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We report on a numerical study of turbulent convection driven by acombination of internal heat sources and sinks. Motivated by a recentexperimental realisation (Lepot et al. 2018), we focus on the situation wherethe cooling is uniform, while the internal heating is localised near the bottomboundary, over approximately one tenth of the domain height. We obtain scalinglaws $Nu \sim Ra^\gamma Pr^\chi$ for the heat transfer as measured by theNusselt number $Nu$ expressed as a function of the Rayleigh number $Ra$ and thePrandtl number $Pr$. After confirming the experimental value $\gamma\approx1/2$ for the dependence on $Ra$, we identify several regimes of dependence on$Pr$. For a stress-free bottom surface and within a range as broad as $Pr \in[0.003, 10]$, we observe the exponent $\chi\approx 1/2$, in agreement withSpiegel's mixing length theory. For a no-slip bottom surface we observe atransition from $\chi\approx 1/2$ for $Pr \leq 0.04$ to $\chi\approx 1/6$ for$Pr \geq 0.04$, in agreement with scaling predictions by Bouillaut et al. Thelatter scaling regime stems from heat accumulation in the stagnant layeradjacent to a no-slip bottom boundary, which we characterise by comparing thelocal contributions of diffusive and convective thermal fluxes.

On the role of the Prandtl number in convection driven by heat sources and sinks