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Showing papers on "Rayleigh number published in 2012"


Journal ArticleDOI
TL;DR: In this paper, the effect of static radial magnetic field on the thermal conductivity and viscosity of a concentric annulus between a cold outer square and heated inner circular cylinders was investigated numerically using the lattice Boltzmann method.

287 citations


Journal ArticleDOI
TL;DR: In this paper, a semi-annulus enclosure filled with nanofluid is used for natural convection heat transfer in a control volume based finite element method (CVFEM).

237 citations


Journal ArticleDOI
TL;DR: In this article, the authors used the control volume based finite element method (CVFEM) to simulate the fluid flow and heat transfer of Cu-water nanofluid in the presence of a horizontal magnetic field.

216 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied rapid rotating Rayleigh-benard convection using an asymptotically reduced equation set valid in the limit of low Rossby numbers and identified four distinct dynamical regimes: a disordered cellular regime near threshold, a regime of weakly interacting convective Taylor columns at larger Rayleigh numbers, followed by a breakdown of the convective columns into disordered plume regime characterized by reduced efficiency and finally by geostrophic turbulence.
Abstract: Rapidly rotating Rayleigh–Benard convection is studied using an asymptotically reduced equation set valid in the limit of low Rossby numbers. Four distinct dynamical regimes are identified: a disordered cellular regime near threshold, a regime of weakly interacting convective Taylor columns at larger Rayleigh numbers, followed for yet larger Rayleigh numbers by a breakdown of the convective Taylor columns into a disordered plume regime characterized by reduced efficiency and finally by geostrophic turbulence. The transitions are quantified by examining the properties of the horizontally and temporally averaged temperature and thermal dissipation rate. The maximum of the thermal dissipation rate is used to define the width of the thermal boundary layer. In contrast to the non-rotating Rayleigh–Benard convection, the temperature drop across this layer decreases monotonically with increasing Rayleigh number and does not saturate. The breakdown of the convective Taylor column regime is attributed to the onset...

215 citations


Journal ArticleDOI
TL;DR: In this paper, an exact scaling law for heat transfer by geostrophic convection, by considering the stability of the thermal boundary layers, where, and are the Nusselt, Rayleigh and Ekman numbers, respectively, and is the critical Rayleigh number for the onset of convection.
Abstract: Turbulent, rapidly rotating convection has been of interest for decades, yet there exists no generally accepted scaling law for heat transfer behaviour in this system. Here, we develop an exact scaling law for heat transfer by geostrophic convection, , by considering the stability of the thermal boundary layers, where , and are the Nusselt, Rayleigh and Ekman numbers, respectively, and is the critical Rayleigh number for the onset of convection. Furthermore, we use the scaling behaviour of the thermal and Ekman boundary layer thicknesses to quantify the necessary conditions for geostrophic convection: . Interestingly, the predictions of both heat flux and regime transition do not depend on the total height of the fluid layer. We test these scaling arguments with data from laboratory and numerical experiments. Adequate agreement is found between theory and experiment, although there is a paucity of convection data for low .

185 citations


Journal ArticleDOI
TL;DR: In this article, the Galerkin finite element method has been employed to solve momentum and energy balance as well as post processing streamfunctions and heatfunctions in the presence of hot and cold side walls.

172 citations


Journal ArticleDOI
TL;DR: It is demonstrated, via simulations of asymptotically reduced equations describing rotationally constrained Rayleigh-Bénard convection, that the efficiency of turbulent motion in the fluid bulk limits overall heat transport and determines the scaling of the nondimensional Nusselt number Nu with the Rayleigh number Ra, the Ekman number E, and the Prandtl number σ.
Abstract: We demonstrate, via simulations of asymptotically reduced equations describing rotationally constrained Rayleigh-Benard convection, that the efficiency of turbulent motion in the fluid bulk limits overall heat transport and determines the scaling of the nondimensional Nusselt number Nu with the Rayleigh number Ra, the Ekman number E, and the Prandtl number σ. For E << 1 inviscid scaling theory predicts and simulations confirm the large Ra scaling law Nu-1 ≈ C(1)σ(-1/2)Ra(3/2)E(2), where C(1) is a constant, estimated as C(1) ≈ 0.04 ± 0.0025. In contrast, the corresponding result for nonrotating convection, Nu-1 ≈ C(2)Ra(α), is determined by the efficiency of the thermal boundary layers (laminar: 0.28 ≤ α ≤ 0.31, turbulent: α ~ 0.38). The 3/2 scaling law breaks down at Rayleigh numbers at which the thermal boundary layer loses rotational constraint, i.e., when the local Rossby number ≈ 1. The breakdown takes place while the bulk Rossby number is still small and results in a gradual transition to the nonrotating scaling law. For low Ekman numbers the location of this transition is independent of the mechanical boundary conditions.

