Showing papers on "Natural convection published in 2000"

Recent Developments in Rayleigh-Bénard Convection

Abstract: ▪ Abstract This review summarizes results for Rayleigh-Benard convection that have been obtained over the past decade or so. It concentrates on convection in compressed gases and gas mixtures with Prandtl numbers near one and smaller. In addition to the classical problem of a horizontal stationary fluid layer heated from below, it also briefly covers convection in such a layer with rotation about a vertical axis, with inclination, and with modulation of the vertical acceleration.

Turbulent convection at very high Rayleigh numbers

Abstract: Turbulent convection occurs when the Rayleigh number (Ra)--which quantifies the relative magnitude of thermal driving to dissipative forces in the fluid motion--becomes sufficiently high. Although many theoretical and experimental studies of turbulent convection exist, the basic properties of heat transport remain unclear. One important question concerns the existence of an asymptotic regime that is supposed to occur at very high Ra. Theory predicts that in such a state the Nusselt number (Nu), representing the global heat transport, should scale as Nu proportional to Ra(beta) with beta = 1/2. Here we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (10(6) < or = Ra < or = 10(7)), using cryogenic helium gas as the working fluid. Our data, over the entire range of Ra, can be described to the lowest order by a single power-law with scaling exponent beta close to 0.31. In particular, we find no evidence for a transition to the Ra(1/2) regime. We also study the variation of internal temperature fluctuations with Ra, and probe velocity statistics indirectly.

The onset of thermal convection in a rapidly rotating sphere

Abstract: The linear stability of convection in a rapidly rotating sphere studied here builds on well established relationships between local and global theories appropriate to the small Ekman number limit. Soward (1977) showed that a disturbance marginal on local theory necessarily decays with time due to the process of phase mixing (where the spatial gradient of the frequency is non-zero). By implication, the local critical Rayleigh number is smaller than the true global value by an O(1) amount. The complementary view that the local marginal mode cannot be embedded in a consistent spatial WKBJ solution was expressed by Yano (1992). He explained that the criterion for the onset of global instability is found by extending the solution onto the complex s-plane, where s is the distance from the rotation axis, and locating the double turning point at which phase mixing occurs. He implemented the global criterion on a related two-parameter family of models, which includes the spherical convection problem for particular O(1) values of his parameters. Since he used one of them as the basis of a small-parameter expansion, his results are necessarily approximate for our problem.Here the asymptotic theory for the sphere is developed along lines parallel to Yano and hinges on the construction of a dispersion relation. Whereas Yano's relation is algebraic as a consequence of his approximations, ours is given by the solution of a second-order ODE, in which the axial coordinate z is the independent variable. Our main goal is the determination of the leading-order value of the critical Rayleigh number together with its first-order correction for various values of the Prandtl number.Numerical solutions of the relevant PDEs have also been found, for values of the Ekman number down to 10−6; these are in good agreement with the asymptotic theory. The results are also compared with those of Yano, which are surprisingly good in view of their approximate nature.

Natural convection in enclosures with localized heating from below and symmetrical cooling from sides

Abstract: Natural convection of air in a two‐dimensional, rectangular enclosure with localized heating from below and symmetrical cooling from the sides has been numerically investigated Localized heating is simulated by a centrally located heat source on the bottom wall, and four different values of the dimensionless heat source length, 1/5, 2/5, 3/5 and 4/5 are considered Solutions are obtained for Rayleigh number values from 103 to 106 Local results are presented in the form of streamline and isotherm plots as well as the variation of local Nusselt number on the heated wall Finally, the average Nusselt number at the heated part of the lower wall, \overline Nu, was shown to increase with an increase the Rayleigh number, Ra, or of the nondimensional heat source thickness, e

Laminar natural convection in isosceles triangular enclosures heated from below and symmetrically cooled from above

Abstract: A numerical study of natural convection in an isosceles triangular enclosure with a heated horizontal base and cooled upper walls is presented. Nearly every previous study conducted on this subject to date has assumed that the geometric plane of symmetry is also a plane of symmetry for the flow. This problem is re-examined over aspect ratios ranging from 0.2 to 1.0 and Grashof numbers from 10 3 to 10 5 . A pitchfork bifurcation occurs at a critical Grashof number for each of the aspect ratios considered, above which the symmetric solutions are unstable to finite perturbations and asymmetric solutions are instead obtained. Results are presented detailing the occurrence of the pitchfork bifurcation in each of the aspect ratios considered, and the resulting flow patterns are described. A flow visualization study is used to validate the numerical observations. Computed local and mean heat transfer coefficients are also presented and compared with results obtained when flow symmetry is assumed. Differences in local values of the Nusselt number between asymmetric and symmetric solutions are found to be more than 500 percent due to the shifting of the buoyancy-driven cells

