Presence Of Convection Research Articles

Thermodiffusion (thermomigration) and convection in molten semiconductor–metal layers

Thermodiffusion or thermomigration phenomenon and the presence of convection are investigated in a binary molten semiconductor–metal layer heated from top or bottom. These phenomena may be locally present in the zone melting temperature gradient (ZMTG) method used for the fabrication of semiconductor devices and solar cells. Thermodiffusion is studied using the linear nonequilibrium thermodynamics, whereas convection is studied by solving the transport equations numerically in a stationary molten cell. An expression is obtained to estimate thermodiffusion factor in stationary binary semiconductor–metal mixtures. The presence of convection in various cases is studied as well. In the absence of any experimental data on stationary semiconductor–metal mixtures, the prediction power of the developed expression is tested against the experimental data of the moving melting zone in the ZMTG process on mixtures comprised of silicon as a semiconductor and aluminum, gallium, and gold as metal dopants. The expression can only qualitatively predict the migration velocity of the melting zone, perhaps due to the inadequacy of the nonequilibrium thermodynamics to model this process, and the uncertainties in the experimental data due to the presence of both thermodiffusion and the gravity-induced convection in the molten zone.

Ensemble data assimilation in the presence of cloud

In numerical weather prediction (NWP) data assimilation (DA) methods are used to combine available observations with numerical model estimates. This is done by minimising measures of error on both observations and model estimates with more weight given to data that can be more trusted. For any DA method an estimate of the initial forecast error covariance matrix is required. For convective scale data assimilation, however, the properties of the error covariances are not well understood. An effective way to investigate covariance properties in the presence of convection is to use an ensemble-based method for which an estimate of the error covariance is readily available at each time step. In this work, we investigate the performance of the ensemble square root filter (EnSRF) in the presence of cloud growth applied to an idealised 1D convective column model of the atmosphere. We show that the EnSRF performs well in capturing cloud growth, but the ensemble does not cope well with discontinuities introduced into the system by parameterised rain. The state estimates lose accuracy, and more importantly the ensemble is unable to capture the spread (variance) of the estimates correctly. We also find, counter-intuitively, that by reducing the spatial frequency of observations and/or the accuracy of the observations, the ensemble is able to capture the states and their variability successfully across all regimes.

Phase-field investigation of microstructure evolution under the influence of convection

Numerical simulation of solidification and crystal growth has attracted industrial attention as a powerful engineering tool for processes and alloy optimization. In this work, we present a detailed study of the influence of flow on microstructure evolution during solidification. First, we include convection effects into an existing quantitative phase-field model that is meant to simulate dendritic growth of a binary alloy. We apply it to investigate the solidification of a Fe-Mn alloy under external flow conditions. In addition, we present an extension of the quantitative phase-field model of two-phase growth which includes natural and forced convection effects in the melt phase. We use this extension to investigate directional solidification of eutectic lamellae under the influence of convection as well as microstructure formation of peritectic growth in the presence of convection.

Dissolution kinetics or pure mass transfer? A mechanistic study of dissolution

AbstractIn many cases, classic in vitro tests are used to investigate dissolution from powders and solids. A problem with these kinds of tests is the frequent use of agitation, leading to a lumped description of the properties at the solid–liquid interface. The hydrodynamic forces arising from agitation might have a nontrivial impact on the dissolution properties, thus calling for a comparison of results with those stemming from stagnant dissolution with the aim to increase the understanding of the dissolution process. Stagnant dissolution of compressed solid benzoic acid was examined using the noninvasive electronic speckle pattern interferometry technique in this study. The diffusion coefficient for benzoic acid in 37°C water was measured using the same technique, and, by combining the results, the surface kinetics at the solid–liquid interface were calculated. A comparison with previous dissolution data from a rotating disk suggests that the presence of convection can increase the observed surface kinetics. © 2010 American Institute of Chemical Engineers AIChE J, 2011

