Optimum finned surfaces with longitudinal rectangular fins

This study investigates both one- and two-dimensional heat conduction throu gh the fins in an array, the optimum aspect ratios of fins and the optimum spacings of longitudinal fin arrays are obtained at a given geometry of bas e plate, total fin volume, and Biot number. The heat transfer from fins' fr ee ends is taken into consideration. For convenience of design, two design approaches are given for the optimized array system. It shows that the opti mum aspect ratios of fins from one-dimensional analysis have higher accurac y for smaller Biot numbers. The larger the heat transfer coefficient at fin tip, the smaller the error of the one-dimensional solutions. One optimum a spect ratio of fins in arrays is obtained at two different Biot numbers. Ho wever, it is suggested that smaller Biot numbers should be selected in desi gn for higher overall surface efficiencies.