Optimum design of longitudinal rectangular fins with base-to-fin radiant interaction

The optimum dimensions of rectangular longitudinal radiating fins with radi ant interaction bern fen the fin and its base are determined The basic assu mptions are one-dimensional heat conduction and ideal black-surface radiati on. The governing differential equation is formulated by means of dimension less variables and is solved using a variable-step Runge-Kutta [1, 2] algor ithm, with local extrapolation [3], in order to carry out the required mini mization procedure. The optimum thickness, height, and percent contribution of the fin heat dissipation are presented in dimensionless form in several diagrams that give insight into the operational characteristics of the hea t rejection mechanism. It has been found that the results are strong affect ed by the surface Biot number B-r = h(r)R/k. Several examples that highligh t design criteria with regard to the selection of the material, amount of h eat rejected, and tube and fin base temperature are given. A comparison of our results with those existing in the literature shows some significant di fferences that are discussed.