An Analysis of the Developing Turbulent Hydrodynamic and Thermal Boundary Layers in an Internally Heated Annulus

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Abstract
The problems of the simultaneous growth of the hydrodynamic and thermal boundary layers in the entrance region of a concentric annulus with a uniformly heated core are investigated using the momentum and energy integral equations, along with a modified Reichardt momentum eddy diffusivity variation. A radius ratio range of 0.2 to 0.8 was investigated over a Reynolds number range from 104 to 3 × 105 for a Prandtl number of 0.7. The analysis predicts velocity and temperature profiles and local variations of normalized pressure gradients and Nusselt numbers which are in satisfactory agreement with experimental data. The analysis also shows that the flow is hydrodynamically fully developed within 10 equivalent diameters of the annulus inlet, while a further 30 equivalent diameters are required for the thermal boundary layers to reach the outer insulated wall of the annulus.

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