The effect of various factors on the turbulent heat transfer and friction in the entrance regions of smooth passages is investigated analytically. The influence of Reynolds number, Prandtl number, initial velocity distribution, wall-boundary condition, passage shape, and of variable fluid properties is predicted. Integral heat-transfer and momentum equations are used for calculating the thicknesses of the thermal and flow boundary layers. The results indicate that approximately fully developed heat transfer and friction are, in general, attained in an entrance length less than 10 diameters. Substantial agreement between analysis and experiment was obtained for heat transfer to air in the entrance regions of tubes and parallel plates.

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