Showing papers on "Natural convection published in 1997"
TL;DR: In this article, a two-component lattice Boltzmann equation (LBE) method was used to simulate Rayleigh-B\'enard convection in two and three dimensions.
Abstract: Rayleigh-B\'enard convection is numerically simulated in two and three dimensions using a recently developed two-component lattice Boltzmann equation (LBE) method. The density field of the second component, which evolves according to the advection-diffusion equation of a passive scalar, is used to simulate the temperature field. A body force proportional to the temperature is applied, and the system satisfies the Boussinesq equation except for a slight compressibility. A no-slip, isothermal boundary condition is imposed in the vertical direction, and periodic boundary conditions are used in horizontal directions. The critical Rayleigh number for the onset of the Rayleigh-B\'enard convection agrees with the theoretical prediction. As the Rayleigh number is increased higher, the steady two-dimensional convection rolls become unstable. The wavy instability and aperiodic motion observed, as well as the Nusselt number as a function of the Rayleigh number, are in good agreement with experimental observations and theoretical predictions. The LBE model is found to be efficient, accurate, and numerically stable for the simulation of fluid flows with heat and mass transfer.
519 citations
TL;DR: The present study used an articulated thermal manikin with 16 body segments to generate radiative heat transfer coefficients as well as natural- and forced-mode convective coefficients to simulate both transient and spatial inhomogeneities in the thermal environment.
Abstract: Human thermal physiological and comfort models will soon be able to simulate both transient and spatial inhomogeneities in the thermal environment With this increasing detail comes the need for anatomically specific convective and radiative heat transfer coefficients for the human body The present study used an articulated thermal manikin with 16 body segments (head, chest, back, upper arms, forearms, hands, pelvis, upper legs, lower legs, feet) to generate radiative heat transfer coefficients as well as natural- and forced-mode convective coefficients The tests were conducted across a range of wind speeds from still air to 50 m/s, representing atmospheric conditions typical of both indoors and outdoors Both standing and seated postures were investigated, as were eight different wind azimuth angles The radiative heat transfer coefficient measured for the whole-body was 45 W/m2 per K for both the seated and standing cases, closely matching the generally accepted whole-body value of 47 W/m2 per K Similarly, the whole-body natural convection coefficient for the manikin fell within the mid-range of previously published values at 34 and 33 W/m2 per K when standing and seated respectively In the forced convective regime, heat transfer coefficients were higher for hands, feet and peripheral limbs compared to the central torso region Wind direction had little effect on convective heat transfers from individual body segments A general-purpose forced convection equation suitable for application to both seated and standing postures indoors was hc=103v06 for the whole-body Similar equations were generated for individual body segments in both seated and standing postures
369 citations
TL;DR: In this paper, the authors present an account of various studies of buoyancy-driven convection in mushy layers, paying particular attention to the complex interactions between solidification and flow that lead to novel styles of convective behavior, including focusing of the flow to produce chimneys.
Abstract: As a molten alloy or any multi-component liquid is cooled and solidified the growing solid phase usually forms a porous matrix through which the residual liquid can flow. The reactive two-phase medium comprising the solid matrix and residual liquid is called a mushy layer. Buoyancy forces, owing primarily to compositional depletion as one or more of the components of the alloy are extracted to form the solid phase, can drive convection in the layer. In this review, I present an account of various studies of buoyancy-driven convection in mushy layers, paying particular attention to the complex interactions between solidification and flow that lead to novel styles of convective behavior, including focusing of the flow to produce chimneys: narrow, vertical channels devoid of solid. I define an ‘ideal’ mushy layer and argue that chimneys are an inevitable consequence of convection in ideal mushy layers. The absence of chimneys in certain laboratory experiments is explained in terms of nonideal effects.
304 citations
TL;DR: In this article, an analysis of flow and heat transfer characteristics in an electrically conducting fluid near an isothermal sheet is carried out, and the resulting coupled nonlinear differential equations are integrated numerically.
264 citations
TL;DR: In this paper, the authors describe a series of laboratory experiments in which aqueous salt solutions were cooled and solidied from above, serving as model systems of metallic castings, magma chambers and sea ice.
