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

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(degrees)-150(degrees)) for a given range of Rayleigh numbers (1.85 x 10(6) <= Ra <= 1.04 x 10(11)). 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 (theta) 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 similar to 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 similar to 10%.

Automated summary

A detailed review of the literature on high-Rayleigh-number thermal convection in inclined enclosures reveals that existing correlations for the Nusselt number are either specific to a certain inclination angle or do not consider all control parameters. This study proposes a set of empirical correlations to predict the Nusselt number in differentially-heated, tilted, rectangular enclosures of various aspect ratios and inclination angles, within a given range of Rayleigh numbers. The predicted Nusselt numbers show a mean absolute percentage error of approximately 5% compared to experimental results.