Heat transfer in rotating Rayleigh–Bénard convection with rough plates

Abstract

This experimental study focuses on the effect of horizontal boundaries with pyramid-shaped roughness elements on the heat transfer in rotating Rayleigh–Bénard convection. It is shown that the Ekman pumping mechanism, which is responsible for the heat transfer enhancement under rotation in the case of smooth top and bottom surfaces, is unaffected by the roughness as long as the Ekman layer thickness $\unicode[STIX]{x1D6FF}_{E}$ is significantly larger than the roughness height $k$. As the rotation rate increases, and thus $\unicode[STIX]{x1D6FF}_{E}$ decreases, the roughness elements penetrate the radially inward flow in the interior of the Ekman boundary layer that feeds the columnar Ekman vortices. This perturbation generates additional thermal disturbances which are found to increase the heat transfer efficiency even further. However, when $\unicode[STIX]{x1D6FF}_{E}\approx k$, the Ekman boundary layer is strongly perturbed by the roughness elements and the Ekman pumping mechanism is suppressed. The results suggest that the Ekman pumping is re-established for $\unicode[STIX]{x1D6FF}_{E}\ll k$ as the faces of the pyramidal roughness elements then act locally as a sloping boundary on which an Ekman layer can be formed.

Natural convection in cylindrical containers with isothermal ring-shaped obstacles

“…These studies generally report an increase of the heat transport compared to the case of smooth plates, as soon as the roughness height becomes comparable to or larger than the boundary-layer thickness in the smooth case. Thus, it was reported in earlier works that, compared to the case of smooth plates, the scaling exponent γ in the scaling relation Nu ∼ Ra γ can be larger (Roche et al 2001;Qiu, Xia & Tong 2005;Stringano, Pascazio & Verzicco 2006;Tisserand et al 2011;Salort et al 2014;Liot et al 2016;Toppaladoddi, Succi & Wettlaufer 2017;Xie & Xia 2017;Jiang et al 2018) and/or the pre-factor in this relation can be increased (Shen, Xia & Tong 1996;Du & Tong 2000;Wei & Ahlers 2014;Joshi et al 2017).…”

“…2018) and/or the pre-factor in this relation can be increased (Shen, Xia & Tong 1996; Du & Tong 2000; Wei & Ahlers 2014; Joshi et al. 2017).…”

Influence of pressure on flow and heat transfer in partitioned thermal convection

“…Chong等 人 [14] 计算研究了不同Pr数RB对流的传热和流动结构 对几何约束的依赖性, 发现对于Pr≥0.5, 几何约束可以 导致热量输送显著增强, 在计算的参数范围内, 最大传 热相对增强率一般随Pr增大而增大. Joshi等人 [15] 通过 实验研究在上下底板上的金字塔形粗糙元素对旋转 RB对流换热的影响, 结果表明, 在光滑的上下表面时, Ekman抽吸效应对于传热增强起主要作用, 当Ekman 层厚度 E明显大于粗糙高度k时, 系统传热就不受粗 糙度的影响. Bao等人 [16,17] 在微管道流动中关于系统压降和压力分布已有较 多的相关研究 [19,20] .…”

Regimes in rotating Rayleigh–Bénard convection over rough boundaries

“…Towards understanding such flows, the present work focuses on the effect of rough horizontal boundaries on the heat transfer in rotating Rayleigh-Bénard convection (RBC), a canonical system used to study rotating natural convection. There has been only one prior study on rotating RBC (RRBC) with rough walls, that of Joshi et al (2017), in which heat transfer data at moderately high Rayleigh number and Prandtl number 6.2 are used to propose a dependence of the enhancement in heat transfer due to rotation on the thickness of the Ekman boundary layer (the special form a boundary layer takes on rotating surfaces), δ E , relative to the height of the roughness elements (k). In the present study, we focus on the heat transfer behaviour in RRBC with rough boundaries at low to moderate Rayleigh number and Prandtl number 5.7.…”