fields and performance for the considered plate fins are shown to be dependent on a set of three Biot numbers characterizing the ratio between conduction resistances through every direction and convection resistance at the fin surface. Effectiveness and shape factor are found to be hierarchically organized by an including-figure rule. For the rectangular, zero-tip, and convergent trapezoidal cases, effectiveness is limited by a maximum possible value of Bit-1/2, and two-dimensional effects are very small. For the divergent trapezoidal case instead, effectiveness can be larger than Bit-1/2, and one-dimensional over-estimation of the actual heat transfer can be substantially large.

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