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This study examines how the Prandtl number (a fluid property ratio) affects convection driven by internal heating in both rotating and non-rotating systems through computer simulations. The research finds that while global mean temperature is relatively insensitive to Prandtl number variations, the heat transport behavior and stability of lower fluid layers depend strongly on this parameter, with rotation enhancing heat flux across all Prandtl numbers but only improving cooling efficiency for fluids with Prandtl number equal to or greater than 1. The work reveals fundamental differences between internally heated convection and classical boundary-heated convection systems.
Why it matters
These findings are essential for accurately modeling heat transport in planetary cores and stellar interiors where internal heating dominates, potentially improving predictions of magnetic field generation and thermal evolution in these systems.
arXiv:2602.21860v3 Announce Type: replace
Abstract: We investigate the influence of the Prandtl number ($Pr$) on penetrative internally heated convection (IHC) in both non-rotating and rotating regimes using three-dimensional direct numerical simulations. By varying $Pr$ between 0.1 and 100, we show that the global mean temperature $langle overline{T} rangle$ is not very sensitive to $Pr$, and is primarily controlled by the dynamics of the unstably stratified top boundary layer. In contrast, the Prandtl number dictates the behavior of the lower, stably stratified region and affects the vertical convective heat flux $langle overline{wT} rangle$. In the non-rotating case, low $Pr$ fluids exhibit a “symmetry recovery” where turbulent stirring agitates the stable layer, whereas high $Pr$ fluids transition toward a “dead zone” of suppressed fluctuations. Under rotation, we find that $langle overline{wT} rangle$ is enhanced across all Prandtl numbers, though global cooling efficiency, measured by the reduction in $langle overline{T} rangle$, is only improved for $Prge1$ due to the emergence of Ekman pumping. These results demonstrate that while IHC shares some scaling similarities with Rayleigh-B’enard convection at the top boundary, the internal stratification creates a unique sensitivity to $Pr$ that is critical for understanding heat transport in planetary and stellar interiors.
Source: Prandtl number dependence of rotating internally heated convection