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Showing papers on "Combined forced and natural convection published in 1995"


Journal ArticleDOI
TL;DR: In this paper, Jive k-e, two-equation models are evaluated for their performance in predicting natural convection, forced convection and mixed convection in rooms, as well as an impinging jet flow.
Abstract: In this article, Jive k-e, two-equation models are studied: the standard k-e model, a low-Reynolds-number k-e model, a two-layer k-e model, a two-scale k-e model, and a renormalization group (RNG) k-e model. They are evaluated for their performance in predicting natural convection, forced convection, and mixed convection in rooms, as well as an impinging jet flow. Corresponding experimental data from the literature are used for validation. It is found that the prediction of the mean velocity is more accurate than that of the turbulent velocity. These models are neither able to predict anisotropic turbulence correctly nor to pick up the secondary recirculation of indoor air flow; otherwise the performance of the standard k-e model is good. The RNG k-e model is slightly better than the standard k-e model and is therefore recommended for simulations of indoor airflow. The performance of the other models is not stable.

686 citations


Journal ArticleDOI
TL;DR: In this article, a simple scaling analysis of temperature and stress-dependent viscosity convection with free-slip boundaries suggests three convective regimes: the small contrast regime, the transitional regime, and the asymptotic regime.
Abstract: Simple scaling analysis of temperature‐ and stress‐dependent viscosity convection with free‐slip boundaries suggests three convective regimes: the small viscosity contrast regime which is similar to convection in a fluid whose viscosity does not depend on temperature, the transitional regime characterized by self‐controlled dynamics of the cold boundary layer and the asymptotic regime in which the cold boundary becomes stagnant and convection involves only the hottest part of the lid determined by a rheological temperature scale. The first two regimes are usually observed in numerical experiments. The last regime is similar to strongly temperature‐dependent viscosity convection with rigid boundaries studied in laboratory experiments.

598 citations


Journal ArticleDOI
TL;DR: In this article, a finite element multigrid scheme was employed for large viscosity variations and convection with up to 1014 contrasts was systematically investigated in a 2D square cell with free slip boundaries.
Abstract: Previous experimental studies of convection in fluids with temperature‐dependent viscosity reached viscosity contrasts of the order of 105. Although this value seems large, it still might not be large enough for understanding convection in the interiors of Earth and other planets whose viscosity is a much stronger function of temperature. The reason is that, according to theory, above 104–105 viscosity contrasts, convection must undergo a major transition—to stagnant lid convection. This is an asymptotic regime in which a stagnant lid is formed on the top of the layer and convection is driven by the intrinsic, rheological, temperature scale, rather than by the entire temperature drop in the layer. A finite element multigrid scheme appropriate for large viscosity variations is employed and convection with up to 1014 viscosity contrasts has been systematically investigated in a 2D square cell with free‐slip boundaries. We reached the asymptotic regime in the limit of large viscosity contrasts and obtained s...

509 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the idea of formulating free convection in large-scale models as a special case of forced convection and showed that the wind speed in the surface transfer law is related to the velocity of the large eddies in the mixed layer and is proportional to the convection velocity scale.
Abstract: This paper investigates the idea of formulating free convection in large-scale models as a special case of forced convection. In free convection, the wind speed in the surface transfer law is related to the velocity of the large eddies in the mixed layer and is proportional to the convection velocity scale. The empirical coefficient is estimated with the help of large eddy simulation data by Sykes et al. (1993) and the resulting formulation is compared with field data by Stull (1994). This concept is shown to be applicable to smooth ocean surfaces as well as rough land surfaces. It is argued that within this framework, free convection is a natural extension of forced convection and only needs a minor modification of traditional transfer laws.

499 citations


Journal ArticleDOI
TL;DR: In this paper, a finite difference scheme consisting of modified ADI (Alternating Direction Implicit) method and SLOR (Successive Line Over Relaxation) method is used to solve the vorticity-stream function formulation of the problem.

