A combined analytical, numerical and experimental study was conducted to investigate the problem of natural convection underneath a horizontal rectangular hot fin array. This subject has not been explored before. The purpose of the investigation was to provide useful and reliable heat transfer coefficients. In addition to the experimental and numerical results, a useful approximate closed form analytical solution is offered. The analytical solution clearly reveals the dependence of the Nusselt number on the Rayleigh number, the Prandtl number and the fin's height to spacing ratio. Optimum analyses were conducted to determine the minimum fin height that provides the necessary cooling capability of a specified array base area. In this context it is shown that the optimal fin spacing varies within a narrow range which depends primarily on the array length. Those findings have important industrial application because they impact both the cost and size of cooling finned surfaces.
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