Aspect ratio effect on the prediction of boundary layer interference in steady natural convection inside heterogeneous enclosures

Flow interference, caused by solid obstacles placed within an enclosed fluid undergoing natural convection, can have a tremendous impact on the flow pattern and heat transfer process. Disconnected, conductive, solid square blocks uniformly distributed inside a rectangular, horizontally heated enclosure are used as a platform to investigate this flow interference, which can be caused: (1) adjacent to the enclosure walls – when the (hot or cold) vertical fluid stream boundary layers grow enough to reach the solid blocks; and, (2) along the enclosure horizontal surfaces – when the top (or bottom) horizontal fluid streams get impeded by the adjacent blocks. Analytical equations, based on scale analysis, are derived for predicting the minimum number of blocks beyond which vertical and horizontal interferences take place, as function of the Rayleigh number (Ra), fluid volume fraction (porosity ϕ), and the enclosure length-to-height aspect ratio (A). The analytical predictions are validated against numerical simulation results, covering the ranges 105 ⩽ Ra ⩽ 108, 0.36 ⩽ ϕ ⩽ 0.84, and 0.25 ⩽ A ⩽ 4. The predictions prove the horizontal interference predominates in relation to the vertical interference in shallow (A > 1) enclosures.