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Experimental Methodology for Estimation of Local Heat Fluxes and Burning Rates in Steady Laminar Boundary Layer Diffusion Flames
Published on: June 1, 2016
Bounds on heat flux for Rayleigh-Bénard convection between Navier-slip fixed-temperature boundaries
Theodore D Drivas1, Huy Q Nguyen2, Camilla Nobili3
1Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USA.
Abstract:
We study two-dimensional Rayleigh-Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number [Formula: see text], this estimate interpolates between the Whitehead-Doering bound by [Formula: see text] for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501) and the classical Doering-Constantin [Formula: see text] bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 5957-5981). This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.
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