Imperial College London
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DrAndrewWynn

Faculty of Engineering, Department of Aeronautics

Reader in Control and Optimization
 
 
 
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Contact

 

+44 (0)20 7594 5047a.wynn Website

 
 
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Location

 

340City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Arslan:2021:10.1017/jfm.2021.360,
author = {Arslan, A and Fantuzzi, G and Craske, J and Wynn, A},
doi = {10.1017/jfm.2021.360},
journal = {Journal of Fluid Mechanics},
pages = {1--34},
title = {Bounds on heat transport for convection driven by internal heating},
url = {http://dx.doi.org/10.1017/jfm.2021.360},
volume = {919},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The mean vertical heat transport wT in convection 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 quadratic auxiliary functions. 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 wT≤1/2 can only be improved up to finite R. Indeed, we demonstrate analytically that wT≤2−21/5R1/5 and therefore prove that wT<1/2 for R<65536. However, if the minimum principle for temperature is invoked, which asserts that internal temperature is at least as large as the temperature of the isothermal boundaries, then numerically optimised bounds are strictly smaller than 1/2 until at least R=3.4×105. While the computational results suggest that the best bound on wT approaches 1/2 asymptotically from below as R→∞, we prove that typical analytical constructions cannot be used to prove this conjecture.
AU  - Arslan,A
AU  - Fantuzzi,G
AU  - Craske,J
AU  - Wynn,A
DO  - 10.1017/jfm.2021.360
EP  - 34
PY  - 2021///
SN  - 0022-1120
SP  - 1
TI  - Bounds on heat transport for convection driven by internal heating
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2021.360
UR  - https://arxiv.org/abs/2102.06458
UR  - https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/bounds-on-heat-transport-for-convection-driven-by-internal-heating/9EF4A1F987922ED674B8B1EF23F79C10
UR  - http://hdl.handle.net/10044/1/89314
VL  - 919
ER  -
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