484 citations


Journal ArticleDOI
TL;DR: In this article, a closed system of equations and boundary conditions is derived that governs core convection and the geodynamo, and it is concluded that compositional convection may not dominate thermal convection, as had previously been argued by Braginsky.
Abstract: Convection in Earth's fluid core is regarded as a small deviation from a well-mixed adiabatic state of uniform chemical composition. The core is modeled as a binary alloy of iron and some lighter constituent, whose precise chemical composition is unknown but which is here assumed to be FeAd, where Ad = Si, O or S. The turbulent transport of heat and light constituent is considered, and a simple ansatz is proposed in which this is modeled by anisotropic diffusion. On this basis, a closed system of equations and boundary conditions is derived that governs core convection and the geodynamo. The dual (thermal + compositional) nature of core convection is reconsidered. It is concluded that compositional convection may not dominate thermal convection, as had previously been argued by Braginsky (Soviet Phys. Dokl., v. 149, p. 8, 1963; Geomag, and Aeron., v. 4, p. 698, 1964), but that the two mechanisms are most probably comparable in importance. The key parameters leading to this conclusion are isolated...

483 citations


Book
01 Feb 1995
TL;DR: In this article, Navier-Stokes and Pohlhausen provided an energy equation for Laminar Boundary-Layer Equations of the Boundary Layer and Energy Equation Problems.
Abstract: Foundations of Heat Transfer Nomenclature Introductory Remarks Modes of Heat Transfer Continuum Concept Some Definitions and Concepts of Thermodynamics General Laws Particular Laws Problems References Suggested Reading Governing Equations of Convective Heat Transfer Nomenclature Introduction Continuity Equation Momentum Equations Energy Equation Discussion of the Fundamental Equations Similarities in Fluid Flow and Heat Transfer Problems References Boundary-Layer Approximations for Laminar Flow Nomenclature Introduction Momentum Equations of the Boundary Layer Boundary-Layer Energy Equation Problems References Heat Transfer in Incompressible Laminar External Boundary Layers: Similarity Solutions Nomenclature Introduction Laminar Velocity Boundary Layer Thermal Boundary Layer Fluid Friction and Heat Transfer Flows with Pressure Gradients Problems References Integral Method Nomenclature Introduction Momentum Integral Equation Energy Integral Equation Laminar Forced Flow over a Flat Plate Thermal Boundary Layer on an Isothermal Flat Plate Thermal Boundary Layer on a Flat Plate with Constant Surface Heat Flux Flat Plate with Varying Surface Temperature Flows with Pressure Gradient Problems References Laminar Forced Convection in Pipes and Ducts Nomenclature Introduction Laminar and Turbulent Flows in Ducts Some Exact Solutions of Navier-Stokes Equations Friction Factor Noncircular Cross-Sectional Ducts Laminar Forced Convection in Ducts Thermal Boundary Conditions Laminar Forced Convection in Circular Pipes with Fully Developed Conditions Laminar Forced Convection in the Thermal Entrance Region of a Circular Duct Laminar Flow Heat Transfer in the Combined Entrance Region of Circular Ducts Laminar Convective Heat Transfer between Two Parallel Plates Integral Method Asymptotic Values of Heat-Transfer Coefficients in Ducts Effect of Circumferential Heat-Flux Variation Heat Transfer in Annular Passages Problems References Forced Convection in Turbulent Flow Nomenclature Introduction Governing Equations with Steady Turbulent Flow Turbulence Models Velocity Distribution in Turbulent Flow Friction Factors for Turbulent Flow Analogies between Heat and Momentum Transfer Further Analogies in Turbulent Flow Turbulent Heat Transfer in a Circular Duct with Variable Circumferential Heat Flux Turbulent Heat Transfer in Annular Passages Effect of Boundary Conditions on Heat Transfer Turbulent Flow on a Flat Plate Problems References Unsteady Forced Convection in Ducts Nomenclature Introduction Transient Laminar Forced Convection in Ducts Transient Turbulent Forced Convection in Ducts Analysis of Transient Forced Convection for Timewise Variation of Inlet Temperature Problems References Empirical Correlations for Single-Phase Forced Convection in Ducts Nomenclature Introduction Dimensional Analysis of Forced Convection Laminar Forced Convection Effects of Variable Physical Properties Turbulent Forced Convection Turbulent Flow in Smooth Straight Noncircular Ducts Effects of Variable Physical Properties in Turbulent Forced Convection Liquid Metal Heat Transfer Summary Problems References Heat Transfer in Natural Convection Nomenclature Introduction Basic Equations of Laminar Boundary Layer Pohlhausen Solution for Laminar Boundary Layer over a Constant Temperature Vertical Flat Plate Exact Solution of Boundary-Layer Equations for Uniform Heat Flux Inclined and Horizontal Surfaces Property Variation in Free Convection Approximate Solution of Laminar Free Convection on a Vertical Plate: Von Karman-Pohlhausen Integral Method Turbulent Heat Transfer on a Vertical Plate Dimensional Analysis in Natural Convection Interferometric Studies Natural Convection in Enclosed Spaces Correlations for Natural Convection in Enclosures Combined Free and Forced Convection Problems References Heat Transfer in High-Speed Flow Nomenclature Introduction Stagnation Temperature Adiabatic Wall Temperature and Recovery Factor Governing Equations in High-Velocity Flow Thermal Boundary Layer over a Flat Plate in High-Speed Flow Heat Transfer in 2D Turbulent Boundary Layers Problems References Convective Heat Transfer in Microchannels Nomenclature Introduction Definitions in Microchannels Convective Heat Transfer for Gaseous Flow in Microchannels Effects of Temperature Jump Effects of Viscous Dissipation Effects of Channel Roughness Effects of Variable Fluid Properties Empirical Correlations for Gaseous Forced Convection in Microchannels Empirical Correlations for Liquid Forced Convection in Microchannels Problems References Enhancement of Convective Heat Transfer with Nanofluids Nomenclature Introduction Nanofluid Convective Heat-Transfer Modeling Empirical Correlation for Single-Phase Forced Convection with Nanofluids Problems References Appendices Index