Variability of ozone in the marine boundary layer of the equatorial Pacific Ocean

This study examines the processes controlling the diurnal variability of ozone (O3) in the marine boundary layer of the Kwajalein Atoll, Republic of the Marshall Islands (latitude 8° 43′ N, longitude 167° 44′ E), during July to September 1999. At the study site, situated in the equatorial Pacific Ocean, O3 mixing ratios remained low, with an overall average of 9–10 parts per billion on a volume basis (ppbv) and a standard deviation of 2.5 ppbv. In the absence of convective storms, daily O3 mixing ratios decreased after sunrise and reached minimum during the afternoon in response to photochemical reactions. The peak-to-peak amplitude of O3 diurnal variation was approximately 1–3 ppbv. During the daytime, O3 photolysis, hydroperoxyl radicals, hydroxyl radicals, and bromine atoms contributed to the destruction of O3, which explained the observed minimum O3 levels observed in the afternoon. The entrainment of O3-richer air from the free troposphere to the local marine boundary layer provided a recovery mechanism of surface O3 mixing ratio with a transport rate of 0.04 to 0.2 ppbv per hour during nighttime. In the presence of convection, downward transport of O3-richer tropospheric air increased surface O3 mixing ratios by 3–12 ppbv. The magnitude of O3 increase due to moist convection was lower than that observed over the continent (as high as 20–30 ppbv). Differences were ascribed to the higher O3 levels in the continental troposphere and weaker convection over the ocean. Present results suggest that moist convection plays a role in surface-level O3 dynamics in the tropical marine boundary layer.

Buoyancy-driven convection around exothermic autocatalytic chemical fronts traveling horizontally in covered thin solution layers

Spatial variations of concentrations and temperature across exothermic chemical fronts can initiate buoyancy-driven convection. We investigate here theoretically the spatiotemporal dynamics arising from such a coupling between exothermic autocatalytic reactions, diffusion, and buoyancy-driven flows when an exothermic autocatalytic front travels perpendicularly to the gravity field in a thin solution layer. To do so, we numerically integrate the incompressible Stokes equations coupled to evolution equations for the concentration of the autocatalytic product and temperature through buoyancy terms proportional to, respectively, a solutal R(C) and a thermal R(T) Rayleigh number. We show that exothermic fronts can exhibit new types of dynamics in the presence of convection with regard to the isothermal system. In the cooperative case (R(C) and R(T) are of the same sign), the dynamics asymptotes to one vortex surrounding, deforming, and accelerating the front much like in the isothermal case. However, persistent local stratification of heavy zones over light ones can be observed at the rear of the front when the Lewis number Le (ratio of thermal diffusivity over molecular diffusion) is nonzero. When the solutal and thermal effects are antagonistic (R(C) and R(T) of opposite sign), temporal oscillations of the concentration, temperature, and velocity fields can, in some cases, be observed in a reference frame moving with the front. The various dynamical regimes are discussed as a function of R(C), R(T), and Le.

Influence of buoyancy-driven convection on the dynamics of A+B→C reaction fronts in horizontal solution layers

The dynamics of initially vertical A + B → C reaction fronts propagating in covered horizontal solution layers can be influenced by buoyancy-driven convection. Experiments have provided evidence that a much faster propagation of the front occurs in solutions than that predicted by reaction–diffusion (RD) theories, thereby suggesting the influence of convective effects arising if A, B, and C have different densities. Here we analyze numerically and theoretically the dynamics resulting from the coupling of a simple A + B → C chemical reaction with diffusion and convection induced by density differences across the reaction front. The important parameters of the related reaction–diffusion–convection (RDC) model are the three dimensionless Rayleigh numbers, quantifying the contribution of each species concentration to the density of the solution, the layer thickness, and the initial reactant concentration ratio. The presence of buoyancy-driven convection at the front induces a propagation of this front even in the case of equal diffusion coefficients and equal initial reactant concentrations for which RD theories predict a non-moving front. In the case of equal initial concentrations, even in the presence of convection, the classification of the various possible dynamics and the prediction of the direction of front propagation can be obtained from simple criteria on the Rayleigh numbers. In the case of different initial reactant concentrations for which, in the absence of convection, the RD front propagates towards the side of the less concentrated reactant, the introduction of buoyancy convection not only invalidates the long time RD scalings but can lead to a double reversal in the direction of propagation of the reaction front for intermediate times. The influence of the different parameters on the RDC dynamics is presented.

