Levchenko V.A., Kascheev M.V., Dorokhovich S.L., Zaytsev A.A.
The Limited Liability Company “Simulation Systems Ltd.”, Obninsk, Russia
The article is devoted to determining the effect of energy release in the straight fin of a triangular profile on its characteristics. An analytical solution of the heat conduction problem in a straight fin with a triangular profile and continuously operating heat sources is obtained. As boundary conditions, the temperature of the base of the fin is set, and the temperature limitation condition is imposed at the fin vertex. The heat conduction equation for the fin of a triangular 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 linear heat flow through the base of the fin must be greater than zero. If the linear heat flow is less than zero, the fin plays the opposite role: the flow is directed in the reverse side. Optimal sizes of the fin are determined. In the article, an expression is obtained for the surface build-up coefficient kb. When calculating the heating (cooling) of a body with a finned surface, the heat transfer coefficient should be increased by kb times.
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