Abstract: We describe a series of laboratory experiments in which aqueous salt solutions were cooled and solidied from above. These solutions serve as model systems of metallic castings, magma chambers and sea ice. As the solutions freeze they form a matrix of ice crystals and interstitial brine, called a mushy layer. The brine initially remains conned to the mushy layer. Convection of brine from the interior of the mushy layer begins abruptly once the depth of the layer exceeds a critical value. The principal path for brine expelled from the mushy layer is through ‘brine channels’, vertical channels of essentially zero solid fraction, which are commonly observed in sea ice and metallic castings. By varying the initial and boundary conditions in the experiments, we have been able to determine the parameters controlling the critical depth of the mushy layer. The results are consistent with the hypothesis that brine expulsion is initially determined by a critical Rayleigh number for the mushy layer. The convection of salty fluid out of the mushy layer allows additional solidication within it, which increases the solid fraction. We present the rst measurements of the temporal evolution of the solid fraction within a laboratory simulation of growing sea ice. We show how the additional growth of ice within the layer aects its rate of growth.
183 citations
TL;DR: In this article, the effect of surface radiation on the flow field, temperature distribution, and heat transfer is predicted, and it is shown that surface radiation significantly altered the temperature distribution and the flow patterns, especially at higher Rayleigh numbers.
Abstract: The interaction of natural convection with thermal radiation of gray surfaces in a square enclosure filled with air has been numerically investigated. The effect of radiation on the flow field, temperature distribution, and heat transfer is predicted. The result shows that surface radiation significantly altered the temperature distribution and the flow patterns, especially at higher Rayleigh numbers. The average convection Nusselt number increases with the increase of Ra. The presence of surface radiation can change the value of average convection Nusselt number, but only little variation can be observed with the increase of emissivity. The average radiative Nusselt number rises quickly with the increase of emissivity, and radiation heat transfer plays an important part in overall heat flux at larger emissivity. The correlation of entire average Nusselt number has also been discussed for evaluating heat transfer through the enclosure,
140 citations
TL;DR: In this article, a numerical model is developed to predict transient behaviors of electric vehicle lead-acid batteries during discharge and charge processes, which not only accounts for coupled processes of electrochemical kinetics and mass transport occurring in a battery cell, but also considers free convection resulting from density variations due to acid stratification.
Abstract: A numerical model is developed to predict transient behaviors of electric vehicle lead-acid batteries during discharge and charge processes. The model not only accounts for coupled processes of electrochemical kinetics and mass transport occurring in a battery cell, but also considers free convection resulting from density variations due to acid stratification. A single set of conservation equations valid for both porous electrodes and the free electrolyte region is derived and numerically solved using a computational fluid dynamics technique. This numerical methodology is capable of simulating a two-dimensional cell with the fluid flow taken into consideration and requires only tens of minutes of central processing unit time on engineering workstations. Four sample calculations are presented in this work to provide rigorous validation of the developed simulator. The simulator is capable of predicting the transient behavior of the acid concentration, the porosity of the electrodes, and the state of charge of the battery during discharge, rest, and charge cycles. The model can also be used to investigate the effects of various system parameters, such as electrode dimensions, separator design, temperature, and electrolyte composition on the battery performance (voltage, power, cold cranking amperage, etc.).
140 citations
127 citations
TL;DR: In this article, the authors considered finite-amplitude convection in rotating spherical fluid shells for a variety of Prandtl numbers P and Rayleigh numbers Ra up to about 10 times the critical value.
Abstract: Finite-amplitude convection in rotating spherical fluid shells is considered for a variety of Prandtl numbers P and Rayleigh numbers Ra up to about 10 times the critical value. Convection at low Rayleigh numbers in the form of azimuthally periodic or weakly aperiodic drifting waves is characterized by relatively low heat transport, especially for P ≤ 1. The transition to strongly time-dependent convection leads to a rapid increase of the heat transport with increasing Rayleigh numbers. Onset of convection in the polar regions is delayed, but contributes a disproportionate fraction of the heat transport at high Rayleigh number. The differential rotation generated by convection, the distributions of helicity, and the role of asymmetry with respect to the equatorial plane are also studied.
127 citations
TL;DR: In this paper, volume-averaged equations are developed governing steady, laminar, fully developed, hydromagnetic mixed convection non-Darcian flow of an electrically conducting and heat-generating / absorbing fluid in a channel embedded in a uniform porous medium.
