On the effect of conducting lid for natural convection in a horizontal fluid layer

Abstract

In this study, effect of conducting lid attached in the horizontal fluid layer for Rayleigh-Bénard natural convection was discussed. Geometry which was taken into account was horizontal layer of fluid with conducting lid at the bottom. Conducting lid was heated from the bottom wall and the thermal energy was transferred to fluid layer through the solid/fluid interface, and then was cooled down from above. Thermal conductivity ratio varied to investigate the thermal behavior at the solid/fluid interface. Periodic boundary conditions were employed in the horizontal direction to allow lateral freedom for the convection cells. Prior to investigate thermal behavior of fluid layer with conducting lid, pure Rayleigh-Bénard natural convection without conducting body was reproduced. From two-dimensional Rayleigh-Bénard natural convection, an extension of wavelength of circulating roll cell was examined. A two-dimensional solution was obtained using Chebyshev spectral multi-domain methodology for different Rayleigh number at which the thermal behavior was evolved from steady state to chaotic pattern. Three-dimensional pure Rayleigh-Bénard natural convection was calculated from relatively low Rayleigh number such as 4×103 in order to investigate an evolution of thermal plume undergoing a representative zig-zag instability. In order to compare thermal behavior of fluid layer between with- and without conducting lid, effective Rayleigh numbers, Raeff, was introduced and 106 was applied. A solid lid at the bottom affects the flow pattern in that the flow is restricted to increase the dimensionless thermal conductivity. For three-dimensional simulation, periodic boundary condition was also applied along the span-wise direction which was discretized through a Fourier serious expansion with a uniform mesh configuration. For high effective Rayleigh number, thermal flow field was captured by visualizing the three-dimensional vortical structure. The flow behavior at the provided effective Rayleigh number showed a coherent pattern regardless of the magnitude of the thermal conductivity ratio.