Nonfree Space Radiating Fin Optimum Dimension and Efficiency Correlations

摘要

Correlation (15) is suggested to evaluate the efficiency of a longitudinal rectangular fin radiating to a nonfree space. This correlation covers a wide range of the values of the parameter radiation-conduction number N_r, in comparison to Chang's correlation, and is useful in estimating the heat transferred by the fin to the surroundings without the need of solving a nonlinear second-order differential equation. The fin efficiency evaluated using Chang's correlation when used to find out the fin tip temperature for the case of nonfree-space condition led to meaningless results. This emphasizes the need to use the value of fin efficiency for the correct θ_∞ condition and should not be approximated by that at θ_∞ = 0. A correlation, Eq. (17), to estimate the optimum N_r yielding the least fin material for different background temperatures also is given. Optimum N_r decreases with increasing background temperature.