The paper presents a comprehensive analysis of conditions for numerical simulation and physical modeling of convective heat transfer in the vicinity of dimpled surface relief. Contradictory results, unreasonable assumptions, and non-justified conclusions are marked. Based on the analysis of physical experiments the correlation between the predictions and measured data is discussed. Detailed numerical study of turbulent air flow and heat transfer in the narrow channel with three types of dimples (spherical, conic and oval) was carried out. Various mathematical and discrete models, including, those based on solving Reynolds-averaged Navier-Stokes equations (RANS/URANS-SST), and also adaptive scale models (SAS-SST) are compared. The influence of flow parameters (Reynolds number) and geometric sizes (dimple diameter, depth, radius of rounding off of an edge, channel width and height) on local and integral characteristics of flow and heat transfer (total heat output and hydraulic losses) is determined. Special attention is given to reorganizing vortex structures and flow regime (with periodic fluctuations) with increasing relative dimple depth and Reynolds number. For the first time the influence of the scale factor of a constant cross-section channel is detailed. Thermal-hydraulic characteristics of various dimpled reliefs are compared, and the advantage of an oval dimple over a spherical one is shown.

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