Prandtl Number Influence on Heat Transfer and Flow Dynamics in Narrow and Unbounded Differentially Heated Cavities

In this study, we investigate the influence of the Prandtl number on turbulent natural convection thermal transport in a Differentially Heated Cavity (DHC) at high Rayleigh numbers. The range of Rayleigh numbers explored is from 10^5 to 10^9, and Prandtl numbers vary from 1/2 to 10.



At low Prandtl numbers, we find that both the thermal and mean flow field exhibits distinct characteristics such as a higher prevalence of vortices, leading to a more complex and turbulent flow pattern and a more pronounced horizontal velocity. On the other hand, at high Prandtl numbers, a more stable flow field emerges. We conclude that Pr plays a crucial role in shaping the flow and heat transfer characteristics within the DHC, especially for Ra exceeding 10^7.



The turbulent kinetic energy (TKE) distribution in the cavity provides further evidence of the violent and energetic nature of low Prandtl, high Rayleigh number natural convection for both narrow and unbounded cavity geometries.



While a significant increase in the Nusselt (Nu) number is apparent with increases in Pr and Ra, Ra maintains its tradition 1/4-1/3 power law scaling regardless of Pr. Upon comparison of the geometries, narrow cavities exhibit a steep drop in Nu compared to unbounded cavities, especially at low Ra.



These insights shed light on the significance of the Prandtl number in influencing the convective flow patterns in DHC, offering valuable information for engineering applications involving natural convection and thermal transport phenomena.