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Side wall effects in turbulent thermal convection

Profile image of Richard J A M StevensRichard J A M Stevens

2014, J. Fluid Mech. 741, 1 (2014).

https://doi.org/10.1017/JFM.2013.664
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Abstract

We investigate the influence of the temperature boundary conditions at the sidewall on the heat transport in Rayleigh–Bénard (RB) convection using direct numerical simulations. For relatively low Rayleigh numbers Ra the heat transport is higher when the sidewall is isothermal, kept at a temperature Tc C 1=2 (where 1 is the temperature difference between the horizontal plates and Tc the temperature of the cold plate), than when the sidewall is adiabatic. The reason is that in the former case part of the heat current avoids the thermal resistance of the fluid layer by escaping through the sidewall that acts as a short-circuit. For higher Ra the bulk becomes more isothermal and this reduces the heat current through the sidewall. Therefore the heat flux in a cell with an isothermal sidewall converges to the value obtained with an adiabatic sidewall for high enough Ra ('1010). However, when the sidewall temperature deviates from Tc C 1=2 the heat transport at the bottom and top plates is different from the value obtained using an adiabatic sidewall. In this case the difference does not decrease with increasing Ra thus indicating that the ambient temperature of the experimental apparatus can influence the heat transfer. A similar behaviour is observed when only a very small sidewall region close to the horizontal plates is kept isothermal, while the rest of the sidewall is adiabatic. The reason is that in the region closest to the horizontal plates the temperature difference between the fluid and the sidewall is highest. This suggests that one should be careful with the placement of thermal shields outside the fluid sample to minimize spurious heat currents. When the physical sidewall properties (thickness, thermal conductivity and heat capacity) are considered the problem becomes one of conjugate heat transfer and different behaviours are possible depending on the sidewall properties and the temperature boundary condition on the ‘dry’ side. The problem becomes even more complicated when the sidewall is shielded with additional insulation or temperature-controlled surfaces; some particular examples are illustrated and discussed. It has been observed that the sidewall temperature dynamics not only affects the heat transfer but can also trigger a different mean flow state or change the temperature fluctuations in the flow and this could explain some of the observed differences between similar but not fully identical experiments.

Key takeaways
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  1. Isothermal sidewalls enhance heat transport in Rayleigh-Bénard convection at low Rayleigh numbers (Ra < 10^10).
  2. At high Ra (≥ 10^10), heat transport converges to values observed with adiabatic sidewalls.
  3. Variations in sidewall temperature affect heat transfer and flow dynamics significantly, especially near horizontal plates.
  4. Sidewall physical properties complicate heat transfer calculations due to conjugate heat transfer effects.
  5. Insulating layers and thermal shields are crucial for minimizing spurious heat currents in experimental setups.

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    jeffrey cheng

    Journal of Fluid Mechanics

    We experimentally explored the effect of single-sidewall cooling on Rayleigh–Bénard (RB) convection. Canonical RB was also studied to aid insight. The scenarios shared tank dimensions and bottom and top wall temperatures; the single sidewall cooling had the top wall temperature. Turbulence was explored at two canonical Rayleigh numbers, $Ra=1.6\times 10^{10}$ and $Ra=2\times 10^9$ under Prandtl number $Pr=5.4$ . Particle image velocimetry described vertical planes parallel and perpendicular to the sidewall cooling. The two $Ra$ scenarios reveal pronounced changes in the flow structure and large-scale circulation (LSC) due to the sidewall cooling. The density gradient induced by the sidewall cooling led to asymmetric descending and ascending flows and irregular LSC. Flow statistics departed from the canonical case, exhibiting lower buoyancy effects, represented by an effective Rayleigh number with effective height dependent on the distance from the lateral cooling. Velocity spectra s...

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