Simulation to study the effect of natural convection in the voids of a 2D granular packed bed of cylindrical particles on effective thermal conductivity

Natural convection can occur in the voids of a granular material due to temperature difference between neighboring particles. Such an effect of natural convection in voids of a granular material can have a significant impact on effective thermal conductivity of that granular material. In the present study, effective thermal conductivity of a packed bed of solid cylindrical steel rods filled with air and water in the voids is analyzed by simulation. Effective thermal conductivity is obtained for the two systems from a response to step change in wall temperature. In order to quantify the effect of natural convection, a two dimensional array of squarely packed cylinders is simulated with and without the natural convection effect. The simulation is carried out using COMSOL Multiphysics. The temperature versus time data for various particle sizes of 4 mm, 8 mm and 12 mm made of steel are obtained. The maximum velocity magnitude generated in the voids is recorded as a function of time as a measure of natural convection. The effective thermal conductivity is determined for all the conditions using curve fitting between simulation data and analytical function. The effective thermal conductivity calculated from simulation data for two conditions namely with and without natural convection are compared with the literature correlations for both the systems. Role of Grashof number on the intensity of natural convection in voids is discussed. Aspect ratio effect of the packed bed and mesh size effect are also studied.