On Minimum-Weight Rectangular Radiating Fins

Abstract

TEMPERATURE DISTRIBUTION The governing equation of the temperature T(x) in a thin rectangular fin is dT/dx (e<x/kb)T* = 0 (0 < x < L) (1) where e is the emissivity of the fin material, <r is the StefanBoltzmann constant, k is the conductivity, and 2b and L are the fin width and length. The boundary conditions are T = To dT/dx = 0 T = TL Note that the boundary-value problem is completely defined by Eqs. (1), (2), and (3). The additional condition, Eq. (4), is merely used as a parameter which will be uniquely determined. By direct integration of Eq. (1) with boundary conditions, Eqs. (3) and (4), the solution for the temperature distribution along the fin can be written as