scholarly journals Quasistatic magnetoconvection: heat transport enhancement and boundary layer crossing

2019 ◽  
Vol 870 ◽  
pp. 519-542 ◽  
Author(s):  
Zi Li Lim ◽  
Kai Leong Chong ◽  
Guang-Yu Ding ◽  
Ke-Qing Xia
Keyword(s):  
Boundary Layer ◽  
Heat Transport ◽  
Lorentz Force ◽  
Numerical Study ◽  
Temperature Fluctuations ◽  
The Other ◽  
Maximum Heat ◽  
Transport Enhancement ◽  
Viscous Boundary ◽  
Rayleigh Benard

We present a numerical study of quasistatic magnetoconvection in a cubic Rayleigh–Bénard (RB) convection cell subjected to a vertical external magnetic field. For moderate values of the Hartmann number $Ha$ (characterising the strength of the stabilising Lorentz force), we find an enhancement of heat transport (as characterised by the Nusselt number $Nu$). Furthermore, a maximum heat transport enhancement is observed at certain optimal $Ha_{opt}$. The enhanced heat transport may be understood as a result of the increased coherence of the thermal plumes, which are elementary heat carriers of the system. To our knowledge this is the first time that a heat transfer enhancement by the stabilising Lorentz force in quasistatic magnetoconvection has been observed. We further found that the optimal enhancement may be understood in terms of the crossing of the thermal and the momentum boundary layers (BL) and the fact that temperature fluctuations are maximum near the position where the BLs cross. These findings demonstrate that the heat transport enhancement phenomenon in the quasistatic magnetoconvection system belongs to the same universality class of stabilising–destabilising (S–D) turbulent flows as the systems of confined Rayleigh–Bénard (CRB), rotating Rayleigh–Bénard (RRB) and double-diffusive convection (DDC). This is further supported by the findings that the heat transport, boundary layer ratio and temperature fluctuations in magnetoconvection at the boundary layer crossing point are similar to the other three cases. A second type of boundary layer crossing is also observed in this work. In the limit of $Re\gg Ha$, the (traditionally defined) viscous boundary $\unicode[STIX]{x1D6FF}_{v}$ is found to follow a Prandtl–Blasius-type scaling with the Reynolds number $Re$ and is independent of $Ha$. In the other limit of $Re\ll Ha$, $\unicode[STIX]{x1D6FF}_{v}$ exhibits an approximate ${\sim}Ha^{-1}$ dependence, which has been predicted for a Hartmann boundary layer. Assuming the inertial term in the momentum equation is balanced by both the viscous and Lorentz terms, we derived an expression $\unicode[STIX]{x1D6FF}_{v}=H/\sqrt{c_{1}Re^{0.72}+c_{2}Ha^{2}}$ (where $H$ is the height of the cell) for all values of $Re$ and $Ha$, which fits the obtained viscous boundary layer well.

scholarly journals Unsteady Finite Amplitude Convection of Water–Copper Nanoliquid in High-Porosity Enclosures

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
P. G. Siddheshwar ◽  
K. M. Lakshmi
Keyword(s):  
Porous Medium ◽  
Heat Transport ◽  
Heat Storage ◽  
Finite Amplitude ◽  
High Porosity ◽  
Two Phase ◽  
Onset Of Convection ◽  
Maximum Heat ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Unicellular Rayleigh–Bénard convection of water–copper nanoliquid confined in a high-porosity enclosure is studied analytically. The modified-Buongiorno–Brinkman two-phase model is used for nanoliquid description to include the effects of Brownian motion, thermophoresis, porous medium friction, and thermophysical properties. Free–free and rigid–rigid boundaries are considered for investigation of onset of convection and heat transport. Boundary effects on onset of convection are shown to be classical in nature. Stability boundaries in the R1*–R2 plane are drawn to specify the regions in which various instabilities appear. Specifically, subcritical instabilities' region of appearance is highlighted. Square, shallow, and tall porous enclosures are considered for study, and it is found that the maximum heat transport occurs in the case of a tall enclosure and minimum in the case of a shallow enclosure. The analysis also reveals that the addition of a dilute concentration of nanoparticles in a liquid-saturated porous enclosure advances onset and thereby enhances the heat transport irrespective of the type of boundaries. The presence of porous medium serves the purpose of heat storage in the system because of its low thermal conductivity.