151 citations


Journal ArticleDOI
TL;DR: In this paper, a scaling law for the onset of plate tectonics on terrestrial planets was proposed, which states that damage must reduce the viscosity of shear zones in the lithosphere to a critical value equivalent to the underlying mantle viscosities.

136 citations


Journal ArticleDOI
TL;DR: It is shown that the dissolution flux and the rate of fluid mixing are determined by the mean scalar dissipation rate, which supports the universal character of convective mixing and points to the need for alternative explanations for nonlinear scalings of the dissolve flux with the Rayleigh number.
Abstract: Convective mixing in porous media is triggered by a Rayleigh-B\'enard-type hydrodynamic instability as a result of an unstable density stratification of fluids. While convective mixing has been studied extensively, the fundamental behavior of the dissolution flux and its dependence on the system parameters are not yet well understood. Here, we show that the dissolution flux and the rate of fluid mixing are determined by the mean scalar dissipation rate. We use this theoretical result to provide computational evidence that the classical model of convective mixing in porous media exhibits, in the regime of high Rayleigh number, a dissolution flux that is constant and independent of the Rayleigh number. Our findings support the universal character of convective mixing and point to the need for alternative explanations for nonlinear scalings of the dissolution flux with the Rayleigh number, recently observed experimentally.

135 citations


Journal ArticleDOI
TL;DR: In this paper, lattice Boltzmann method is applied to investigate the natural convection flows utilizing nanofluids in a square cavity, where the fluid in the cavity is a water-based Nanofluid containing Al2O3 or Cu nanoparticles.

109 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of internal heat source on the onset of Darcy-Brinkman convection in a porous layer saturated by nanofluid is studied, and the resulting eigenvalue problem is solved numerically using the Galerkin technique with the Rayleigh number as the eigen value.

Journal ArticleDOI
TL;DR: In this article, a simple three noded triangular element is used to divide the porous domain into smaller segments known as elements and then the algebraic set of equations resulting from the finite element equation are assembled into a global matrix and then solved iteratively to get the solution variables.

Journal ArticleDOI
TL;DR: In this paper, a parametric study was conducted and the effects of pertinent parameters such as Rayleigh number, size of the adiabatic square body, and volume fraction of the Cu nanoparticles on the fluid flow and thermal fields and heat transfer inside the cavity were investigated.

Journal ArticleDOI
TL;DR: In this article, a mathematical model of heat transfer in a porous duct was solved by converting the governing partial differential equations into a set of algebraic equations with the help of finite element method.

Journal ArticleDOI
TL;DR: In this paper, the effect of Rayleigh number, solid volume fraction and both Hartmann number and heat generation or absorption coefficient on the iso-contours of streamline and temperature were investigated in a square cavity filled with different nanofluids.

Journal ArticleDOI
TL;DR: In this article, the conservation equations of mass, momentum and energy are solved using the finite volume method for varying inclination angles between 0° and 90° and two cavity height based Rayleigh numbers, Ra = 104 and 105, a Prandtl number of Pr = 102 and three cavity aspect ratios of 1, 4 and 8.

Journal ArticleDOI
TL;DR: In this article, a parametric study was conducted and effects of pertinent parameters such as Rayleigh number, the aspect ratio of the C-shaped enclosure, and the volume fraction of the Cu nanoparticles on the flow and temperature fields and the rate of heat transfer inside the enclosure were investigated.

Journal ArticleDOI
TL;DR: High-resolution numerical simulations of convection in multiphase flows (boiling) using a novel algorithm based on a lattice Boltzmann method show that in the presence of nucleating bubbles non-Oberbeck-Boussinesq effects develop, the mean temperature profile becomes asymmetric, and heat-transfer and heat -transfer fluctuations are enhanced, at all Ra studied.
Abstract: We present high-resolution numerical simulations of convection in multiphase flows (boiling) using a novel algorithm based on a lattice Boltzmann method. We first study the thermodynamical and kinematic properties of the algorithm. Then, we perform a series of 3D numerical simulations changing the mean properties in the phase diagram and compare convection with and without phase coexistence at Rayleigh number Ra � 10 7 . We show that in the presence of nucleating bubbles non-Oberbeck-Boussinesq effects develop,themeantemperatureprofilebecomesasymmetric,andheat-transferandheat-transferfluctuations are enhanced, at all Ra studied. We also show that small-scale properties of velocity and temperature fields arestronglyaffectedbythepresenceofthebuoyantbubbleleadingtohighnon-Gaussianprofilesinthebulk.

Journal ArticleDOI
TL;DR: In this article, the Lattice Boltzmann simulation of natural convection in an open enclosure which subjugated to water/copper nanofluid has been investigated, and the results show that the average Nusselt number increases with augmentation of Rayleigh number and the volume fraction of nanoparticles for whole ranges of aspect ratios.

