Hybrid Lattice Boltzmann Method for 3D Natural Convection Combined with Volumetric Radiation

A hybrid lattice Boltzmann model was developed to examine the effect of volumetric thermal radiation on three-dimensional natural convection. Within this model, a fluid flow was computed by the lattice Boltzmann method in terms of the D3Q19 scheme and Bhatnagar–Gross–Krook approximation. On the other hand, a finite-difference technique was applied to solve the energy equation. To determine the radiative heat flux, the Rosseland approximation was used. The effect of the Rayleigh number Ra and the radiation parameter Rd on the temperature, flow behavior, and the mean Nusselt number was studied in the ranges 10⁴ ≤ Ra ≤ 10⁶ and 0 < Rd ≤ 5. It was found that thermal radiation weakened natural convective mechanism of heat transfer. The mean convective Nusselt number increased with the Rayleigh number and decreased with increase in the radiation parameter.