Internal heating profiles for which downward conduction is impossible
Arslan A, Fantuzzi G, Craske J, Wynn A (2024)
Publication Type: Journal article
Publication year: 2024
Journal
Book Volume: 993
DOI: 10.1017/jfm.2024.590
Abstract
We consider an internally heated fluid between parallel plates with fixed thermal fluxes. For a large class of heat sources that vary in the direction of gravity, we prove that ⟨δT⟩h≥σR−1/3−μ, where ⟨δT⟩h is the average temperature difference between the bottom and top plates, R is a 'flux' Rayleigh number and the constants σ,μ>0 depend on the geometric properties of the internal heating. This result implies that mean downward conduction (for which ⟨δT⟩h 0) is impossible for a range of Rayleigh numbers smaller than a critical value R0:=(σ/μ)3. The bound demonstrates that R0 depends on the heating distribution and can be made arbitrarily large by concentrating the heating near the bottom plate. However, for any given fixed heating profile of the class we consider, the corresponding value of R0 is always finite. This points to a fundamental difference between internally heated convection and its limiting case of Rayleigh-Bénard convection with fixed-flux boundary conditions, for which ⟨δT⟩h is known to be positive for all R.
Authors with CRIS profile
Involved external institutions
Eidgenössische Technische Hochschule Zürich (ETHZ) / Swiss Federal Institute of Technology in Zurich
Switzerland (CH)
Imperial College London / The Imperial College of Science, Technology and Medicine
United Kingdom (GB)
Switzerland (CH)
Imperial College London / The Imperial College of Science, Technology and Medicine
United Kingdom (GB)
How to cite
APA:
Arslan, A., Fantuzzi, G., Craske, J., & Wynn, A. (2024). Internal heating profiles for which downward conduction is impossible. Journal of Fluid Mechanics, 993. https://doi.org/10.1017/jfm.2024.590
MLA:
Arslan, Ali, et al. "Internal heating profiles for which downward conduction is impossible." Journal of Fluid Mechanics 993 (2024).
BibTeX: Download