251 citations


Journal ArticleDOI
TL;DR: In this article, the quasiequilibrium hypothesis is used to show that convection is initiated in the boundary layer when the boundary-layer equivalent potential temperature exceeds a threshold value that is determined by conditions just above cloud base.
Abstract: The mechanisms that regulate moist convection over the warm tropical oceans are not well understood. One school of thought holds that convection is caused by the convergence of moisture, which in turn is produced by an independent dynamical mechanism. Another school maintains that convection occurs as needed to just balance the production of convective instability and that the timescales to establish this balance is much less than the timescales of tropical disturbances. This is called the quasiequilibrium hypothesis. This paper explores how convection is actually governed over the west Pacific warm pool. Convection appears to be initiated there when the boundary-layer equivalent potential temperature exceeds a threshold value that is determined by conditions just above cloud base. Given known surface flux values and the propensity for convection to inject low equivalent potential temperature air into the boundary layer, it is shown that under most circumstances convection is regulated by a balan...

239 citations


Journal ArticleDOI
TL;DR: Convection generated by electric fields can also be important in electrodeposition experiments; the measured electroconvective velocities are found to be much smaller than those predicted by the theory of Fleury and Chazalviel.
Abstract: Measurements of fluid motion during thin-layer electrochemical growth reveal that convection arising from concentration gradients that are transverse to gravity is immediate and substantial for experimental conditions typical to many studies in the literature. A particle tracking technique is used to determine and follow the time evolution of the convective velocity field. The contribution of buoyancy driven convection to local and global transport is compared to that arising from diffusion. A transition is observed from a regime in which the convection rolls near each electrode grow as ${\mathit{t}}^{4/5}$ to a regime with the roll size growing as ${\mathit{t}}^{1/2}$. Convection generated by electric fields can also be important in electrodeposition experiments; the measured electroconvective velocities are found to be much smaller than those predicted by the theory of Fleury and Chazalviel.

127 citations


Journal ArticleDOI
TL;DR: In this paper, an experimental investigation on heat transfer behavior during forced convection condensation inside a horizontal tube for wavy, semi-annular and annular flows is presented.
Abstract: This paper presents the results of an experimental investigation on heat transfer behaviour during forced convection condensation inside a horizontal tube for wavy, semi-annular and annular flows. A qualitative study was made of the effect of various parameters - refrigerant mass flux, vapour quality, condensate film temperature drop and average vapour mass velocity - on average condensing heat transfer coefficient. Akers-Rosson correlations have been found to predict the heat transfer coefficients within ±25% for the entire range of data. A closer examination of the data revealed that the nature of the relation for the heat transfer coefficient changes from annular and semi-annular flow to wavy flow. Akers-Rosson correlations with changed constant and power have been recommended for the two flow regimes.