Abstract: Volume-averaged equations are developed governing steady, laminar, fully developed, hydromagnetic mixed convection non-Darcian flow of an electrically conducting and heat-generating / absorbing fluid in a channel embedded in a uniform porous medium. Proper dimensionless parameters are employed for various thermal boundary conditions on the left and right walk of the channel prescribed as isothermal-isothermal, isothermal-iso-flux, and isoflux-isothermal. Analytical expressions for the velocity and temperature profiles in the channel as well as for the mass flow rate, friction factor, and heat carried out by the fluid in the channel are developed for special cases of the problem. Conditions for the occurrence of fluid backflow zones are reported. The fully nonlinear governing equations are solved numerically by an implicit finite difference method. Favorable comparisons with the developed analytical results and previously published work are performed. Graphical results of the closed-form and numer...
125 citations
TL;DR: In this paper, a mathematical model governing free convection boundary-layer flow over an isothermal inclined plate embedded in a thermally stratified porous medium in the presence of a non-uniform transverse magnetic field is developed.
TL;DR: In this article, the scaling laws that govern the influence of applied magnetic fields on convection in the horizontal Bridgman configuration were derived. But the authors only considered the case of an infinite horizontal layer with upper free surface, and the results showed that the vertical magnetic field stabilizes the flow by increasing the values of the critical Grashof number at which the system becomes unstable.
Abstract: Studies of convection in the horizontal Bridgman configuration were performed to investigate the flow structures and the nature of the convective regimes in a rectangular cavity filled with an electrically conducting liquid metal when it is subjected to a constant vertical magnetic field. Under some assumptions analytical solutions were obtained for the central region and for the turning flow region. The validity of the solutions was checked by comparison with the solutions obtained by direct numerical simulations. The main effects of the magnetic field are first to decrease the strength of the convective flow and then to cause a progressive modification of the flow structure followed by the appearance of Hartmann layers in the vicinity of the rigid walls. When the Hartmann number is large enough, Ha > 10, the decrease in the velocity asymptotically approaches a power-law dependence on Hartmann number. All these features are dependent on the dynamic boundary conditions, e.g. confined cavity or cavity with a free upper surface, and on the type of driving force, e.g. buoyancy and/or thermocapillary forces. From this study we generate scaling laws that govern the influence of applied magnetic fields on convection. Thus, the influence of various flow parameters are isolated, and succinct relationships for the influence of magnetic field on convection are obtained. A linear stability analysis was carried out in the case of an infinite horizontal layer with upper free surface. The results show essentially that the vertical magnetic field stabilizes the flow by increasing the values of the critical Grashof number at which the system becomes unstable and modifies the nature of the instability. In fact, the range of Prandtl number over which transverse oscillatory modes prevail shrinks progressively as the Hartmann number is increased from zero to 5. Therefore, longitudinal oscillatory modes become the preferred modes over a large range of Prandtl number.
TL;DR: In this article, the free convection flow of an electrically conducting fluid along a vertical plate embedded in a thermally stratified porous medium in the presence of a uniform normal magnetic field is investigated.
TL;DR: In this article, a numerical study has been conducted of natural convection-dominated melting and solidification of a phase change material (PCM) from a finned vertical wall.
Abstract: A numerical study has been conducted of natural convection-dominated melting and solidification of a phase change material (PCM) from a finned vertical wall This work was motivated by the need to a...
TL;DR: In this article, a numerical study was conducted to investigate steady state heat transfer and flow characteristics of natural convection in a vertical square enclosure when a temperature difference exists across an enclosure and, at the same time, a conducting body generates heat within the enclosure.
Abstract: A numerical study has been conducted to investigate steady state heat transfer and flow characteristics of natural convection in a vertical square enclosure when a temperature difference exists across an enclosure and, at the same time, a conducting body generates heat within the enclosure. Dimensionless governing equations indicate that the heat transfer and flow characteristics of this system are governed by the Rayleigh and Prandtl numbers, the area ratio, the conductivity ratio, and the temperature-difference ratio. Here the temperature-difference ratio is defined as the ratio of a temperature difference across the enclosure to that caused by the heat source. In the present study, the Rayleigh number ranges from 103 to 104, and the temperature-difference ratio from 0 to 50, while the Prandtl number, the area ratio, and the conductivity ratio are kept constant at 0.71, 0.25, 1, respectively. The analysis is performed by observing variations of streamlines, isotherms, heatlines, and the average Nusselt ...
