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Computational approaches to aspect-ratio-dependent upper bounds and heat flux in porous medium convection |
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| Authors: | Baole Wen Gregory P Chini Navid Dianati Charles R Doering |
| Institution: | 1. Program in Integrated Applied Mathematics, University of New Hampshire, Durham, NH 03824, USA;2. Center for Fluid Physics, University of New Hampshire, Durham, NH 03824, USA;3. Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA;4. Department of Physics, University of Michigan, Ann Arbor, MI 48109-1043, USA;5. Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA;6. Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109-1043, USA |
| Abstract: | Direct numerical simulation (DNS) has shown that Rayleigh–Bénard convection in a fluid-saturated porous medium self-organizes into narrowly spaced plumes at (ostensibly) asymptotically high values of the Rayleigh number Ra. In this Letter a combination of DNS and upper bound theory is used to investigate the dependence of the Nusselt number Nu on the domain aspect ratio L at large Ra . A novel algorithm is introduced to solve the optimization problems arising from the upper bound analysis, allowing for the best available bounds to be extended up to Ra≈2.65×104. The dependence of the bounds on L(Ra) is explored and a “minimal flow unit” is identified. |
| Keywords: | Porous medium convection Heat flux Upper bound theory Euler&ndash Lagrange equations Low-dimensional modeling |
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