99 citations


Journal ArticleDOI
TL;DR: In this article, the effect of magnetic field strength on the local Nusselt number and local wall shear stress in the mixed convection regime was investigated. But the authors focused on the non-Darcian model including both the inertial and boundary effects.
Abstract: Magnetohydrodynamic mixed convection flow about a vertical flat plate embedded in a porous medium is considered. The effect of the magnetic field strength on the local Nusselt number and local wall shear stress is presented. The non-Darcian model including both the inertial and boundary effects is used. A particular transformation for the governing equations is adopted to cover the whole mixed convection regime within two finite limits. Appreciable effects of the magnetic field strength on the local Nusselt number as well as on the local wall shear stress in the mixed convection regime are found.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated how multiple steady states arise in an ocean general circulation model, caused by the fact that many different convection patterns can be stable under the same surface boundary conditions.
Abstract: This paper investigates how multiple steady states arise in an ocean general circulation model, caused by the fact that many different convection patterns can be stable under the same surface boundary conditions. Two alternative boundary conditions are used in the experiments: classical mixed boundary conditions and a diffusive atmospheric heat balance combined with fixed salt fluxes. In both cases, transitions between different quasi-steady convection patterns can be triggered by briefly adding fresh water at convection sites. Either a large-scale freshwater anomaly is used to completely erase the previous convection pattern or a “surgical” anomaly is added to single grid points to turn off convection there. Under classical mixed-boundary conditions, different convection sites can lead to different overturning rates of deep water. The dynamics of the convection-driven flow is analyzed in some detail. With an energy balance atmosphere, in contrast, the overturning rate is very robust, apparently ...

Journal ArticleDOI
TL;DR: A flow regime map for determination of the boundary between forced and mixed convection in a horizontal circular straight tube with reentrant, square-edged, and bellmouth inlets under uniform wall heat flux boundary condition is developed in this article.

Journal ArticleDOI
TL;DR: In this paper, the effect of free and forced convection on crystal dissolution was examined both theoretically and experimentally, and well-established relationships for heat and mass transfer were applied to obtain approximate expressions for the dissolution velocity and the associated thickness of the compositional boundary layer.
Abstract: The effect of free and forced convection on crystal dissolution is examined both theoretically and experimentally. Well-established relationships for heat and mass transfer are applied to obtain approximate expressions for the dissolution velocity and the associated thickness of the compositional boundary layer. These expressions are found to be in good agreement with experimental observations of the dissolution of quartz crystals in basalt and NaCl crystal in water. When applied to light felsic crystals in basaltic magmas, the expressions predict that forced convection will produce a boundary layer thickness of about 100 μm and a dissolution velocity of order 10−6 cm s−1. These velocities are too slow for xenocrysts to be dissolved significantly during magma ascent in dykes, but are sufficient for cm-size crystals to dissolve in the interior of a convecting magma chamber. Larger crystals are likely to accumulate at the chamber's roof, where free convection is predicted to dissolve them at velocities of order 10−7 cm s−1. In an Appendix, the dissolution of the chamber's walls is also considered, and a velocity of order 10−8cm s−1 is predicted.

Journal ArticleDOI
TL;DR: In this article, the heat transfer conditions encountered during hot rolling of steel strip are modelled; it is assumed that the strip loses heat by radiation and convection to the atmosphere, conduction to the work rolls, forced convection and boiling of the water employed in descaling, whereas it gains heat during deformation.
Abstract: The heat transfer conditions encountered during hot rolling of steel strip are modelled; it is assumed that the strip loses heat by radiation and convection to the atmosphere, conduction to the work rolls, forced convection and boiling of the water employed in descaling, whereas it gains heat during deformation. Conduction within the stock is calculated by means of a two-dimensional explicit finite-difference algorithm. The simulation is conducted assuming the existence of an isolating oxide layer, which controls the conduction to the work rolls during the reduction. Results from the simulations compare well with data obtained during actual production in an industrial mill.

Journal ArticleDOI
TL;DR: In this paper, the effect of Rayleigh's vortical acoustic streaming that appears in the region between the plates as a result of the sound wave leading to forced heat convection was analyzed theoretically.

