Optimum fin spacing of rectangular fins on a vertical base in free convection heat transfer

The steady-state natural convection heat transfer from aluminum vertical rectangular fins extending perpendicularly from vertical rectangular base was investigated experimentally. Thirty different fin configurations were tested. Experiments were performed for fin lengths of 250 and 340 mm. Fin thickness was kept fixed at 3 mm. Fin height and fin spacing were varied from 5 to 25 mm and 5.75 to 85.5 mm, respectively. Five heat inputs ranging from 25 to 125 W were supplied for all fin configurations, hence; the base-to-ambient temperature differences were measured in order to evaluate the heat transfer rates from fin arrays. The results of experiments have shown that the convective heat transfer rate from fin arrays depends on geometric parameters and base-to-ambient temperature difference. The separate roles of fin height, fin spacing and base-to-ambient temperature difference were investigated. It was found that, for a given base-to-ambient temperature difference, the convective heat transfer rate from fin arrays takes on a maximum value as a function of fin spacing and fin height and an optimum fin spacing value which maximizes the convective heat transfer rate from the fin array is available for every fin height. These measurements were to extend data obtained earlier from aluminum fin-arrays using the same experimental system and method (Yuncu and Guvenc in Heat Mass Transfer 37:409-416, 2001). Data collated from earlier and present work cover the range of fin spacing from 4.5 to 85.5 mm. The fin length range was from 100 to 340 mm, the fin height from 5 to 25 mm and the number of fins per array 3 to 34. The range of base-to-ambient temperature difference was quite extensive, from 30 to 150 K. These results indicate that the optimum fin spacing is between 6.1 and 11.9 mm, for the fin arrays employed in the earlier and present work. A scale analysis is performed in order to estimate the order-of-magnitude of optimum fin spacing at a given fin length and base-to-ambient temperature difference. From the scale analysis, correlations to evaluate the optimum fin spacing value and the corresponding maximum convective heat transfer rate at a given fin length and base-to-ambient temperature difference were obtained.