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 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.
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