The image illustrates the highly transient nature of natural convection-induced velocity near a hot wall cooling down in air—one of the most common, yet complex scenarios, i.e., a vertically aligned surface with a temperature difference from its surrounding fluid. While its existence is intuitive, capturing this behavior in mathematical models is extremely challenging, as reflected in the literature, where numerous studies attempt to quantify even this single scenario.

Journal Article Presents Study of Natural Convection on a Vertical Surface

December 18, 2024

Accurate fire models are crucial for predicting how heat will affect buildings and other structures. Representing heat transfer from fires to surfaces by natural convection, commonly referred to as convective heat flux, is an essential component of these analyses. In fire models, this heat transfer is typically represented using correlations derived from experimental data and observations. However, since these correlations are often based on specific experimental conditions, they may not universally apply to all scenarios. As such, there is no single universal correlation that considers all influential variables. 

To address this challenge, a new peer-reviewed journal article “Natural Convection on a Vertical Surface: Direct Numerical Simulation versus Empirical Correlations” from the Fire Safety Research Institute (FSRI), part of UL Research Institutes, was recently published in the Journal of Physics Conference Series. This study identified the limitations and suitability of existing models for convective heat transfer. It also comprehensively evaluated prominent natural convection correlations from the literature against a benchmark dataset. This paper was authored by FSRI researchers as part of the Fire Modeling Development and Validation research project. 

Examining and Improving Natural Convection Correlations 

The primary objective of this study was to examine the limitations of the current natural convection correlations by comparing their predictions to a trusted Direct Numerical Simulation (DNS) benchmark. 

To do this, researchers performed three simulations of heat transfer on a vertical, constant-temperature wall in still air using the Fire Dynamics Simulator (FDS) in DNS mode.  They compared their simulation results with real-world experiments to ensure the DNS results were accurate. Next, researchers evaluated thirteen different natural convection correlations by comparing their predictions of heat transfer to the simulation results. To improve these correlations and their accuracy, researchers made adjustments using correction factors, thereby enhancing their applicability in fire safety. 

Implications and Future Directions of Research on Natural Convection Correlations

This comprehensive analysis sheds light on the implications of natural convection heat transfer modeling along vertical surfaces. By validating DNS simulations against experimental data, researchers affirmed their accuracy and established a foundation for further analysis. 

This study is the first step toward advancing convective heat transfer models. It is crucial that future developments eventually consider complex phenomena, such as the influence of different geometrics and configurations, the presence of mixed and forced convection, and the mass-blowing effect in a reactive flow field. 

“This research, with its simple yet effective apparatus, provides a foundational step for exploring more complex scenarios. Despite its simplicity, the analysis and results offer valuable quantitative guidance on the use of existing natural convection correlations tailored to specific setups, while also highlighting the need for caution, as these correlations can result in significant errors when applied outside their intended range.”

- Parham Dehghani, post-doctoral researcher, FSRI 

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