Convective heat transport in a fluid layer of infinite Prandtl number: upper bounds for the case of rigid lower boundary and stress-free upper boundary
نویسنده
چکیده
We present the theory of the multi-α-solutions of the variational problem for the upper bounds on the convective heat transport in a heated from below horizontal fluid layer with rigid lower boundary and stress-free upper boundary. A sequence of upper bounds on the convective heat transport is obtained. The highest bound Nu = 1+(1/6)R is between the bounds Nu = 1+0.152R for the case of a fluid layer with two rigid boundaries andNu = 1+0.3254R1/3 for the case of a fluid layer with two stress-free boundaries. As an additional result of the presented theory we obtain small corrections of the boundary layer thicknesses of the optimum fields for the case of fluid layer with two rigid boundaries. These corrections lead to sistematically lower upper bounds on the convective heat transport in comparison to the bounds obtained in [5]. PACS numbers: 47.27.Te; 47.27.Cn
منابع مشابه
Upper bound on the heat transport in a layer of fluid of infinite prandtl number, rigid lower boundary, and stress-free upper boundary
We obtain an upper bound on the convective heat transport in a heated from below horizontal fluid layer of infinite Prandtl number with rigid lower boundary and stress-free upper boundary. Because of the asymmetric boundary conditions the solutions of the Euler-Lagrange equations of the corresponding variational problem are also asymmetric with different thicknesses of the boundary layers on th...
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