Bounds on heat transfer by incompressible flows between balanced sources and sinks

Song B, Fantuzzi G, Tobasco I (2023)

Publication Type: Journal article, Original article

Publication year: 2023

Journal

Physica D-Nonlinear Phenomena Elsevier

Book Volume: 444

Article Number: 133591

DOI: 10.1016/j.physd.2022.133591

Open Access Link: https://arxiv.org/abs/2208.04421

Abstract

Internally heated convection involves the transfer of heat by fluid motion between a distribution of sources and sinks. Focusing on the balanced case where the total heat added by the sources matches the heat taken away by the sinks, we obtain a priori bounds on the minimum mean thermal dissipation 〈|∇T|2〉 as a measure of the inefficiency of transport. In the advective limit, our bounds scale with the inverse mean kinetic energy of the flow. The constant in this scaling law depends on the source–sink distribution, as we explain both in a pair of examples involving oscillatory or concentrated heating and cooling, and via a general asymptotic variational principle for optimizing transport. Key to our analysis is the solution of a pure advection equation, which we do to find examples of extreme heat transfer by cellular and ‘pinching’ flows. When the flow obeys a momentum equation, our bound is re-expressed in terms of a flux-based Rayleigh number R yielding 〈|∇T|2〉≥CR−α. The power α is 0,2/3 or 1 depending on the arrangement of the sources and sinks relative to gravity.

Authors with CRIS profile

Giovanni Fantuzzi

Involved external institutions

University of Michigan–Ann Arbor US United States (USA) (US) University of Illinois at Chicago US United States (USA) (US) Imperial College London / The Imperial College of Science, Technology and Medicine GB United Kingdom (GB)

How to cite

APA:

Song, B., Fantuzzi, G., & Tobasco, I. (2023). Bounds on heat transfer by incompressible flows between balanced sources and sinks. Physica D-Nonlinear Phenomena, 444. https://dx.doi.org/10.1016/j.physd.2022.133591

MLA:

Song, Binglin, Giovanni Fantuzzi, and Ian Tobasco. "Bounds on heat transfer by incompressible flows between balanced sources and sinks." Physica D-Nonlinear Phenomena 444 (2023).

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