Vortical flow patterns by the cooperative effect of convective and conductive heat transfers in particle-dispersed natural convection

Abstract

Cooperative effect of the conductive and convective heat fluxes on the development of vortical structures is studied in a particle-dispersed natural convection. A numerical approach is proposed that visualizes the heat transfer paths through the fluid and finite-volume particles (i.e., non-point particles) to show the spatial extension of the heat fluxes and its influence on the flow field. The approach is applied to a weakly-convective dense particulate system under the Rayleigh number 105 containing more than 4000 particles (solid volume fraction 42.8%) of various conductivities. With highly-conductive particles (in comparison to the ambient fluid), local downward convection of a large-scale vortical flow strengthens the conductive heat flux near the bottom hot wall in the counter-convective direction by the increase of the vertical temperature gradient, and the observation of the spatial extension of the heat flux lines indicates that the increase of the solid volume fraction near the hot wall further strengthens the conductive heat flux. The paired upward convection causes strengthened conductive heat flux near the top cold wall by the same increase mechanism. The above interplay of the local heat fluxes in the dense solid-dispersed media are found to influence on the formation and transition of the large-scale vortical structures through the distribution of the moment of buoyancy in a horizontal plane. An analytical model for a low-dimensional vortex system shows that buoyancy gradient and vorticity diffusion could determine the time-development of the large-scale vortical structure.