  A series of direct numerical simulations of Rayleigh-B\'enard convection, the
flow in a fluid layer heated from below and cooled from above, were conducted
to investigate the effect of mixed insulating and conducting boundary
conditions on convective flows. Rayleigh numbers between $\text{Ra}=10^7$ and
$\text{Ra}=10^9$ were considered, for Prandtl numbers $\text{Pr}=1$ and
$\text{Pr}=10$. The bottom plate was divided into patterns of conducting and
insulating stripes. The size ratio between these stripes was fixed to unity and
the total number of stripes was varied. Global quantities such as the heat
transport and average bulk temperature and local quantities such as the
temperature just below the insulating boundary wall were investigated. For the
case with the top boundary divided into two halves, one conducting and one
insulating, the heat transfer was found to be approximately two thirds of the
fully conducting case. Increasing the pattern frequency increased the heat
transfer which asymptotically approached the fully conducting case, even if
only half of the surface is conducting. Fourier analysis of the temperature
field revealed that the imprinted pattern of the plates is diffused in the
thermal boundary layers, and cannot be detected in the bulk. With
conducting-insulating patterns on both plates, the trends previously described
were similar, however, the half-and-half division led to a heat transfer of
about a half of the fully conducting case instead of two-thirds. The effect of
the ratio of conducting and insulating areas was also analyzed, and it was
found that even for systems with a top plate with only $25\%$ conducting
surface, heat-transport of $60\%$ of the fully conducting case can be seen.
Changing the 1D stripe pattern to 2D checkerboard tessellations does not result
in a significantly different response of the system.
