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A theoretical model for predicting rough pipe heat transfer. Kiss, Mart

Abstract

A model has been developed for predicting turbulent heat transfer coefficients and associated temperature profiles in rough pipes from a knowledge of the fluid mechanics. The proposed method employs the Lyon heat transfer equation together with the velocity profile equations of Rouse and von Karman. Nusselt numbers were calculated by the proposed method for the following range of variables: f = fs to 0.020 Re = 4 x 10³ to 10⁷ Pr = 0.001 to 1,000 Temperature profiles were calculated for all combinations of the above extreme conditions, as well as for Pr = 1.0. The validity of the proposed model was tested by comparison of the predicted results with the experimental data of Nunner, Smith and Epstein and Dipprey. A similar test was made of Nunner's theoretical equation. It is concluded that, except for fluids with very low Prandtl numbers, e.g. liquid metals, the proposed model gives no better prediction of Nusselt number than Nunner's equation, which is less cumbersome to apply. In the existing form, the proposed model is not adequate. Certain combinations of the independent variables give rise to a discontinuity in the predicted value of Nusselt number. This is inconceivable in the physically real situation. Beyond the discontinuity appears a predicted region of zero net flow in the pipe. Two limiting assumptions can be made regarding the method of heat transport through this layer - viz. by molecular conduction only, or by an infinite conductivity eddy mechanism. Both assumptions have been made, and values of Nu calculated for each, whenever the situation arose. The agreement between the predicted and the experimental temperature profiles is in general good. However, not enough experimental data are available to satisfactorily define the effect of Re and f, and to substantiate the calculated results.

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