  We numerically simulate three-dimensional Rayleigh-B\'enard convection, the
flow in a fluid layer heated from below and cooled from above, with
inhomogeneous temperature boundary conditions to explore two distinct regimes
described in recent literature. We fix the non-dimensional temperature
difference, i.e.~the Rayleigh number to $Ra=10^8$, and vary the Prandtl number
between $1$ and $100$. By introducing stripes of adiabatic boundary conditions
on the top plate, and making the surface of the top-plate only $50\%$
conducting, we modify the heat transfer, average temperature profiles and the
underlying flow properties. We find two regimes: when the pattern wavelength is
small, the flow is barely affected by the stripes. The heat transfer is
reduced, but remains a large fraction of the unmodified case, and the
underlying flow is only slightly modified. When the pattern wavelength is
large, the heat transfer saturates to approximately two-thirds of the value of
the 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 the
distance between two plates, with different quantities transitioning at
slightly different wavelength values. This transition is approximately Prandtl
number independent, even if the statistics in the long-wavelength regime
slightly vary.
