Temperature distributions in fins with uniform and non-uniform heat generation and non-uniform heat transfer coefficient

Abstract

Temperature distributions in a straight fin of rectangular profile (or in a cylindrical fin) with uniform and non-uniform internal heat-generation characteristics and non-uniform heat transfer coefficients are derived analytically. The heat transfer coefficient is assumed to be a power function of the difference between the temperature of the fin and that of the fluid surrounding it. The power of this function is taken as being equal to — 1, 0, 1 and 2. Non-uniform internal heat generation is assumed to depend on the fin temperature and this dependency is expressed in a polynomial equation up to the third degree. The results obtained for uniform internal heat generation are also presented in tabular and graphical forms and an interpolation method is proposed to determine the fin temperature and the fin effectiveness if the foregoing power is a fraction between — 1 and 2.