Transporting passive additives in a turbulent medium under convective mixing

The vertical transport of passive additives in a medium in the presence of both turbulent and convective mixing is studied. It is shown that, despite the fact that turbulent and convective fluxes are uncorrelated, no additive mechanism of mixing exists. On the basis of a theoretical model and a comparison with model calculations, it is shown that, in the presence of both turbulent and convective mixing in a medium, the effect of the interference of turbulent and convective transport mechanisms takes place. This effect is manifested in the following way: the presence of convection decreases the coefficient of turbulent transport and the presence of turbulence decreases the coefficient of convective transport; in this case, this effect depends on the parameter of the inhomogeneity (extension) of convective fluxes. The relative contribution of each of the mechanisms to the total transport is estimated. It is shown that the interference of turbulence and convection results in an anisotropy of the coefficient of turbulent transport in an isotropic turbulent velocity field. The effect of the coefficient of molecular diffusion is assumed to be negligibly small, and its effect is not taken into consideration when analyzing model results. The interference of the turbulent and convective mechanisms of transport is explained by the inclusion of an additional mechanism that decreases the distance of linear particle propagation.

Effect of static magnetic field on a thermal conductivity measurement of a molten droplet using an electromagnetic levitation technique

Recently, a novel method of measuring the thermophysical properties, particularly thermal conductivity, of high-temperature molten materials using the electromagnetic levitation technique has been developed by Kobatake et al. [H. Kobatake, H. Fukuyama, I. Minato, T. Tsukada, S. Awaji, Noncontact measurement of thermal conductivity of liquid silicon in a static magnetic field, Appl. Phys. Lett. 90 (2007) 094102]; this method is based on a periodic laser-heating method, and entails the superimposing of a static magnetic field to suppress convection in an electromagnetically levitated droplet. In this work, to confirm the fact that a static magnetic field really suppresses convection in a molten silicon droplet in an electromagnetic levitator, numerical simulations of convection in the droplet and periodic laser heating in the presence of convection have been carried out. Here, the convections driven by buoyancy force, thermocapillary force due to the temperature dependence of the surface tension on the melt surface, and electromagnetic force in the droplet were considered. As a result, it was found that applying a static magnetic field of 4 T can suppress convection in a molten silicon droplet enough to measure the real thermal conductivity of molten silicon.

Weak solvability for equations of viscoelastic diffusion in polymers with variable coefficients

Diffusion of a penetrant liquid in a polymer does not satisfy Fick's law but requires viscoelastic mechanisms for its description. We study the system of differential equations for such a diffusion in the presence of convection. We construct weak solutions to the initial–boundary value problem for this system in a bounded domain.

Dynamics ofA+B→CReaction Fronts in the Presence of Buoyancy-Driven Convection

The dynamics of A+B-->C fronts in horizontal solution layers can be influenced by buoyancy-driven convection as soon as the densities of A, B, and C are not all identical. Such convective motions can lead to front propagation even in the case of equal diffusion coefficients and initial concentration of reactants for which reaction-diffusion (RD) scalings predict a nonmoving front. We show theoretically that the dynamics in the presence of convection can in that case be predicted solely on the basis of the knowledge of the one-dimensional RD density profile across the front.

