  We perform a two-dimensional numerical study on the thermal effect of porous
media on global heat transport and flow structure in Rayleigh-B\'enard (RB)
convection, focusing on the role of thermal conductivity $\lambda$ of porous
media, which ranges from $0.1$ to $50$ relative to the fluid. The simulation is
carried out in a square RB cell with the Rayleigh number $Ra$ ranging from
$10^7$ to $10^9$ and the Prandtl number $Pr$ fixed at $4.3$. The porosity of
the system is fixed at $\phi=0.812$, with the porous media modeled by a set of
randomly displayed circular obstacles. For a fixed $Ra$, the increase of
conductivity shows a small effect on the total heat transfer, slightly
depressing the Nusselt number. The limited influence comes from the small
number of obstacles contacting with thermal plumes in the system as well as the
counteraction of the increased plume area and the depressed plume strength. The
study shows that the global heat transfer is insensitive to the conduction
effect of separated porous media in the bulk region, which may have
implications for industrial designs.
