Authors & Affiliations

Levchenko V.A., Kascheev M.V., Dorokhovich S.L., Zaytsev A.A.
The Limited Liability Company “Simulation Systems Ltd.”, Obninsk, Russia

Levchenko V.A. – Director, Cand. Sci. (Tech.).
Kascheev M.V. – Chief Researcher, Dr. Sci. (Tech.). Contacts: 133, Lenin avenue, Obninsk, Kaluga region, Russia, 249035. Tel.: +7 (484) 396-03-61; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it..
Dorokhovich S.L. – Chief Engineer, Cand. Sci. (Tech.), Associate Professor.
Zaytsev A.A. – Head of the Laboratory, Cand. Sci. (Tech.), The Limited Liability Company “Simulation Systems Ltd.”.


The article is devoted to determining the effect of energy release in the straight fin of a parabolic profile on its characteristics. Such a fin requires a minimum of material for its preparation to remove a certain amount of heat. An analytical solution of the heat conduction problem in a straight fin with a parabolic 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. By analyzing the temperature distribution along the fin height, it is mathematically confirmed that the presence of energy release in the fin increases its temperature. 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. 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.

surface finning, fins with energy release, extended surface, straight fin of the parabolic profile, the efficiency of the fin, heat flow, heat conduction equation for a fin, Lagrange method of arbitrary constants variation

Article Text (PDF, in Russian)


UDC 536.21

Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2022, issue 2, 1:17