01 Jan 1995
TL;DR: SAINTS as discussed by the authors is a PC-Aided Numerical Heat Transfer (NHT) system that is used in the SAINTS Load Module "Wind Tunnel Simulator" to simulate the flow and heat transfer in Porous media.
Abstract: Introduction Background PC-Aided Numerical Heat Transfer Outline of the Book Governing Equations for Flow and Heat Transfer Transformation From the System Form to the Control Volume Form Equation of Continuity Momentum Equation Energy Equation Complete Set of Governing Equations and Their Simplified Form General Transport Equation Analytical Treatments for Boundary Layer Equations Numerical Integration of Ordinary Differential Equations Transient Conduction in a Semi-Infinite Solid Boundary Layer Approximation for Heat and Fluid Flow Forced Convection From Concentrated Heat Sources Laminar Forced Convection From Plane Bodies Laminar Forced Convection From Axisymmetric Bodies Asymptotic Solutions for Forced Convection of Small and Large Prandtl Number Fluids Integral Method for Laminar Forced Convection Laminar Free Convection From Plane Bodies Integral Method for Laminar Free Convection Transport Equations for Modeling Turbulence Reynolds-Averaged Navier-Stokes Equation and Energy Equation Effective Viscosity Formulation and Mixing Length Models Wall Laws for Turbulent Shear Flows Turbulent Free jets Reynolds Stress Transport Equation Turbulence Kinetic Energy Transport Equation and Two-Equation Model Low Reynolds Number Model and High Reynolds Number Model Convective Flows in Porous Media Darcy's Law Modified Darcy's Laws Volume-Averaged Navier-Stokes Equation Volume-Averaged Energy Equation Effects of Channeling and Thermal Dispersion Magnitude Analysis on Boundary Layer Equations for Porous Media Darcy-Forchheimer Boundary Layer Equations Simple Flow Cases: Isothermal Flat Plates Modified Peclet Number and Flow Regime Map Unified Treatment for Darcy-Forchheimer Boundary Layer Equations Forced Convection Regime Darcy Free Convection Regime Forchheimer Free Convection Regime Intermediate Flow Regimes Convective Flows Over an Impermeable Horizontal Surface Buoyancy-Induced Flows From Concentrated Heat Sources Boundary Layer Flow and Heat Transfer in Highly Porous Media Description of Numerical Solution Procedure Basic Concept of Discretization Governing Equations and Auxiliary Relationships General Form of Governing Equations: General Transport Equation Coordinate System and Normalization Discretization of General Transport Equation Staggered Grid and Discretized Momentum Equations Pressure Correction Procedure: SIMPLE High Flux Modification: Hybrid Difference Scheme Solution of Discretized Equations PC Program "SAINTS" For Conduction and Convection Problems Overall Aspect of the Program "SAINTS" Classification of Boundaries Specification of Non-Zero Boundary Values Along the Known-Velocity Boundary Description of the Program "SAINTS" Input Procedure: Input Data and Problem-Dependent Subprograms Layout of Output Illustrative Applications of "SAINTS" Applications of the SAINTS Load Module "Wind Tunnel Simulator" Illustrative Applications to Conduction Problems Further Application of SAINTS to Complex Turbulent Flows Applications to Convection Problems in Porous Media Concluding Remarks Appendices Important Dimensionless Numbers Potential Flow Analysis Based on Source-and-Sink Method Listing of Program "SAINTS" Listing of Problem Dependent Subroutine "USERIN" Input Data for Forced Convection in a Tube Sample Output of Program "SAINTS" Program Instructions References Index

Journal ArticleDOI
TL;DR: In this article, a numerical simulation of the turbulent transport from an isolated heat source in a square cavity with side openings is presented, by employing a suitable, high-Reynolds-number form of the K-E turbulence model.
Abstract: A numerical simulation of the turbulent transport from an isolated heat source in a square cavity with side openings is presented in this work. The openings allow an externally induced air stream at ambient temperature to flow through the cavity and, thus, mixed convection arises. Results for the turbulent regime are obtained, by employing a suitable, high-Reynolds-number form of the K-E turbulence model. A stream junction-vorticity mathematical formulation is used, along with the kinetic energy and dissipation rate equations and an expression for the eddy viscosity. A time-marching scheme is employed, using the ADI method. The values of the Reynolds number Re, associated with the external flow, and the Grashof number Gr, based on the heat flux from the source, for which turbulent flow sets in are sought. Two typical values of the Reynolds number are chosen, Re = 1000 and Re = 2000, and turbulent results are obtained in the range Gr = 5 X 10{sup 7}-5 X 10{sup 8}. For both values of Re, the average Nusselt number over the surface of the source is found to vary with Gr in a fashion consistent with previous numerical and experimental results for closed cavities, while the effect of Remore » in the chosen range of values was small. 25 refs., 11 figs., 2 tabs.« less


Journal ArticleDOI
Adrian Bejan1
TL;DR: In this paper, a new fundamental aspect of the heat transfer performance of a bundle of parallel cylinders with crossflow forced convection, namely, the maximization of the thermal contact between the bundle and the fluid, when the volume occupied by the bundle is fixed, is discussed.
Abstract: In this note I draw attention to a new fundamental aspect of the heat transfer performance of a bundle of parallel cylinders with crossflow forced convection, namely, the maximization of the thermal contact between the bundle and the fluid, when the volume occupied by the bundle is fixed. In the experiments described by Jubran et al. we have seen empirical evidence that the total heat transfer rate is maximum when the cylinder-to-cylinder spacing S has a certain value. This finding is important because it has been overlooked for decades, while forced convection from cylinders in crossflow grew into one of the most researched topics in heat transfer. 8 refs., 3 figs.

