CHARACTERISTICS OF AN ANNULAR FIN OF A RECTANGULAR PROFILE WITH ENERGY RELEASE

Abstract

The heat conduction equation for an annular fin with an arbitrary profile in the presence of energy release in the fin is obtained in the article. The resulting equation differs from the approximate equation given in the literature by the presence of energy release and a more accurate determination of the length of the arc element. As boundary conditions, the temperature of the base of the fin is set, and at the end of the fin, heat exchange occurs according to the Newton - Richmann law with the environment. The equation for the fin of a rectangular profile is an inhomogeneous modified Bessel equation. Its solution contains the Bessel functions of the imaginary argument of the first and second kind of zero order. The efficiency of the fin and the heat flow through the base of the fin are determined. The energy release in the fin increases its efficiency compared to the efficiency of the fin in the absence of energy release, and also reduces the heat flow. The restriction by the values of energy release in the fin is found as condition for the applicability of the finning. The fin efficiency must be less than one. If the efficiency exceeds one, the fin plays the opposite role: the flow is directed in the reverse side. In the article, an expression is obtained for the surface build-up coefficient kh. When calculating the heating (cooling) of a body with a finned surface, the heat transfer coefficient should be increased by kh times.