Numerical Study of Effect of Polymer Additives on Heat Transport in Turbulent Rayleigh- Bénard Convection

2012 ◽  
Vol 472-475 ◽  
pp. 1283-1288 ◽  
Author(s):  
Chen Hui Zheng ◽  
Chang Feng Li ◽  
Hua Hong Jiang
Keyword(s):  
Heat Transport ◽  
Large Scale ◽  
Numerical Study ◽  
Navier Stokes ◽  
Polymer Additive ◽  
Bénard Convection ◽  
Turbulence Regime ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In this study, the Reynolds-Averaged-Navier-Stokes (RANS) model combined with the Cross Viscosity Equation is used, applied to the soft turbulence regime (Ra =5×105~4×107) and hard turbulence regime (Ra>4×107) of Rayleigh-Bénard convection (RBC). The relation curves between heat transport (Nusselt number) and other parameters, as well as flow pattern changes of RBC are obtained for the cases with different Rayleigh number and concentration of the polymer additive. The simulations show that the presence of polymer additive can lead to an enhancement of the heat transfer with larger effect in the hard turbulence regime than those in the soft turbulence regime. It is also shown that in the soft turbulence regime the reversal cycles are shorter than in hard turbulence regime. The symmetric vortices in the diagonal corner of enclosed space shrink and the velocities of large-scale circulation (LSC) increase accordingly.

Heat transport properties of plates with smooth and rough surfaces in turbulent thermal convection

2014 ◽  
Vol 740 ◽  
pp. 28-46 ◽  
Author(s):  
Ping Wei ◽  
Tak-Shing Chan ◽  
Rui Ni ◽  
Xiao-Zheng Zhao ◽  
Ke-Qing Xia
Keyword(s):  
Boundary Layer ◽  
Transport Properties ◽  
Heat Transport ◽  
Thermal Convection ◽  
The Other ◽  
Scaling Exponent ◽  
Present Level ◽  
Experimental Resolution ◽  
Rough Plate ◽  
Heat Transport Properties

AbstractWe present an experimental study of turbulent thermal convection with smooth and rough surface plates in various combinations. A total of five cells were used in the experiments. Both the global $\mathit{Nu}$ and the $\mathit{Nu}$ for each plate (or the associated boundary layer) are measured. The results reveal that the smooth plates are insensitive to the surface (rough or smooth) and boundary conditions (i.e. nominally constant temperature or constant flux) of the other plate of the same cell. The heat transport properties of the rough plates, on the other hand, depend not only on the nature of the plate at the opposite side of the cell, but also on the boundary condition of that plate. It thus appears that, at the present level of experimental resolution, the smooth plate can influence the rough plate, but cannot be influenced by either the rough or the smooth plates. It is further found that the scaling of $\mathit{Nu}$ with $\mathit{Ra}$ for all of the smooth plates is consistent with the classical $1/ 3$ exponent. But the scaling exponent for the global $\mathit{Nu}$ for the cell with both plates being smooth is definitely less than $1/ 3$ (this result itself is consistent with all previous studies at comparable parameter range). The discrepancy between the $\mathit{Nu}$ behaviour at the whole-cell and individual-plate levels is not understood and deserves further investigation.

Heat transport enhancement in confined Rayleigh-Bénard convection feels the shape of the container

2021 ◽  
Author(s):  
Robert Hartmann ◽  
Kai Leong Chong ◽  
Richard J. A. M. Stevens ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Heat Transport ◽  
Transport Enhancement ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

scholarly journals Vibration-induced boundary-layer destabilization achieves massive heat-transport enhancement

2020 ◽  
Vol 6 (21) ◽  
pp. eaaz8239 ◽  
Author(s):  
Bo-Fu Wang ◽  
Quan Zhou ◽  
Chao Sun
Keyword(s):  
Boundary Layer ◽  
Heat Transport ◽  
Boundary Layers ◽  
Thermal Flux ◽  
Mechanical Vibration ◽  
Industrial Applications ◽  
The Body ◽  
Convection Cell ◽  
Thermal Plumes ◽  
Transport Enhancement

Thermal turbulence is well known as a potent means to convey heat across space by a moving fluid. The existence of the boundary layers near the plates, however, bottlenecks its heat-exchange capability. Here, we conceptualize a mechanism of thermal vibrational turbulence that breaks through the boundary-layer limitation and achieves massive heat-transport enhancement. When horizontal vibration is applied to the convection cell, a strong shear is induced to the body of fluid near the conducting plates, which destabilizes thermal boundary layers, vigorously triggers the eruptions of thermal plumes, and leads to a heat-transport enhancement by up to 600%. We further reveal that such a vibration-induced shear can very efficiently disrupt the boundary layers. The present findings open a new avenue for research into heat transport and will also bring profound changes in many industrial applications where thermal flux through a fluid is involved and the mechanical vibration is usually inevitable.

