Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Benard convection in glycerol

TL;DR

This study numerically investigates Non-Oberbeck-Boussinesq effects in glycerol-driven Rayleigh-Benard convection, revealing dominant boundary layer thickness effects over center temperature shifts in Nusselt number deviations at high NOBness.

Contribution

It provides the first detailed analysis of NOB effects in glycerol convection, highlighting the dominant physical mechanisms influencing heat transfer deviations.

Findings

Center temperature $T_c$ exceeds mean temperature $T_m$ by over 5 K at high NOBness.

In glycerol, boundary layer thickness effects dominate Nusselt number deviations.

NOB effects in glycerol differ from water, with boundary layer effects being more significant.

Abstract

We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change in the viscosity with temperature. The results are presented both as functions of the Rayleigh number (Ra) up to $10^8$ (for fixed temperature difference between the top and bottom plates) and as functions of "non-Oberbeck-Boussinesqness'' or "NOBness'' ($\Delta$) up to 50 K (for fixed Ra). For this large NOBness the center temperature $T_c$ is more than 5 K larger than the arithmetic mean temperature $T_m$ between top and bottom plate and only weakly depends on Ra. To physically account for the NOB deviations of the Nusselt numbers from its Oberbeck-Boussinesq values, we apply the decomposition of $Nu_{NOB}/Nu_{OB}$ into the product of two effects, namely first the change in the sum of the top and bottom thermal BL thicknesses, and second the shift of the center temperature $T_c$ as compared to $T_m$. While for water the origin of the $Nu$ deviation is totally dominated by the second effect (cf. Ahlers et al., J. Fluid Mech. 569, pp. 409 (2006)) for glycerol the first effect is dominating, in spite of the large increase of $T_c$ as compared to $T_m$.