Journal ArticleDOI
TL;DR: In this article, a systematic study of the triggering of the regime with an enhanced heat transfer, originally named the "Ultimate Regime" of convection, was conducted in convection cells with various aspect ratios and different specificities such as altered boundary conditions or obstacles inserted in the flow.
Abstract: Rayleigh-B\'enard cells are one of the simplest systems to explore the laws of natural convection in the highly turbulent limit. However, at very high Rayleigh numbers (Ra > 1E12) and for Prandtl numbers of order one, experiments fall into two categories: some evidence a steep enhancement of the heat transfer while others do not. The origin of this apparent disagreement is presently unexplained. This puzzling situation motivated a systematic study of the triggering of the regime with an enhanced heat transfer, originally named the "Ultimate Regime" of convection. High accuracy heat transfer measurements have been conducted in convection cells with various aspect ratios and different specificities, such as altered boundary conditions or obstacles inserted in the flow. The two control parameters, the Rayleigh and Prandtl numbers have been varied independently to disentangle their relative influence. Among other results, it is found that i) most experiments reaching very high $Ra$ are not in disagreement if small differences in Prandtl numbers are taken into account, ii) the transition is not directly triggered by the large scale circulation present in the cell, iii) the sidewall of the cell have a significant influence on the transition. The characteristics of this Ultimate regime are summarized and compared with R. Kraichnan prediction for the asymptotic regime of convection.

Journal ArticleDOI
TL;DR: In this article, the problem of mixed convection fluid flow and heat transfer of Al 2 O 3 -water nanofluid with temperature and nanoparticles concentration dependent thermal conductivity and effective viscosity inside a square cavity was investigated numerically.

Journal ArticleDOI
TL;DR: In this paper, the effect of rotation on the onset of thermal convection in a horizontal layer of nanofluid saturated by a Darcy-Brinkman porous medium is considered.

Journal ArticleDOI
TL;DR: In this paper, a vertical annular cylinder is embedded with saturated porous medium and the governing partial differential equations are non-dimensionalised and solved by using finite element method (FEM).
Abstract: The present study is intended to study heat and mass transfer in a vertical annular cylinder embedded with saturated porous medium. The inner surface of cylinder is maintained at uniform wall temperature and uniform wall concentration. The governing partial differential equations are non-dimensionalised and solved by using finite element method (FEM). The porous medium is discritised using triangular elements with uneven element size. Large number of smaller-sized elements are placed near the walls of the annulus to capture the smallest variation in solution parameters. The results are reported for both aiding and opposing flows. The effects of various non-dimensional numbers such as buoyancy ratio, Lewis number, Rayleigh number, aspect ratio, etc on heat and mass transfer are discussed. The temperature and concentration profiles are presented.

01 Apr 2012
TL;DR: In this paper, the authors extend the density functional theory (DFT) calculations of post-perovskite activation enthalpy to a pressure of 1 TPa for both slowest diffusion and fastest diffusion directions.
Abstract: The discovery of extra-solar “super-Earth” planets with sizes up to twice that of Earth has prompted interest in their possible lithosphere and mantle dynamics and evolution. Simple scalings suggest that super-Earths are more likely than an equivalent Earth-sized planet to be undergoing plate tectonics. Generally, viscosity and thermal conductivity increase with pressure while thermal expansivity decreases, resulting in lower convective vigour in the deep mantle, which, if extralopated to the largest super-Earths might, according to conventional thinking, result in no convection in their deep mantles due to the very low effective Rayleigh number. Here we evaluate this. First, as the mantle of a super-Earth is made mostly of post-perovskite we here extend the density functional theory (DFT) calculations of post-perovskite activation enthalpy of to a pressure of 1 TPa, for both slowest diffusion (upper-bound rheology) and fastest diffusion (lower-bound rheology) directions. Along a 1600 K adiabat the upper-bound rheology would lead to a post-perovskite layer of a very high (∼10 30 Pa s) but relatively uniform viscosity, whereas the lower-bound rheology leads to a post-perovskite viscosity increase of ∼7 orders of magnitude with depth; in both cases the deep mantle viscosity would be too high for convection. Second, we use these DFT-calculated values in statistically steady-state numerical simulations of mantle convection and lithosphere dynamics of planets with up to ten Earth masses. The models assume a compressible mantle including depth-dependence of material properties and plastic yielding induced plate-like lithospheric behaviour. Results confirm the likelihood of plate tectonics for planets with Earth-like surface conditions (temperature and water) and show a self-regulation of deep mantle temperature. The deep mantle is not adiabatic; instead feedback between internal heating, temperature and viscosity regulates the temperature such that the viscosity has the value needed to facilitate convective loss of the radiogenic heat, which results in a very hot perovskite layer for the upper-bound rheology, a super-adiabatic perovskite layer for the lower-bound rheology, and an azimuthally-averaged viscosity of no more than 10 26 Pa s. Convection in large super-Earths is characterised by large upwellings (even with zero basal heating) and small, time-dependent downwellings, which for large super-Earths merge into broad downwellings. In the context of planetary evolution, if, as is likely, a super-Earth was extremely hot/molten after its formation, it is thus likely that even after billions of years its deep interior is still extremely hot and possibly substantially molten with a “super basal magma ocean” – a larger version of the proposal of Labrosse et al. (Labrosse, S., Hernlund, J.W., Coltice, N. [2007]. Nature 450, 866–869), although this depends on presently unknown melt–solid density contrast and solidus.