TL;DR: In this article, an infrared camera system was used to obtain a complete and accurate distribution of local heat transfer coefficients on the impingement surface, and a numerical code was developed and verified by comparison with experimental data.
Abstract: Heat and mass transfer between a surface and the surrounding gas can be enhanced by the application of electric body forces that induce jet or plume-like fluid motion. Such enhancement causes no noise or vibration, can be applied in complex, isolated geometries, and allows simple control of surface temperatures. This paper examines the potentially useful case of multiple fine-wire electrodes suspended in the open air above a grounded and heated horizontal surface. An infrared camera system was used to obtain a complete and accurate distribution of local heat transfer coefficients. on the impingement surface. A numerical code was developed and verified by comparison with experimental data. This code was then used to investigate and compare the heat transfer generated by novel electrode geometries.
TL;DR: In this paper, a general theory for convection within mushy layers is applied to develop a hypothesis for when brine drainage occurs, which is tested against the experimental results, showing that brine initially remains trapped in the interstices of the sea ice, only draining into the underlying ocean once the depth of the seafloor layer exceeds a critical value.
Abstract: We present new experimental results relating to the growth and evolution of sea ice. These show, in particular, that brine initially remains trapped in the interstices of the sea ice, only draining into the underlying ocean once the depth of the sea-ice layer exceeds a critical value. A general theory for convection within mushy layers is applied to develop a hypothesis for when brine drainage occurs, which is tested against the experimental results.
TL;DR: In this article, natural convection flow of an absorbing fluid up a uniform porous medium supported by a semi-infinite, ideally transparent, vertical flat plate due to solar radiation is considered.
Abstract: Natural convection flow of an absorbing fluid up a uniform porous medium supported by a semi-infinite, ideally transparent, vertical flat plate due to solar radiation is considered. Boundary-layer equations are derived using the usual Boussinesq approximation and accounting for applied incident radiation flux. A convection type boundary condition is used at the plate surface. These equations exhibit no similarity solution. However, the local similarity method is employed for the solution of the present problem so as to allow comparisons with previously published work. The resulting approximate nonlinear ordinary differential equations are solved numerically by a standard implicit iterative finite-difference method. Graphical results for the velocity and temperature fields as well as the boundary friction and Nusselt number are presented and discussed.
TL;DR: In this paper, the authors investigated large Rayleigh number (106−109) and large Prandtl number (102−103) thermal convection in glycerol in an aspect ration one cubic cell.
Abstract: We investigate large Rayleigh number (106–109) and large Prandtl number (102–103) thermal convection in glycerol in an aspect ration one cubic cell. The kinematic viscosity of the fluid strongly depends upon the temperature. The symmetry between the top and bottom boundary layers is thus broken, the so-called non-Boussinesq regime. In a previous paper Wu and Libchaber have proposed that in such a state the two thermal boundary layers adjust their length scales so that the mean hot and cold temperature fluctuations are equal in the center of the cell. We confirm this equality. A simplified two-dimensional model for the mean center temperature based on an equation for the thermal boundary layer is presented and compared with the experimental results. The conclusion is that the central temperature adjusts itself so that heat fluxes from boundaries are equal, temperature fluctuations at the center symmetrical, at a cost of very different temperature drops and Rayleigh number for each boundary.
TL;DR: In this article, the SULTAN facility was designed to study large-scale structure coolability by water in boiling natural convection and the main characteristics of two-dimensional, two-phase flow, in order to evaluate the recirculation mass flow in large systems, and the limits of the critical heat flux (CHF) for a wide range of thermodynamic parameters.
TL;DR: In this paper, the authors present the results of 5 years of field investigation in Pilot Valley, Nevada, of a literature search for field studies in closed basins around the world, and of numerical simulations to examine the effect of heterogeneity on free convection.
TL;DR: In this paper, three-dimensional numerical convection calculations in a wide (8 × 8 × 1) cartesian box and in a spherical shell (ratio of inner to outer radius of 0.55, characteristic of terrestrial planets) both display two fundamental transitions as the viscosity contrast is progressively increased from unity to a factor of 105.
