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

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.

Designing a Convection‐Cloud Chamber for Collision‐Coalescence Using Large‐Eddy Simulation With Bin Microphysics

“…An alternate approach is to apply a temperature difference across the water‐saturated side walls as well as between the top and bottom of the convection chamber, thereby allowing the side walls to augment rather than deplete the supersaturation field. Thermal convection driven by side walls is typically referred to as vertical convection or tilted Rayleigh‐Bénard convection, and has been studied in the literature (Chand et al., 2022; Shishkina, 2016; Q. Wang et al., 2021). We will build on that work by exploring how various specifications of side wall temperature and moisture can enhance the supersaturation, the LWC, and as a consequence the droplet collision rate.…”

Optimal wall shapes and flows for steady planar convection

“…Variations of these problems include the effect of tilting the rough walls, for triangular (Chand, Sharma & De 2022) and ratchet-shaped (Jiang et al 2023) surfaces, and the heat transfer enhancement that can be obtained by moving the rough plates (Jin et al 2022). Zhang et al (2018) showed computationally that in some cases with small roughness heights, roughness can actually decrease the rate of heat transfer.…”

Rayleigh–Bénard convection in mono and hybrid nanoliquids in an inclined slot

“…Mansour et al [22] experimentally investigated nanoliquids in an inclined tube and demonstrated the influence of inclination angles on the convective heat transfer process. Chand et al [23] conducted direct numerical simulations on inclined RBC and observed smooth and roughness-facilitated convection cells of double aspect ratio (Γ = 2) for air as a working fluid. Liang and Acrivos [24] were the first to study the linear stability of natural convection in inclined geometry, wherein a Rayleigh number expression for steady longitudinal rolls (LRs) was derived using the perturbation method.…”