A study on heat transfer characteristics and the development of empirical correlation with error analysis for smooth channels

To optimize the internal cooling design of turbine blades, this study investigates the heat transfer characteristics of radially rotating smooth channels. Rather than a simple parametric study, this research focuses on the complex coupled effects of the Reynolds number ( Re ), rotation number ( Ro ), temperature ratio ( TR ), rotational radius ratio ( r/D ), and buoyancy number ( Buo ) on the heat transfer coefficient (HTC), and develops a multi-parameter empirical correlation for HTC. The uncertainty in Re is approximately 1.02%, and the maximum uncertainty in the Nusselt number ( Nu ) is 11.56%. Under stationary conditions, the symmetrical radial outflow structure of the channel results in consistent HTC trends for the LS and TS, with significant enhancement observed near the entrance and exit regions. Additionally, a low Re (e.g., Re = 10,000) amplifies the inlet effect. Under rotating conditions, TR regulates HTC by modulating centrifugal buoyancy: at Ro = 0.1, a high TR suppresses LS heat transfer due to stable flow stratification; at Ro = 0.2, a high TR enhances HTC on the LS owing to buoyancy-driven counter flow, and TR = 0.13 is the critical point for HTC convergence. The contribution of r/D to HTC is found to be highly Re -dependent: it significantly enhances LS inlet heat transfer at low Re by inducing centrifugal-driven swirling flow; at Re > 10,000, this influence weakens as inertia dominates. Based on the experimental data, a multi-parameter empirical correlation incorporating TR and r/D is developed. Validation results demonstrate that the correlation accurately captures the coupled effects with high predictive accuracy, particularly in the high-inertia regime ( Re = 70,000). Despite these advances, this study is limited to smooth channels with fixed aspect ratios; the effects of advanced turbulators and varying cross-sections remain important topics for future investigation.