English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Thermal convection driven by internal heat sources and sinks was recentlyshown experimentally to exhibit the mixing-length, or "ultimate",scaling-regime: the Nusselt number $Nu$ (dimensionless heat flux) increases asthe square-root of the Rayleigh-number $Ra$ (dimensionless internal temperaturedifference). While for standard Rayleigh-B\'enard convection this scalingregime was proven to be a rigorous upper bound on the Nusselt number, we showthat this is not so for convection driven by internal sources and sinks. Towit, we introduce an asymptotic expansion to derive steady nonlinear solutionsin the limit of large $Ra_Q$, the Rayleigh-number based on the strength of theheat source. We illustrate this procedure for a simple sinusoidal heat sourceand show that it achieves heat transport enhancement beyond the mixing-lengthscaling regime: $Nu$ increases linearly with $Ra$ over this branch ofsolutions. Using rigorous upper bound theory, we prove that the scaling regime$Nu \sim Ra$ of the asymptotic solution corresponds to a maximization of theheat flux subject to simple dynamical constraints, up to a dimensionlessprefactor. Not only do 2D numerical simulations confirm the analytical solutionfor the sinusoidal source, but, more surprisingly, they indicate that it isstable and indeed achieved by the system up to the highest $Ra_Q$ investigatednumerically, with a heat transport efficiency orders of magnitude higher thanthe standard mixing-length estimate.

Convection driven by internal heat sources and sinks: heat transport beyond the mixing-length or "ultimate" scaling regime