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Natural convection in a corrugated slot

Published online by Cambridge University Press:  23 February 2017

Arman Abtahi Open the ORCID record for Arman Abtahi [Opens in a new window]  and
J. M. Floryan
Arman Abtahi*
Affiliation:
Department of Mechanical and Materials Engineering, University of Western Ontario, London, Ontario, N6A 5B9, Canada
J. M. Floryan
Affiliation:
Department of Mechanical and Materials Engineering, University of Western Ontario, London, Ontario, N6A 5B9, Canada
*
†Email address for correspondence: sabtahi4@uwo.ca
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Abstract

Analysis of natural convection in a horizontal slot formed by two corrugated isothermal plates has been carried out. The analysis is limited to subcritical Rayleigh numbers $Ra$ where no secondary motion takes place in the absence of corrugations. The corrugations have a sinusoidal form characterized by the wavenumber, the upper and lower amplitudes and the phase difference. The most intense convection occurs for corrugation wavelengths comparable to the slot height; it increases proportionally to $Ra$ and proportionally to the corrugation height. Placement of corrugations on both plates may either significantly increase or decrease the convection depending on the phase difference between the upper and lower corrugations, with the strongest convection found for corrugations being in phase, i.e. a ‘wavy’ slot, and the weakest for corrugations being out of phase, i.e. a ‘converging–diverging’ slot. It is shown that the shear forces would always contribute to the corrugation build-up if erosion was allowed, while the role of pressure forces depends on the location of the corrugations as well as on the corrugation height and wavenumber, and the Rayleigh number. Placing corrugations on both plates results in the formation of a moment which attempts to change the relative position of the plates. There are two limiting positions, i.e. the ‘wavy’ slot and the ‘converging–diverging’ slot, with the latter being unstable. The system would end up in the ‘wavy’ slot configuration if relative movement of the two plates was allowed. The presence of corrugations affects the conductive heat flow and creates a convective heat flow. The conductive heat flow increases with the corrugation height as well as with the corrugation wavenumber; it is largest for short-wavelength corrugations. The convective heat flow is relevant only for wavenumbers of $O(1)$, it increases proportionally to $Ra^{3}$ and proportionally to the second power of the corrugation height. Convection is qualitatively similar for all Prandtl numbers $Pr$, with its intensity increasing for smaller $Pr$ and with the heat transfer augmentation increasing for larger $Pr$.

JFM classification

Convection: Convection
Type
Papers
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Journal of Fluid Mechanics , Volume 815 , 25 March 2017 , pp. 537 - 569
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© 2017 Cambridge University Press 

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