Limit cycles in the presence of convection: A traveling wave analysis

We consider a diffusion model with limit cycle reaction functions. In an unbounded domain, diffusion spreads the pattern outwards from the source. Convection adds instability to the reaction-diffusion system. The result of this instability is a readiness to create a pattern. We choose the Lambda-Omega reaction functions for their simple limit cycle. We carry out a transformation of the dependent variables into polar form. From this we consider the initiation of the pattern to approximate a traveling wave. We carry out numerical experiments to test our analysis. These confirm the premise of the analysis, that the initiation can be modeled by a traveling wave. Furthermore, the analysis produces a good estimate of the numerical results. Most significantly, we confirm that the pattern consists of two different types.

The Impact of Convective Momentum Transport on Tropical Cyclone Track Forecasts Using the Emanuel Cumulus Parameterization

Abstract The influence of convective momentum transport (CMT) on tropical cyclone (TC) track forecasts is examined in the Navy Operational Global Atmospheric Prediction System (NOGAPS) with the Emanuel cumulus parameterization. Data assimilation and medium-range forecast experiments show that for 35 tropical cyclones during August and September 2004 the inclusion of CMT in the cumulus parameterization significantly improves the TC track forecasts. The tests show that the track forecasts are very sensitive to the magnitude of the Emanuel parameterization’s convective momentum transport parameter, which controls the CMT tendency returned by the parameterization. While the overall effect of this formulation of CMT in NOGAPS data assimilation/medium-range forecasts results in the surface pressure of tropical cyclones being less intense (and more consistent with the analysis), the parameterization is not equivalent to a simple diffusion of winds in the presence of convection. This is demonstrated by two data assimilation/medium-range forecast tests in which a vertical diffusion algorithm replaces the CMT. Two additional data assimilation/medium-range forecast experiments were conducted to test whether the skill increase primarily comes from the CMT in the immediate vicinity of the tropical cyclones. The results show that the inclusion of the CMT calculation in the vicinity of the TC makes the largest contribution to the increase in forecast skill, but the general contribution of CMT away from the TC also plays an important role.

Entropy generation in double diffusive convection in presence of the Soret effect

Influence of the Soret effect on entropy generation in a square cavity filled with a binary gas mixture in double diffusive convection is numerically studied. It was found that entropy generation increases with the increase of thermal diffusion and buoyancy ratios for fixed thermal Grashof number. Total irreversibility takes a minimum value at a special buoyancy ratio ranging between 1 and 0. Soret effect causes the increase of total irreversibility by more than 50% at higher values of thermal Grashof number and buoyancy ratio. More details of the irreversibilities localisation are discussed.

Equation of convective diffusion of a multicomponent mixture in a capillary for an arbitrary velocity field

It is shown that the convective transport in a binary mixture in the presence of vortex convection can be described in terms of Fick’s law with an effective diffusion coefficient independent of the concentration. The form of the effective diffusion coefficient is found for arbitrary convection in the mixture. A generalization of the Stefan-Maxwell diffusion equation is proposed to include an arbitrary rotational mixture velocity field. The characteristics of convective transport are considered with reference to a three-component mixture. A solution of the equation of three-component mixture transport through a long capillary in the presence of convection homogeneous along the capillary axis is presented. It is established that for sharply different component diffusion coefficients a mixture density extremum may appear inside the capillary and then change or disappear depending on the convective flow intensity.

Limit cycles in the presence of convection: a first-order analysis

We consider a diffusion model with limit cycle reaction functions. In an unbounded domain, diffusion spreads pattern outwards from the source. Convection adds instability to the reaction–diffusion system. We see the result of the instability in a readiness to create pattern. In the case of strong convection, we consider that the first-order approximation may be valid for some aspects of the solution behaviour. We employ the method of Riemann invariants and rescaling to transform the reduced system into one invariant under parameter change. We carry out numerical experiments to test our analysis. We find that most aspects of the solution do not comply with this, but we find one significant characteristic which is approximately first order. We consider the correspondence of the Partial Differential Equation with the Ordinary Differential Equation along rays from the initiation point in the transformed system. This yields an understanding of the behaviour.

