Convection driven by internal heating

Two-dimensional direct numerical simulations are conducted for convection sustained by uniform internal heating in a horizontal fluid layer. Top and bottom boundary temperatures are fixed and equal. Prandtl numbers range from 0.01 to 100, and Rayleigh numbers (R  ) are up to 5⋅1055⋅105 times the critical R at the onset of convection. The asymmetry between upward and downward heat fluxes is non-monotonic in R. In a broad high-R   regime, dimensionless mean temperature scales as R−1/5R−1/5. We discuss the scaling of mean temperature and heat-flux-asymmetry, which we argue are better diagnostic quantities than the conventionally used top and bottom Nusselt numbers.

► Convection driven by internal heating in a 2D plane layer is studied by direct numerical simulation.
► We simulate Rayleigh numbers (R  ) up to 5⋅1055⋅105 times critical and Prandtl numbers from 0.01 to 100.
► The fraction of produced heat that flows out the top boundary is non-monotonic in R  .
► The dimensionless mean temperature scales as R−1/5R−1/5 in a broad high-R   regime.
► Scaling arguments for mean temperature predict R−1/5R−1/5 in certain parameter regimes.