Preliminary Numerical Study of Natural Convection in a Heterogeneous Horizontal Layer Heated From Below

In the present preliminary study the natural convection in a horizontal fluid layer heated isothermally from below and cooled from above, and having disconnected and conducting square solid blocks uniformly distributed in a square array within it, is numerically investigated. Nondimensional steady balance equations are presented, for a Newtonian fluid, with fluid and solid properties being considered constant and uniform. Among the nondimensional parameters ruling the phenomenon, the layer Rayleigh number is set as 10⁵ and 10⁶, the aspect ratio of the layer varies from 1 to 8, and the fluid Prandtl number and the solid-to-fluid thermal conductivity ratio are set as unity. The focus is on the effect of increasing the number of blocks in the layer, the blocks having progressively smaller size as to maintain the solid volume-fraction inside the layer constant and equal to 26% — this is equivalent to dispersing a fixed amount of solid material in smaller and large number of solid blocks within the layer. In general, the increase in the layer aspect ratio, with all other parameters kept constant, affects the results more as Ra increases — as expected because large Ra yields stronger convection effects. The increase in the number of blocks per unit of square cell in the layer affects the flow as to hinder convection; i.e., the finer the dispersion of solid material within the layer is (as the number of blocks increases) the weaker the resulting flow.