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.2021.527,
author = {Arslan, A and Fantuzzi, G and Craske, J and Wynn, A},
doi = {10.1017/jfm.2021.527},
journal = {Journal of Fluid Mechanics},
pages = {R1--R1},
title = {Bounds on internally heated convection with fixed boundary heat flux},
url = {http://dx.doi.org/10.1017/jfm.2021.527},
volume = {992},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We prove a new rigorous bound for the mean convective heat transport wT, where w and T are the non-dimensional vertical velocity and temperature, in internally heated convection between an insulating lower boundary and an upper boundary with a fixed heat flux. The quantity wT is equal to half the ratio of convective to conductive vertical heat transport, and also to 12 plus the mean temperature difference between the top and bottom boundaries. An analytical application of the background method based on the construction of a quadratic auxiliary function yields wT≤12(12+13√)−1.6552R−(1/3) uniformly in the Prandtl number, where R is the non-dimensional control parameter measuring the strength of the internal heating. Numerical optimisation of the auxiliary function suggests that the asymptotic value of this bound and the −1/3 exponent are optimal within our bounding framework. This new result halves the best existing (uniform in R) bound (Goluskin, Internally Heated Convection and Rayleigh–Bénard Convection, Springer, 2016, table 1.2), and its dependence on R is consistent with previous conjectures and heuristic scaling arguments. Contrary to physical intuition, however, it does not rule out a mean heat transport larger than 12 at high R, which corresponds to the top boundary being hotter than the bottom one on average.
AU  - Arslan,A
AU  - Fantuzzi,G
AU  - Craske,J
AU  - Wynn,A
DO  - 10.1017/jfm.2021.527
EP  - 1
PY  - 2021///
SN  - 0022-1120
SP  - 1
TI  - Bounds on internally heated convection with fixed boundary heat flux
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2021.527
UR  - https://arxiv.org/abs/2103.16498
UR  - https://doi.org/10.1017/jfm.2021.527
UR  - http://hdl.handle.net/10044/1/90371
VL  - 992
ER  -
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