Natural convection with mixed insulating and conducting boundary conditions: low and high Rayleigh numbers regimes

Abstract

We investigate the stability and dynamics of natural convection in two dimensions, subject to inhomogeneous boundary conditions. In particular, we consider a Rayleigh-Bènard (RB) cell, where the horizontal top boundary contains a periodic sequence of alternating thermal insulating and conducting patches, and we study the effects of the heterogeneous pattern on the global heat exchange, both at low and high Rayleigh numbers. At low Rayleigh numbers, we determine numerically the transition from a regime characterized by the presence of small convective cells localized at the inhomogeneous boundary to the onset of bulk convective rolls spanning the entire domain. Such a transition is also controlled analytically in the limit when the boundary pattern length is small compared with the cell vertical size. At higher Rayleigh number, we use numerical simulations based on a lattice Boltzmann method to assess the impact of boundary inhomogeneities on the fully turbulent regime up to $Ra\sim 10^{10}$.

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Cited by in corpus (7)

• Mixed insulating and conducting thermal boundary conditions in Rayleigh-Bénard convection
• Tailoring boundary geometry to optimize heat transport in turbulent convection
• Thermal convection with mixed thermal boundary conditions: Effects of insulating lids at the top
• Lattice Boltzmann Simulations of Droplet formation in confined Channels with Thermocapillary flows
• TLBfind: a Thermal Lattice Boltzmann code for concentrated emulsions with FINite-size Droplets
• Controlling secondary flows in Taylor-Couette flow using stress-free boundary conditions
• Regime crossover in Rayleigh-Benard convection with mixed boundary conditions