Influence of Rayleigh number and solid volume fraction in particle-dispersed natural convection

To study the heat transfer in a natural convection under dense particulate condition with finite-size spherical particles of uniform diameter, a direct numerical simulation is conducted. For calculating the momentum-interaction between the particle and fluid, our original immersed solid method is applied. The heat transfer in the particle-dispersed flow is treated in Eulerian way with the interfacial flux decomposition method. The results shows that, with fixing the thermal conductivity ratio (of the solid to the fluid) to be 100, the temporal- and horizontal-average Nusselt number 〈Nu〉t increases monotonically with solid volume fraction (vf) at Rayleigh number Ra = 104, while 〈Nu〉t at Ra = 105 exhibits a local maximum at around vf = 40%, although 〈Nu〉t at Ra = 105 is always larger than that at Ra = 104. The heat flux in the particulate system is decomposed into the contributions by convection and conduction through the particles, fluid and interface, and the result shows that the conduction through the interface is the dominant factor to the vertical heat flux in the media. Through visualization of the heat flux through the particle surface, the importance of directly resolving the local heat conduction within the individual particle and through the interface is highlighted.