Journal ArticleDOI
TL;DR: In this paper, the authors used heatline visualization technique to understand heat transport path in an inclined non-uniformly heated enclosure filled with water-based CuO nanofluid.

01 Jan 2012
TL;DR: In this article, mixed convection and entropy generation of Cu-water nanofluid and pure water in a lid-driven square cavity have been studied, and the results have shown that addition of nanoparticles to the base fluid affects the entropy generation, flow pattern and thermal behavior especially at higher Rayleigh and low Reynolds numbers.
Abstract: In this numerical work, mixed convection and entropy generation of Cu–water nanofluid and pure water in a lid-driven square cavity have been studied. Horizontal walls of the cavity are adiabatic and vertical walls have constant temperature but different values. The top wall has been considered as moving from left to right at a constant speed, U0. Rayleigh numbers of 104, 105 and 106 and Reynolds numbers of 1, 10 and 100 have been considered. The results have shown that addition of nanoparticles to the base fluid affects the entropy generation, flow pattern and thermal behavior especially at higher Rayleigh and low Reynolds numbers. For pure fluid as well as nanofluid, increasing Reynolds number increases the average Nusselt number, linearly. The maximum entropy generation occurs in nanofluid at low Rayleigh number but high Reynolds number. The minimum entropy generation occurs in pure fluid at low Rayleigh and low Reynolds numbers. For the cases studied, at Rayleigh numbers greater than 105, most of the entropy generation is due to heat transfer effects, thus the Bejan number converges to a constant value. A proper choice of Reynolds number is important, if enhanced heat transfer and minimum increased entropy generation is expected. © 2012 Elsevier Masson SAS. All rights reserved.

Journal ArticleDOI
TL;DR: In this article, a numerical investigation is performed into the natural convection heat transfer characteristics within an enclosed cavity filled with nanofluid, where the left and right walls of the cavity have a complex-wavy geometry and are maintained at a high and low temperature, respectively.

Journal ArticleDOI
TL;DR: In this article, the mean Nusselt number Nu ¯ is found to increase with increasing values of Rayleigh number for both Newtonian and Bingham fluids, but weaker convective transport in Bingham fluid leads to smaller values of Nu ¯ than that obtained in the case of Newtonian fluids with the same nominal value of Ra and Pr in the differentially heated vertical sidewall configuration.
Abstract: In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with differentially heated horizontal walls with the bottom wall at higher temperature have been conducted for yield-stress fluids obeying the Bingham model. Heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 103–105 and a Prandtl number (Pr) range of 0.1–100. The mean Nusselt number Nu ¯ is found to increase with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, weaker convective transport in Bingham fluids leads to smaller values of Nu ¯ than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra. The mean Nusselt number Nu ¯ decreases with increasing Bingham number in the case of yield stress fluids, and, for large values of Bingham number Bn, the value rapidly approaches to unity ( Nu ¯ = 1.0 ) as thermal conduction dominates the heat transfer. However, this variation in the present configuration is found to be markedly different from the corresponding variation of Nu ¯ with Bn for the same nominal values of Ra and Pr in the differentially-heated vertical sidewall configuration. The effects of Prandtl number have also been investigated in detail and physical explanations are provided for the observed behaviour. Guided by a detailed scaling analysis, new correlations are proposed for the mean Nusselt number Nu ¯ for both Newtonian and Bingham fluids which are demonstrated to satisfactorily capture the correct qualitative and quantitative behaviours of Nu ¯ for the range of Ra, Pr and Bn considered in this analysis.

Journal ArticleDOI
TL;DR: In this article, the effect of inclination of the cavity on the natural convection is studied for five inclinations; 0° (aperture facing sideways), 30°, 45°, 60° and 90°.

Journal ArticleDOI
TL;DR: In this article, the effects of magnetic field on convection in a trapezoidal enclosure were investigated using finite element method to solve the governing equations for different parameters such as Rayleigh number, Hartmann number and inclination angle of inclined wall of the enclosure.