Heat transfer scaling in volumetrically heated and cooled convection

Adequately modelling of the amount of heat transferred in a thermally driven flow is crucial for understanding many processes in Nature and technology. For this purpose, many studies of thermal convection have been performed which historically focus on systems where heat is injected through the boundaries. However, systems where the heat is added partially or fully into the volume are common and the difference between both configurations has not been studied systematically. We set out to do so by conducting a series of simulations to determine how the heat transfer behaves when a system is volumetrically heated, while being cooled through a combination of boundary and volume. If the cooling happens exclusively through the boundary, we find that homogeneously heated flows are driven by falling plumes near the top plate, and that inhomogeneously heating from the bottom can trigger a more symmetric distribution that also includes upwards plumes. However, the effective heat transfer laws remain largely unaffected despite the increasing the level of turbulence in the system. By removing heat through volumetric sinks we can increase the effective heat transfer rate. When the heat is fully removed this way such there is no boundary heat transfer we achieve viscosity-independent scaling laws for the total heat transfer.