Journal ArticleDOI
TL;DR: In this article, a numerical simulation based on finite difference techniques has been developed in order to analyse turbulent natural and mixed convection of air in internal flows, restricted to two-dimensional cavities with the possibility of inlet and outlet ports, and with internal heat sources.
Abstract: In this paper a numerical simulation, based on finite difference techniques, has been developed in order to analyse turbulent natural and mixed convection of air in internal flows. The study has been restricted to two‐dimensional cavities with the possibility of inlet and outlet ports, and with internal heat sources. Turbulence is modelled by means of two‐equation k‐e turbulence models, both in the simplest form using wall functions and in the more general form of low‐Reynolds‐number k‐e models. The couple time average governing equations (continuity, momentum, energy, and turbulence quantities) are solved in a segregated manner using the SIMPLEX method. An implicit control volume formulation of the differential equations has been employed. Some illustrative numerical results are presented to study the influence of geometry and boundary conditions in cavities. A comparison of different k‐e turbulence models has also been presented.

Journal ArticleDOI
TL;DR: This work investigates the onset of convection for chemical-wave propagation in the Belousov-Zhabotinsky reaction based on the two-variable Oregonator model coupled with the fluid dynamic equations and results are compared with experiments.
Abstract: We investigate the onset of convection for chemical-wave propagation in the Belousov-Zhabotinsky reaction based on the two-variable Oregonator model coupled with the fluid dynamic equations. For chemical waves in a vertical slab, two-dimensional convection occurs only for slab widths greater than a critical threshold width. The convective threshold is different for ascending and descending waves. Convectionless waves are flat and propagate with constant speed. Above the onset of convection, the wave velocity increases and the flat wave deforms due to two counterrotating steady rolls. For a horizontal slab, convection is always present and the wave velocity increases with increasing slab width. Our results are compared with experiments.

Journal ArticleDOI
TL;DR: In this article, the effect of combined buoyancy forces of thermal and mass diffusion on turbulent forced convection heat and mass transfer in downward flow were numerically examined in detail for air-water system under different conditions.

Journal ArticleDOI
TL;DR: In this paper, the effect of variable viscosity is more pronounced on the friction factor than on Nusselt numbers, and the results indicate that the effects of inlet Rayleigh number and inlet velocity profile only exist in the near-inlet region.

Journal ArticleDOI
TL;DR: In this article, a mathematical vent flow model is proposed to calculate flow through shallow, horizontal, circular vents under high-Grashof-number conditions, where the vent-connected spaces are filled with fluids of different density in an unstable configuration.
Abstract: Combined buoyancy and pressure-driven (i.e., forced) flow through a horizontal vent is considered where the vent-connected spaces are filled with fluids of different density in an unstable configuration (density of the top is larger than that of the bottom). With zero-to-moderate cross-vent pressure difference, Δp, the instability leads to bidirectional exchange flow between the two spaces, e.g., as in the emptying from the bottom of a liquid-filled can with a single vent opening. For relatively large Δp, the flow through the vent is unidirectional, from the high to the low-pressure space, e.g., as is the case when the can has a large enough second vent at the top. Problems of a commonly used unidirectional orifice vent flow model, with Bernoulli's equation and a constant flow coefficient, C D , are discussed. First, the orifice model does not predict bidirectional flows at zero-to-moderate Δp. Also, when Δp exceeds the critical value, Δp FL , which defines the onset of unidirectional or flooding flow, there is a significant dependence of C D on the relative buoyancy of the upper and lower fluids (i.e., C D is not constant). Analysis of relevant boundary value problems and of available experimental data leads to a mathematical vent flow model, which removes the problems of the orifice flow model. The result is a general algorithm to calculate flow through shallow, horizontal, circular vents under high-Grashof-number conditions.

