Turbulent Convection in a Rayleigh-Bénard Cell with Solid Horizontal Plates of Finite Conductivity

Abstract

For the present study turbulent thermal convection in a rectangular Rayleigh-Bénard cell filled with air (Prandtl number Pr=0.7) is equipped with heating and cooling plates with finite thickness, and hence finite conductivity. To obtain reliable results for Rayleigh numbers Ra ≈ 10⁷, Direct Numerical Simulations (DNS) of turbulent Rayleigh-Bénard convection as well as of the heat transport between the plates are performed with a high-order finite volume method. Our results are compared with those obtained by [4, 5] who studied Rayleigh-Bénard convection in the same cell and for the same Pr and Ra. It is found, that the material properties of the horizontal solid plates affect the boundary conditions at the solid-fluid interfaces. In particular, thermal plumes interacting with poorly conducting plates modify the plate temperature such that the local temperature at the solid-fluid interfaces differs up to 10% to the plate temperature of infinite conductivity plates. Further, the lower temperature difference between top and bottom interfaces leeds to lower effective Rayleigh numbers for the poorly conducting plates. The present analysis shows that the temperature fluctuations in the boundary layer and at the interfaces are similar for highly conducting and infinitely thin plates. Further, we conclude that the solid plates have a damping effect on the temperature fluctuations in the boundary layer and the interaction of the large scale flow structures with the fluid boundaries causes temperature fluctuations at the interfaces.