Direct numerical simulation of turbulent Rayleigh–Bénard convection with imperfectly conducting plates

Turbulent Rayleigh–Bénard (RB) convection is a common phenomenon in nature and is also frequently encountered in a wide range of industrial processes. However, most studies on turbulent RB convection are based on ideal isothermal boundaries, leaving the effects of finite plate conductivity on turbulent flow and heat transport insufficiently understood. In this work, the lattice Boltzmann method is employed to study turbulent RB convection in a square cavity with finite conductivity of the top and bottom walls. The effects of wall thickness d and the solid-to-fluid thermal conductivity ratio λ r are investigated in detail for two representative Prandtl numbers, P r = 0.7 and 5.3, with the Rayleigh number mainly fixed at R a = 1 0 8 . The results indicate that increasing λ r enlarges the effective temperature difference across the fluid layer and leads to a more uniform temperature distribution at the fluid–solid interface, thereby enhancing both flow intensity and heat transfer, and this effect is further strengthened by reducing d under low λ r conditions. Meanwhile, compared with cases under the ideal isothermal boundary condition, the power-law scaling exponents of global quantities with respect to the Rayleigh number are reduced for finite thermal conductivity walls. In addition, local statistical analyses reveal that, as λ r increases, the extended tail of the normalized temperature probability density function in the near-wall region gradually shortens, while the small-scale intermittency of the thermal energy dissipation rate intensifies. Boundary layer analyses further indicate that the spatial non-uniformity of the local thermal boundary layer intensifies with increasing λ r , whereas the local velocity boundary layer is insensitive to this parameter. Overall, this study clarifies the effects of finite thermal conductivity walls on flow organization, the statistics of temperature and thermal energy dissipation rate, and boundary layer structures in RB convection.