Flow of Two-Immiscible Fluids in Porous and Nonporous Channels

Abstract: This study considers steady, laminar flow of two viscous, incompressible, electrically-conducting and heat-generating or absorbing immiscible fluids in an infinitely-long, impermeable parallel-plate channel filled with a uniform porous medium. A magnetic field of uniform strength is applied normal to the flow direction. The channel walls are assumed to be electrically nonconducting and are maintained at two different temperatures. When present, the porous medium is assumed to act as an electrical insulator and that it is in local thermal equilibrium with the fluid. The transport properties of both fluids are assumed to be constant. This study is expected to be useful in understanding the influence of the presence of slag layers on the flow and heat transfer aspects of coal-fired Magnetohydrodynamic (MHD) generators when the porous medium is absent and the effects of thermal buoyancy and a magnetic field on enhanced oil recovery and filtration systems where the porous medium is present. The problem is formulated by employing the balance laws of mass, linear momentum, and energy for both phases. Continuous conditions for the velocity and temperature as well as the shear stress and heat flux of both phases at the interface are employed

Double diffusive convection in a cubic enclosure with opposing temperature and concentration gradients

Abstract: A three-dimensional numerical study has been performed to investigate double-diffusive, natural convection in a cubic enclosure subject to opposing and horizontal gradients of heat and solute. The flow is driven by buoyancy forces due to temperature and solutal gradients. Constant temperature and concentration are imposed along the two vertical side walls of the cubic enclosure, while the remaining walls are impermeable and adiabatic. The numerical simulations presented here span a wide range of thermal Rayleigh number (10.0

Hydromagnetic combined heat and mass transfer by natural convection from a permeable surface embedded in a fluid‐saturated porous medium

Abstract: The problem of coupled heat and mass transfer by natural convection from a vertical, semi‐infinite flat plate embedded in a porous medium in the presence of an external magnetic field and internal heat generation or absorption effects is formulated. The plate surface is maintained at either constant temperature or constant heat flux and is permeable to allow for possible fluid wall suction or blowing. The resulting governing equations are non‐dimensionalized and transformed using a non‐similarity transformation and then solved numerically by an implicit, iterative, finite‐difference scheme. Comparisons with previously published work are performed and excellent agreement is obtained. Useful correlations containing the various physical parameters for both isothermal and isoflux wall conditions are reported. A parametric study of all involved parameters is conducted and a representative set of numerical results for the velocity, temperature and concentration profiles as well as the skin‐friction parameter, Nusselt number, and the Sherwood number is illustrated graphically to show typical trends of the solutions.

An experimental investigation of bubble-induced free convection in a small electrochemical cell

Abstract: The sodium chlorate production process is run in large electrolysers where electrolyte flows between the electrodes due to the natural convection from hydrogen gas evolution. A brief review is given of electrolytic gas generation at electrode surfaces and of previous studies. A small, enclosed rectangular cell was used to electrolyse both a Na2SO4 and a NaCl/NaClO3 solution, in order to produce hydrogen and oxygen bubbles at one or both of the electrodes. The two-phase flow regimes, bubble sizes, gas fraction and fluid velocities between the electrodes were investigated using microscope enhanced visualisation, laser doppler velocimetry and particle image velocimetry. The practicality of each of the measuring methods is analysed and it is concluded that laser doppler velocimetry is the most robust method for measuring such systems. The experimental results are discussed and conclusions are drawn relating gas evolution to the hydrodynamics of electrolyte flowing through a narrow vertical channel. The major conclusions are that fluid flow in systems with bubble evolution can transform from a laminar to a turbulent behaviour, throughout the length of the cell, and that both turbulence and laminar behaviour can exist across the cell channel at the same horizontal plane.

A Parameterization of Mesoscale Enhancement of Surface Fluxes for Large-Scale Models

Abstract: The paper investigates the enhancement of surface fluxes by atmospheric mesoscale motions. The authors show that horizontal wind variabilities induced by these motions (i.e., gustiness) need to be considered in the parameterization of surface fluxes used in general circulation models (GCMs), as they always occur at subgrid scale. It is argued that there are two different sources of gustiness: deep convection and boundary layer free convection. The respective scales (time and length) and the convective patterns are very different for each of these sources. A general parameterization of the gustiness distinguishing these two effects is proposed. For boundary layer free convection, the gustiness is related to the free convection velocity. To establish this relationship, both observations and numerical simulations are used. Revisiting the Coupled Ocean–Atmosphere Response Experiment data, the authors propose a new value of the proportionality coefficient that links the free convection velocity and th...

