A set of generic correlations for high-Rayleigh-number thermal convection in inclined rectangular enclosures

Abstract

A detailed review of the high-Rayleigh-number thermal convection literature for inclined enclosures indicates that correlations proposed thus far for the response variable, Nusselt number, have been either for a particular angle of inclination or fail to include all control parameters for the problem. The present study proposes a set of empirical correlations to predict Nusselt number for turbulent thermal convection in differentially-heated, tilted, rectangular enclosures of different aspect ratios (1, 3, 6, and 10) and angles of inclination (0°–150°) for a given range of Rayleigh numbers (1.85×106≤Ra≤1.04×1011). This study utilizes previously published experimental data to devise a set of generic correlations for Nusselt number in terms of Rayleigh number (Ra), aspect ratio (AR), and angle of inclination (θ) of the rectangular enclosure for any given Prandtl number (Pr). Predicted Nusselt numbers obtained from these generic correlations yield a mean absolute percentage error of ∼5% when compared to the corresponding experimental results. Additionally, the predicted values are also compared with literature-reported values for studies pertaining to control parameters outside the scope of the present study and found to be in good agreement, with a maximum deviation of ∼10%.