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Effect of inclination angle on heat transport properties in two-dimensional Rayleigh–Bénard convection with smooth and rough boundaries

Published online by Cambridge University Press:  18 October 2022

Krishan Chand ,
Mukesh Sharma  and
Arnab Kr. De Open the ORCID record for Arnab Kr. De [Opens in a new window]
Krishan Chand
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India
Mukesh Sharma
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India
Arnab Kr. De*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India
*
†Email address for correspondence: [email protected]
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Abstract

Using direct numerical simulations, two-dimensional tilted Rayleigh–Bénard convection (RBC) is studied in both smooth and roughness-facilitated convection cells of double aspect ratio ($\varGamma =2$) for air as a working fluid. We investigate the effect of inclination angle ($0^{\circ } \leq \phi \leq 90^{\circ }$) on heat flux ($Nu$), Reynolds number ($Re$) and flow structures. In a Rayleigh number range $10^{6}\leq Ra\leq 10^{9}$, we address the $Ra$ dependence of $Nu(\phi )$ trend. In the smooth case, while greater tilt results in highest heat flux below $Ra=10^{8}$, $Nu$ drops with $\phi$ monotonically above it (RBC transports heat most efficiently), which explains the different $Nu(\phi )$ trend observed in the previous studies due to $Ra$ dependence (Guo et al., J. Fluid Mech., vol. 762, 2015, pp. 273–287; Shishkina & Horn, J. Fluid Mech., vol. 790, 2016, R3; Khalilov et al., Phys. Rev. Fluids, vol. 3, 2018, 043503). For the smooth case, we identify the control parameters ($\phi =75^{\circ }$ and $Ra=10^{7}$) that yield maximum heat flux (an increment of $18\,\%$ with respect to the level case). On the other hand, among the three roughness set-ups used in the present study, the tallest roughness configuration yields the maximum increment in heat flux ($25\,\%$) in vertical convection ($\phi =90^{\circ }$) at $Ra=10^{6}$. With increase in $Ra$, $Re$ changes with $\phi$ marginally in the smooth case, whereas it shows notable changes in its roughness counterpart. We find that the weakening of thermal stratification is related directly to the height of roughness peaks. While $Ra$ delays the onset of thermal stratification (in terms of inclination angle) in the smooth case, an increase in roughness height plays the same role in roughness-facilitated convection cells.

JFM classification

Convection: Plumes/thermals Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 950 , 10 November 2022 , A16
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© The Author(s), 2022. Published by Cambridge University Press

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