A rectangular fin optimization including comparison between 1-D and 2-D analyses

Both I-D and 2-D analytic methods are used for a rectangular fin optimization. Optimum heat loss is taken as 98% of the maximum heat loss. Temperature profile using 2-D analytic method and relative error of temperature along the fin length between I-D and 2-D analytic methods are presented. Increasing rate of the optimum heat loss with the variation of Biot number and decreasing rate of that with the variation of the fin base length are listed. Optimum fin tip length using 2-D analytic method and relative error of that between I-D and 2-D analytic methods are presented as a function of Biot numbers ratio.