The effect of the boundary condition at a fin tip on the performance of the fin with and without internal heat generation. (English) Zbl 0669.76056

An analytical investigation is carried out on the effect on the rate of heat flow from a one-dimensional straight (or cylindrical) fin with and without internal heat generation of the assumption that no heat transfer takes place at the fin tip. This assumption yields trivial solutions for some values of the parameters considered if internal heat sources exist in the fin. The error in the determination of the foregoing rate of heat flow appears to be large for some conditions important for practical applications. For the quantitative analysis of the fin, the following parameter ranges are used: Biot number, 0.1 - any value lower than 0.1; generation number, 0-0.5; and the ratio of the length of the fin to its half-thickness (or its half-radius), 1-100. The heat transfer coefficient is assumed to be a power function of the temperature difference between the fin and its surroundings and that the power in this function is equal to -1, 0, 1, and 2.


76D10 Boundary-layer theory, separation and reattachment, higher-order effects
80A20 Heat and mass transfer, heat flow (MSC2010)
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