  We study turbulent natural convection in enclosures with conjugate heat
transfer. The simplest way to increase the heat transfer in this flow is
through rough surfaces. In numerical simulations often the constant temperature
is assigned at the walls in contact with the fluid, which is unrealistic in
laboratory experiments. The DNS (Direct Numerical Simulation), to be of help to
experimentalists, should consider the heat conduction in the solid walls
together with the turbulent flow between the hot and the cold walls. Here the
cold wall, $0.5h$ thick (where $h$ is the channel half-height) is smooth, and
the hot wall has two- and three-dimensional elements of thickness $0.2h$ above
a solid layer $0.3h$ thick. The independence of the results on the box size has
been verified. A bi-periodic domain $4h$ wide allows to have a sufficient
resolution with a limited number of grid points. It has been found that, among
the different kind of surfaces at a Rayleigh number $Ra \approx 2 \cdot 10^6$,
the one with staggered wedges has the highest heat transfer. A large number of
simulations varying the $Ra$ from $10^3$ to $10^7$ were performed to find the
different ranges of the Nusselt number ($Nu$) relationship as a function of
$Ra$. Flow visualizations allow to explain the differences in the $Nu(Ra)$
relationship. Two values of the thermal conductivity were chosen, one
corresponding to copper and the other ten times higher. It has been found that
the Nusselt number behaves as $Nu=\alpha Ra^\gamma$, with $\alpha$ and $\gamma$
independent on the solid conductivity, and dependent on the roughness shape.
