An exact general solution for the temperature distribution and the composite radiation convection heat exchange along a constant cross-sectional area fin

Abstract

An exact general solution is obtained for the nonlinear differential equation governing the one-dimensional steady-state heat exchange by composite radiation and convection along constant area fins with uniform temperature at the base and an arbitrary temperature gradient at the other end. The fin can dissipate or receive energy. The fin is assumed to have constant thermal properties, and the radiant interaction between the fin and the base surfaces is neglected.