The effects of discrete conductive blocks on the natural convection in side-heated open cavities

This study considers the thermo-hydraulic effects of discrete solid blocks on the natural convection inside a fluid filled, horizontally heated side-open cavity. The cavity, having adiabatic horizontal surfaces and an isothermal hot wall, is open to a vast reservoir filled with a quiescent fluid maintained at a temperature lower than the cavity wall temperature. A fixed amount of solid material is progressively distributed inside the cavity as disconnected and conductive square blocks of different numbers and sizes, forming a uniform square lattice. The ensuing natural convection process is modeled analytically considering the fluid and solid constituents inside the cavity separately, and simulated through a validated numerically approach following a parametric analysis done in terms of the Rayleigh number (105 ≤ Ra ≤ 108), the total number of blocks (9 ≤ N ≤ 144) and the solid-to-fluid thermal conductivity ratio (0.1 ≤ κ ≤ 100). The cavity aspect ratio and fluid Prandtl number are kept equal to unity, and the volume-fraction of the solid constituent is equal to 0.36. The present study evaluate the thermo-hydraulic effects of the blocks in the permanent convection process through streamlines, isotherms, hot wall Nusselt mean number and dimensionless mass flow through the fluid reservoir cavity. The blocks affect the convection process in three ways: via channeling, flow interference, and discontinuous fin-like diffusion. The most important effect is interference, which is shown to be analytically predictable. The fin-like effect is the most complex and modulates mostly by the magnitude of κ. Finally, analytical correlations are presented for averaged hot-wall Nusselt number and the nondimensional mass flow rate as useful practical tools in helping the design and analysis of similar configurations.