Comparative Study of Hybrid Lattice Boltzmann and Vorticity-vector Potential Modelling of 2D and 3D Natural Convection Combined with Rosseland Radiation

This study deals with numerical simulation of two-dimensional and three-dimensional natural convection in a closed differentially heated cube filled with radiatively participating medium. To examine fluid flow and heat transfer, hybrid mesomacroscopic model was developed. Rosseland radiation model was used to determine radiative heat flux. The effect of the Rayleigh number and radiation parameter on temperature, flow pattern and mean convective Nusselt numbers was discussed in detail. It was found that thermal radiation reduced the convective heat transfer rate by around 50% when radiation parameter is increased from 0 to 4. One-cellular quasi two-dimensional flow pattern was formed when taking into account Rosseland radiation. An oblique thermal stratification was formed as the radiation was enhanced. 2D and 3D models under consideration reproduced the same values of temperatures whereas a discrepancy was revealed in velocity components. Convective mean Nusselt numbers were in a very good agreement for both pure finite difference and hybrid lattice Boltzmann simulations with an error less than 5%. Volumetric radiation lowers the time needed to reach steady-state solution by around 60% when Rayleigh number is equal to 105. Numerical performance of hybrid lattice Boltzmann method was more than 7 times higher than conventional voriticity-vector potential formulation.