Boundary layer fluctuations in turbulent Rayleigh–Bénard convection

2018 ◽  
Vol 840 ◽  
pp. 408-431 ◽  
Author(s):  
Yin Wang ◽  
Wei Xu ◽  
Xiaozhou He ◽  
Hiufai Yik ◽  
Xiaoping Wang ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Numerical Study ◽  
Mixing Zone ◽  
Scaling Properties ◽  
Cell Height ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We report a combined experimental and numerical study of the effect of boundary layer (BL) fluctuations on the scaling properties of the mean temperature profile$\unicode[STIX]{x1D703}(z)$and temperature variance profile$\unicode[STIX]{x1D702}(z)$in turbulent Rayleigh–Bénard convection in a thin disk cell and an upright cylinder of aspect ratio unity. Two scaling regions are found with increasing distance$z$away from the bottom conducting plate. In the BL region, the measured$\unicode[STIX]{x1D703}(z)$and$\unicode[STIX]{x1D702}(z)$are found to have the scaling forms$\unicode[STIX]{x1D703}(z/\unicode[STIX]{x1D6FF})$and$\unicode[STIX]{x1D702}(z/\unicode[STIX]{x1D6FF})$, respectively, with varying thermal BL thickness$\unicode[STIX]{x1D6FF}$. The functional forms of the measured$\unicode[STIX]{x1D703}(z/\unicode[STIX]{x1D6FF})$and$\unicode[STIX]{x1D702}(z/\unicode[STIX]{x1D6FF})$in the two convection cells agree well with the recently derived BL equations by Shishkinaet al.(Phys. Rev. Lett., vol. 114, 2015, 114302) and by Wanget al.(Phys. Rev. Fluids, vol. 1, 2016, 082301). In the mixing zone outside the BL region, the measured$\unicode[STIX]{x1D703}(z)$remains approximately constant, whereas the measured$\unicode[STIX]{x1D702}(z)$is found to scale with the cell height$H$in the two convection cells and follows a power law,$\unicode[STIX]{x1D702}(z)\sim (z/H)^{\unicode[STIX]{x1D716}}$, with the obtained values of$\unicode[STIX]{x1D716}$being close to$-1$. Based on the experimental and numerical findings, we derive a new equation for$\unicode[STIX]{x1D702}(z)$in the mixing zone, which has a power-law solution in good agreement with the experimental and numerical results. Our work demonstrates that the effect of BL fluctuations can be adequately described by the velocity–temperature correlation functions and the new BL equations capture the essential physics.

On non-Oberbeck–Boussinesq effects in three-dimensional Rayleigh–Bénard convection in glycerol

2013 ◽  
Vol 724 ◽  
pp. 175-202 ◽  
Author(s):  
Susanne Horn ◽  
Olga Shishkina ◽  
Claus Wagner
Keyword(s):  
Boundary Layer ◽  
Material Properties ◽  
Three Dimensional ◽  
Bottom Plate ◽  
Two Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Viscous Boundary ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractRayleigh–Bénard convection in glycerol (Prandtl number $\mathit{Pr}= 2547. 9$) in a cylindrical cell with an aspect ratio of $\Gamma = 1$ was studied by means of three-dimensional direct numerical simulations (DNS). For that purpose, we implemented temperature-dependent material properties into our DNS code, by prescribing polynomial functions up to seventh order for the viscosity, the heat conductivity and the density. We performed simulations with the common Oberbeck–Boussinesq (OB) approximation and with non-Oberbeck–Boussinesq (NOB) effects within a range of Rayleigh numbers of $1{0}^{5} \leq \mathit{Ra}\leq 1{0}^{9} $. For the highest temperature differences, $\Delta = 80~\mathrm{K} $, the viscosity at the top is ${\sim }360\hspace{0.167em} \% $ times higher than at the bottom, while the differences of the other material properties are less than $15\hspace{0.167em} \% $. We analysed the temperature and velocity profiles and the thermal and viscous boundary-layer thicknesses. NOB effects generally lead to a breakdown of the top–bottom symmetry, typical for OB Rayleigh–Bénard convection. Under NOB conditions, the temperature in the centre of the cell ${T}_{c} $ increases with increasing $\Delta $ and can be up to $15~\mathrm{K} $ higher than under OB conditions. The comparison of our findings with several theoretical and empirical models showed that two-dimensional boundary-layer models overestimate the actual ${T}_{c} $, while models based on the temperature or velocity scales predict ${T}_{c} $ very well with a standard deviation of $0. 4~\mathrm{K} $. Furthermore, the obtained temperature profiles bend closer towards the cold top plate and further away from the hot bottom plate. The situation for the velocity profiles is reversed: they bend farther away from the top plate and closer towards to the bottom plate. The top boundary layers are always thicker than the bottom ones. Their ratio is up to 2.5 for the thermal and up to 4.5 for the viscous boundary layers. In addition, the Reynolds number $\mathit{Re}$ and the Nusselt number $\mathit{Nu}$ were investigated: $\mathit{Re}$ is higher and $\mathit{Nu}$ is lower under NOB conditions. The Nusselt number $\mathit{Nu}$ is influenced in a nonlinear way by NOB effects, stronger than was suggested by the two-dimensional simulations. The actual scaling of $\mathit{Nu}$ with $\mathit{Ra}$ in the NOB case is $\mathit{Nu}\propto {\mathit{Ra}}^{0. 298} $ and is in excellent agreement with the experimental data.

scholarly journals Boundary Layer Heat Transport in turbulent Rayleigh-Bénard Convection in Air

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 657-658
Author(s):  
Ronald du Puits ◽  
Christian Resagk ◽  
Christian Willert
Keyword(s):  
Boundary Layer ◽  
Heat Transport ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard
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