Natural convection in a horizontal layer of fluid with a periodic array of square cylinders in the interior

Abstract

This study of thermal convection uses the following geometry: a horizontal layer of fluid heated from below and cooled from above, with a periodic array of evenly spaced square cylinders occupying the center of the layer (whose aspect ratio is 6). Periodic boundary conditions are employed in the horizontal direction to allow for lateral freedom for the convection cells. A two-dimensional solution for unsteady natural convection is obtained, using an accurate and efficient Chebyshev spectral multi-domain methodology, for different Rayleigh numbers varying over the range of ${10}^3$ to ${10}^6.$ In order to assess the impact of different geometric approximations on the flow structure, dynamics and overall heat transfer, the results for the above case, denoted WC (wide aspect ratio cell with periodic side boundaries and six internal bodies), are compared with those for the cases of UCNS (unit cell with no-slip adiabatic side boundaries with a single internal body), UCPC (unit cell with periodic side boundaries with a single internal body) and pure Rayleigh–Bénard convection. The results for the case of WC with six adiabatic bodies are also compared to those with six neutral isothermal bodies to consider the effects of the thermal boundary condition on time-dependent natural convection in the enclosure.