Role of convection in global‐scale transport in the troposphere

The role of convection in global‐scale transport in the troposphere is studied by using climatological Green's functions of the mass conservation equation for a conserved, passive tracer. The Green's functions are calculated from long‐term atmospheric trajectory calculations based on three‐dimensional winds from a 19‐year simulation by Version 3 of the NCAR Community Climate Model (CCM3). Two trajectory calculations are compared: one that includes the effects of the model's parameterized convection and one that neglects the convective transport. The global transport properties of the two cases are qualitatively similar. The global troposphere can be divided into three parts: the tropics, and the Northern and Southern Hemisphere extratropics. Transport within each region is rapid, while the exchange of air between the regions is comparatively slow. Semipermeable barriers to transport exist in the subtropics in both cases. Convection slightly suppresses transport across the subtropical barriers. Convective transport enhances the vertical dispersion of air parcels, particularly in the rising branch of the Hadley circulation. Localized differences between the two runs can reach 50–80%. The differences are largest in the upper troposphere. Interannual transport variations related to the El Niño–Southern Oscillation (ENSO) phase can be detected in both cases, with the vertical transport being enhanced in the presence of convection.

The signature of mid‐latitude convection observed by VHF wind‐profiling radar

The signature of mid‐latitude convection observed by a 46.5 MHz wind‐profiling radar at Aberystwyth, UK (52.4°N, 4.0°W), is demonstrated by way of a case study. A key feature of such radars is their ability to measure the vertical air velocity directly, even under conditions of precipitation. Higher frequency radars, which have more typically been used for such studies, measure the net effect of hydrometeor terminal velocities and the air motion under such conditions. The radar is capable of observing both updrafts and downdrafts, with peak updrafts of the order of 10 m s−1. The signature of convection additionally consists of enhanced values of the radar return spectral width, which cannot be interpreted in terms of turbulence intensity, and reduced reliability of the corresponding radar‐derived horizontal wind components. When convection reaches the uppermost troposphere, the radar return signal power can be anomalously large leading to the radar‐derived tropopause altitude being overestimated. The presence of convection is confirmed by thermal infrared satellite imagery of high‐topped clouds. Use is also made of radiosonde and UHF wind‐profiler data.

Modelling Columnar Dendritic Growth into an Undercooled Metallic Melt in the Presence of Convection

of the alloy latent heat of fusion is included in this single-domain model through a careful definition of source terms in the energy conservation equation to account for both the advance of solidification front and subsequent thickening of the mushy zone within a control volume. The model is compared with the enthalpy approach showing its superiority in the detection of the undercooled liquid zone and, thus, in potentially modelling of columnar/equiaxed grain structures. It is used to predict the influence of both alloy composition and convective heat transfer coefficient on the size of the undercooled liquid zone in front of columnar dendrite tips during solidification of Al–Cu in a square mould. The predictions obtained confirm that natural convection in the melt reduces local temperature gradients and thus widens the undercooled liquid zone ahead of a curve joining columnar dendrite tips, increasing the potential for growth of equiaxed grains.

Modeling of dendritic growth in the presence of convection

A two-dimensional coupling modified cellular automatons (MCA)-transport model has been employed to investigate the asymmetrical dendritic growth behavior in a flowing melt. In the present model, the cellular automaton method for crystal growth is incorporated with a transport model, for numerical calculating of the fluid flow and mass transport by both convection and diffusion. The MCA takes into account the effects of the thermal, the constitutional and the curvature undercoolings on dendritic growth. It also considers the preferred growth orientation of crystal and solute redistribution during solidification. In the transport model, the SIMPLE scheme and a fully implicit finite volume method are employed to solve the governing equations of momentum and species transfers. The present model was applied to simulating the evolution of a single dendrite and multi-dendrites of an Al-3mass%Cu alloy in a forced flow. The simulated results show that dendritic growth morphology is strongly influenced by melt convection.