Bounds on heat transport for convection driven by internal heating
Arslan A, Fantuzzi G, Craske J, Wynn A (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 919
Article Number: A15
DOI: 10.1017/jfm.2021.360
Abstract
The mean vertical convective heat transport between isothermal plates driven by uniform internal heating is investigated by means of rigorous bounds. These are obtained as a function of the Rayleigh number R by constructing feasible solutions to a convex variational problem, derived using a formulation of the classical background method in terms of a quadratic auxiliary function. When the fluid's temperature relative to the boundaries is allowed to be positive or negative, numerical solution of the variational problem shows that best previous bound (Goluskin & Spiegel, Phys. Lett. A, vol. 377, issue 1-2, 2012, pp. 83-92) can only be improved up to finite R. Indeed, we demonstrate analytically that and therefore prove that
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APA:
Arslan, A., Fantuzzi, G., Craske, J., & Wynn, A. (2021). Bounds on heat transport for convection driven by internal heating. Journal of Fluid Mechanics, 919. https://dx.doi.org/10.1017/jfm.2021.360
MLA:
Arslan, Ali, et al. "Bounds on heat transport for convection driven by internal heating." Journal of Fluid Mechanics 919 (2021).
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