Effect of sidewall conductance on heat-transport measurements for turbulent Rayleigh-Bénard convection.

Abstract: For measurements of turbulent heat transport in Rayleigh-B\'enard convection the correction for the sidewall conductance is usually neglected or based on measurements or estimates for the empty cell. It is argued that the lateral thermal coupling between the fluid and the wall can invalidate these approaches, and that corrections based on calculations of the two-dimensional temperature fields are required in some cases. These corrections can increase $\ensuremath{\gamma}$ obtained from fits of $\mathcal{N}={\mathcal{N}}_{0}{R}^{\ensuremath{\gamma}}$ $(R$ is the Rayleigh number) to the Nusselt number $\mathcal{N}(R)$ by 0.02 or more, yielding values in the range 0.30 to 0.33, which are larger than most theoretical predictions.

Analytical forced convection modeling of plate fin heat sinks

Abstract: An analytical model is presented that predicts the average heat transfer rate for forced convection, air cooled, plate fin heat sinks for use in the design and selection of heat sinks for electronics applications. Using a composite solution based on the limiting cases of fully-developed and developing flow between isothermal parallel plates, the average Nusselt number can be calculated as a function of the heat sink geometry and fluid velocity. The resulting model is applicable for the full range of Reynolds number, , and accurately predicts the experimental results to within an RMS difference of 2.1%.

Convection energy generator

Abstract: An energy generation system utilizes convection flow of a fluid media caused by differences in temperature to generate useful energy therefrom. A conduit for directing convection circulation permits conversion of forces associated with the movement of the fluid media in the conduit into a usable energy by its effect of a generation device as the fluid media flows past such device.

effects of driving mechanisms in geodynamo models

Abstract: We compare the influence of different mechanisms for driving convection in the Earth's core on the structure of the magnetic and velocity fields using a 3D numerical dynamo model. We find dynamos with a dipolar magnetic field in cases of chemical convection or convection driven by an imposed temperature contrast. With purely internal heating we obtain only dynamos with a quadrupolar or more complex field. The relative strength of convection and magnetic field generation in the regions close to the poles depends on whether a condition of fixed composition or of fixed chemical flux is specified on the inner core boundary. If applicable to the geodynamo, our results favor the dominance of chemical convection during the past 3 Gyr.

Vertical free convective boundary-layer flow in a porous medium using a thermal nonequilibrium model

Abstract: In this article we study the effect of adopting a two-temperature model of microscopic heat transfer on the classical Cheng and Minkowycz (1977) vertical free convection boundary-layer flow in a porous medium. Such a model, which allows the solid and fluid phases not to be in local thermal equilibrium, is found to modify substantially the behavior of the flow relatively close to the leading edge, where the boundary layer is comprised of two distinct asymptotic regions. The numerical simulation of the developing boundary-layer relies heavily on near-leading-edge analysis to provide suitable boundary conditions. At increasing distances from the leading edge the difference between the temperatures of the fluid and solid phases decreases to zero, which corresponds to thermal equilibrium between the phases; this is confirmed by an asymptotic analysis.

Thermal and Grain Structure Simulation in a Land-based Turbine Blade Directionally Solidified with the Liquid Metal Cooling Process

Abstract: The thermal field and the grain structure of a cored superalloy turbine blade, which has been directionally solidified with the liquid metal cooling (LMC) process, has been simulated in three dimensions using a cellular automaton (CA) coupled with finite-element (CAFE) model. The cooling induced by the liquid aluminum bath has been replaced by a heat-transfer coefficient, whose temperature- and time-dependence has been adjusted on the basis of natural convection simulations and dimensionless analyses. The simulated grain structure and crystallographic texture have been compared with the microstructure, and the electron back-scattered diffraction (EBSD) results were obtained for a real blade. In both the experiment and the simulation, it has been found that the grains do not exhibit a well-defined texture, even near the top of the blade, mainly as a result of a concave liquidus surface. In order to improve the texture and decrease the number of stray crystals, the LMC process was then optimized by changing several parameters. The baffle geometry, the liquid bath level, and the thermal conductivity of the ceramic mold were found to be the dominant parameters. Using the optimized design, the effect of the withdrawal rate on the resulting grain structure was investigated.