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- W3099684898 abstract "The divergence-free time-independent velocity field has been determined so as to maximise heat transfer between two parallel plates with a constant temperature difference under the constraint of fixed total enstrophy. The present variational problem is the same as that first formulated by Hassanzadeh et al. ( J. Fluid Mech. , vol. 751, 2014, pp. 627–662); however, the search range for optimal states has been extended to a three-dimensional velocity field. A scaling of the Nusselt number $Nu$ with the Péclet number $Pe$ (i.e., the square root of the non-dimensionalised enstrophy with thermal diffusion time scale), $Nusim Pe^{2/3}$ , has been found in the three-dimensional optimal states, corresponding to the asymptotic scaling with the Rayleigh number $Ra$ , $Nusim Ra^{1/2}$ , expected to appear in an ultimate state, and thus to the Taylor energy dissipation law in high-Reynolds-number turbulence. At $Pesim 10^{0}$ , a two-dimensional array of large-scale convection rolls provides maximal heat transfer. A three-dimensional optimal solution emerges from bifurcation on the two-dimensional solution branch at $Pesim 10^{1}$ , and the three-dimensional solution branch has been tracked up to $Pesim 10^{4}$ (corresponding to $Raapprox 2.7times 10^{6}$ ). At $Pegtrsim 10^{3}$ , the optimised velocity fields consist of convection cells with hierarchical self-similar vortical structures, and the temperature fields exhibit a logarithmic-like mean profile near the walls." @default.
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- W3099684898 date "2018-07-31" @default.
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- W3099684898 title "Maximal heat transfer between two parallel plates" @default.
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- W3099684898 doi "https://doi.org/10.1017/jfm.2018.557" @default.
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