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We numerically simulate three-dimensional Rayleigh-B\'enard convection, theflow in a fluid layer heated from below and cooled from above, withinhomogeneous temperature boundary conditions to explore two distinct regimesdescribed in recent literature. We fix the non-dimensional temperaturedifference, i.e.~the Rayleigh number to $Ra=10^8$, and vary the Prandtl numberbetween $1$ and $100$. By introducing stripes of adiabatic boundary conditionson the top plate, and making the surface of the top-plate only $50\%$conducting, we modify the heat transfer, average temperature profiles and theunderlying flow properties. We find two regimes: when the pattern wavelength issmall, the flow is barely affected by the stripes. The heat transfer isreduced, but remains a large fraction of the unmodified case, and theunderlying flow is only slightly modified. When the pattern wavelength islarge, the heat transfer saturates to approximately two-thirds of the value ofthe unmodified problem, the temperature in the bulk increases substantially,and velocity fluctuations in the directions normal to the stripes are enhanced.The transition between both regimes happens at pattern wavelength around thedistance between two plates, with different quantities transitioning atslightly different wavelength values. This transition is approximately Prandtlnumber independent, even if the statistics in the long-wavelength regimeslightly vary.

Regime crossover in Rayleigh-Benard convection with mixed boundary conditions