Natural Convection on a Vertical Surface: Direct Numerical Simulation versus Empirical Correlations

Abstract

Convective heat flux to surfaces is an essential component of fire safety analyses. Heat transfer from fires to surfaces by natural convection is typically represented in fire models using empirical correlations; however, these models are often constrained by specific experimental conditions and may not universally apply to all scenarios. A universal correlation that considers all influential variables has yet to be established. The limitations of these models for convective heat transfer, and their suitability for fire modelling, must be identified. This study performs a comprehensive evaluation of prominent natural convection correlations from the literature against a benchmark dataset. The primary objective was to examine the existing correlations quantitatively, and adjust the correlations using a universal and systematic approach. Direct numerical simulation was employed to investigate convective heat transfer on a vertical plate in a still ambient, and simulation results were validated against experimental data. Predictions of the natural convection correlations were then compared to the simulation results, and their effectiveness over differing ranges of Rayleigh numbers and surface temperatures was evaluated. Correction factors were determined to improve the accuracy of the top-performing correlations in each flow regime, thereby enhancing their applicability in fire safety.