Journal ArticleDOI
TL;DR: The Dufour--induced changes in the bifurcation topology and the existence regimes of stationary and traveling wave convection are elucidated and the scaling behaviour of linear properties of the stationary instability is reported.
Abstract: Linear and nonlinear properties of convection in binary fluid layers heated from below are investigated, in particular for gas parameters. A Galerkin approximation for realistic boundary conditions that describes stationary and oscillatory convection in the form of straight parallel rolls is used to determine the influence of the Dufour effect on the bifurcation behaviour of convective flow intensity, vertical heat current, and concentration mixing. The Dufour--induced changes in the bifurcation topology and the existence regimes of stationary and traveling wave convection are elucidated. To check the validity of the Galerkin results we compare with finite--difference numerical simulations of the full hydrodynamical field equations. Furthermore, we report on the scaling behaviour of linear properties of the stationary instability.

Journal ArticleDOI
TL;DR: In this paper, a numerical study for magnetohydrodynamic free convection of an electrically conducting fluid in a shallow cavity heated from below and cooled from above is presented, where a uniform magnetic field, inclined with an angle 0 with respect to the horizontal plane, is externally imposed.
Abstract: A numerical study is presented for magnetohydrodynamic free convection of an electrically conducting fluid in a shallow cavity heated from below and cooled from above. The side walls are maintained adiabatic. A uniform magnetic field, inclined with an angle 0 with respect to the horizontal plane, is externally imposed. The investigation covers the range of the Rayleigh number, Ra, from 1.8 × 103 to 3 x 104the Hartmann number, Ha, from 0 to 35, the Prandtl number, Pr, from 0.005 to 1 and aspect ratio of the cavity, A = 6. The effect of the magnetic field on the flow structure is presented. For supercritical convection it is found that, upon increasing Ha, the number of roll cells in the cavity increases when it is perpendicular to it. The imposition of an inclined magnetic field gives rise to new flow patterns with tilted lateral cell walls. The effect of both strength and orientation of the magnetic field on the overall heat transfer is found to be significant.

Journal ArticleDOI
TL;DR: In this paper, the authors examined the linear stability of the fully developed mixed-convection flow in a differentially heated tall vertical channel under non-Boussinesq conditions.
Abstract: We have examined the linear stability of the fully developed mixed-convection flow in a differentially heated tall vertical channel under non-Boussinesq conditions. The Three-dimensional analysis of the stability problem was reduced to an equivalent two-dimensional one by the use of Squire's transformation. The resulting eigenvalue problem was solved using an integral Chebyshev pseudo-spectral method. Although Squire's theorem cannot be proved analytically, two-dimensional disturbances are found to be the most unstable in all cases. The influence of the non-Boussinesq effects on the stability was studied. We have investigated the dependence of the critical Grashof and Reynolds numbers on the temperature difference. The results show that four different modes of instability are possible, two of which are new and due entirely to non-Boussinesq effects.

Journal ArticleDOI
TL;DR: In this article, a three-dimensional, spherical-shell model of mantle convection with strongly temperature-dependent viscosity is investigated. But the model is not suitable for the analysis of the Earth's geoid and seismic tomography.
Abstract: We investigate a three-dimensional, spherical-shell model of mantle convection with strongly temperature-dependent viscosity. Numerical calculations of convection in an infinite Prandtl number, Boussinesq fluid heated from below at a Rayleigh number of Ra = 10 5 are carried out for the isoviscous case and for a viscosity contrast across the shell of 1,000. In the isoviscous case, convection is time dependent with quasi-cylindrical upflow plumes and sheet-like downflows. When viscosity varies strongly across the shell, convection is also time dependent, but major quasi-cylindrical downflows with spider-like extensions occur at both poles and interconnected upflow plumes occur all around the equator. The surface expression of mantle convection in the Earth (downwelling sheets at trenches, upwelling plumes at hot spots, and upwelling sheets at midocean ridges) resembles structures seen in both the isoviscous and variable viscosity models. The dominance of spherical harmonic degree l = 2 in the variable viscosity model agrees with the l = 2 dominance in the Earth's geoid, topography, and seismic tomography. The overall pattern of convection in the variable viscosity case is similar to the distribution of major highlands and volcanic rises on Venus.

Journal ArticleDOI
TL;DR: In this paper, a simple model of the influence of natural convection on the selection of the operating state (dendrite tip velocity, V, and tip radius, ϱ) for dendritic growth of a pure material was developed.