Differentiated heated lid driven cavity interacting with tube: A lattice Boltzmann study

The multiple-relaxation time lattice-Boltzmann method is implemented to investigate combined natural and forced convection occurring in a 2-D square cavity. The top wall slides to the right at constant speed, while the other three remain stationary. The solution is performed for a left vertical wall at a constant temperature, which is higher than of the right wall. This yields a "co-operating" case, in which dynamic and buoyancy forces are added together. The enclosure is filled with air and contains a heat conducting circular cylinder, which is placed at various positions. The double distribution model used in lattice-Boltzmann methods has been adopted to simulate the hydrodynamic and thermal fields, with the D₂Q₉ and D₂Q₅ lattices selected to perform the corresponding computations. Simulations have been conducted over a wide range of Rayleigh and Reynolds numbers, and the features of dynamic and thermal fields are presented for the spectra of this mixed convection phenomenon. The flow and heat transfer characteristics of the cylinder position are described and analyzed in terms of the average Nusselt number. The computed results show the influence of the cylinder on the corresponding heat transfer in the enclosure. It has been found that the power (i.e. shear stress) needed to lid the upper surface will depend on the governing parameters.