Effect of Rayleigh and Prandtl Numbers upon Natural Convection and Flow Field in a Differentially Heated Cavity

In this poster presentation, direct simulation of 2D and 3D differentially heated square cavities (DHC) filled with fluids of Prandtl (Pr) numbers ranging from 0.5 to 100 is conducted to explore and visualize the influence of the Prandtl and Rayleigh (Ra) numbers upon the temperature and velocity fields within the cavity. 

It is observed that for constant Ra, the velocity and temperature fields between low Pr and high Pr fluids differ significantly, especially near the corners of the cavity due to inertial effects. These inertial effects are found to drastically impact the temperature and velocity fields for Ra larger than 10⁵. For Ra > 10⁵, there is a clear divergence between the flow fields of Pr  < 1 and Pr > 1 as increases in Ra led to chaotic yet symmetric vortex formations for low Pr fluids. The scaling of Nusselt number to the Rayleigh and Prandtl numbers, Nu = f(Ra,Pr) was investigated. Excellent agreement is obtained with previous numerical-benchmark solutions at Pr = 0.71 to ensure model accuracy. It is discovered that increasing Pr leads to increased Nu at high Ra-values and that Nu is most sensitive to Pr near Pr = 1. Results underline the importance of Pr upon the temperature and velocity fields and formation of vortices in differential heated cavities.