Turbulent Heat Transfer in Concentric Annuli With Constant Wall Temperatures

The problem of turbulent heat transfer in concentric annuli is analyzed for the case in which one wall has a constant temperature while the other is insulated. The solution is given for both, the thermal entrance region and the fully developed situation with heating at either one of the annular surfaces. The description of the velocity profile properly takes into account the Reynolds number and radius ratio dependence of the nondimensional turbulent velocity profile in concentric annuli. Results are presented for radius ratios 2.88, 5.625, and 9.37 with the Reynolds number range from 20,000 to 240,000 and for Prandtl numbers 0.01, 0.7, and 1000. The calculated Nusselt numbers for the constant wall temperature boundary condition are smaller than the corresponding result for a uniform heat-flux boundary condition. The available experimental evidence for concentric annuli is insufficient to provide a direct test of the analysis. However some calculated results for the radius ratios 1.05 and 50 are in agreement with available theory and experiments for the parallel plate channel and circular tube, respectively. There is also good agreement, between the calculated results for the extension of the analysis to the case of a linear rise in wall temperature and experiments for a uniform heat-flux boundary condition for the annuli considered.