A previous analysis for fully developed turbulent heat transfer and flow with variable fluid properties is extended and applied to the entrance regions of smooth tubes and parallel flat plates. Integral heat-transfer and momentum equations are used for calculating the thicknesses of the thermal and flow boundary layers. The effect of variable properties is determined for the case of uniform heat flux, uniform initial temperature distribution, and fully developed velocity distribution. A number of other cases in which the fluid properties are considered constant are analyzed. The predicted Nusselt numbers for air with a uniform wall temperature and uniform initial temperature and velocity distributions agree closely with experimentally determined values.
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