TL;DR: In this paper, the authors investigated linear and non-linear properties of thermal convection in rotating spherical shells of varying radius ratios and determined the range of validity of the simple "equatorial" approximation through a comparison with the more complete numerical analysis based on the Galerkin approximation.
TL;DR: In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium.
Abstract: In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium (C) 1997 by John Wiley & Sons, Ltd
TL;DR: In this article, the authors studied double diffusive steady natural convection in a vertical stack of square enclosures, with heat and mass diffusive walls, and presented and analyzed some significant results.
TL;DR: In this article, the horizontal scale of rotating convection with rigid boundary conditions is studied, and the experimental results agree fairly well with the estimated scale, which depends on the ratio between the thicknesses of the Ekman layer and the thermal boundary layer, and does not depend monotonically on the Rayleigh number.
Abstract: The horizontal scale of rotating convection with rigid boundary conditions is studied. The range of Rayleigh number concerned is moderate, i.e. large enough to induce a finite-amplitude convection but small enough so that the geostrophic processes are significant.On considering an experimental law of the Nusselt number and some constraints of elemental geostrophic processes, the horizontal scale of the convection can be estimated. This estimation strongly depends on the ratio between the thicknesses of the Ekman layer and the thermal boundary layer, and does not depend monotonically on the Rayleigh number. This dependency is compatible with the experimental results of Rossby (1969).The estimated horizontal scale was checked by laboratory experiments. The horizontal temperature distribution was visualized by thermal liquid-crystal capsules dispersed in the working fluid. The horizontal scale was measured by counting vortices. The experimental results agree fairly well with the estimated scale.
TL;DR: In this article, a numerical study of combined heat and mass transfer by natural convection adjacent to vertical surfaces situated in fluid-saturated porous media is reported, where the structure of the flow, temperature and concentration fields are governed by complex interactions among the diffusion rates and the buoyancy ratio.
TL;DR: In this paper, the transition from the onset of convection to fully developed turbulence of a Rayleigh-Benard flow, in a low-aspect-ratio cell and in mercury, is studied through three-dimensional numerical simulation of the Navier-Stokes equations.
Abstract: The transitions from the onset of convection to fully developed turbulence of a Rayleigh–Benard flow, in a low-aspect-ratio cell and in mercury, are studied through three-dimensional numerical simulation of the Navier–Stokes equations. The calculation of the growth rate of the azimuthal energy modes permitted the accurate determination of the critical Rayleigh number for the establishment of the convective regime (Rac=3750) which is in good agreement with analytical and other numerical results. Increasing the Rayleigh number, the flow remained steady up to Ra≃2.11×104 when an oscillatory instability was observed. Further increases in the Rayleigh produced a chaotic state through the period doubling mechanism and finally the turbulent state was achieved. It is shown that for Ra⩾Rac the mean flow consists of a large-scale convective cell which persists in the whole range of studied Rayleigh numbers (Ra⩽106). The dependence of the Nusselt number over the Rayleigh number is also analyzed and, for Ra⩾3.75×104,...
TL;DR: In this article, a numerical study of double-diffusive natural convection in a square cavity filled with a porous medium is presented, which is driven by a combined buoyancy effect due to both temperature and concentration variations.
Abstract: This work describes a numerical study of double-diffusive natural convection in a square cavity filled with a porous medium. The flow is driven by a combined buoyancy effect due to both temperature and concentration variations. Several different flow models for porous media, such as Darcy flow, Forchheimer's extension, Brinkman's extension, and the generalized flow are considered. The coupled equations are solved using a finite volume approach with a projection algorithm for the momentum equation. Non-Darcian effects are analyzed through investigating the average heat and mass transfer rates. This study consists of a global analysis of each model and the comparison between them when the Darcy number varies. This work also focuses on the influence of the Lewis number on the inertial and boundary effects. It is shown that the inertial and boundary effects have a profound effect on the double-diffusive convection.
TL;DR: In this paper, the combined free convection and forced convection in a partially divided enclosure with a finite-size heat source is studied numerically, where the enclosure is partially divided by a conductive vertical divider protruding from the floor or the ceiling of the enclosure.
Abstract: Combined free convection and forced convection in a partially divided enclosure with a finite-size heat source is studied numerically. The enclosure is partially divided by a conductive vertical divider protruding from the floor or the ceiling of the enclosure. The present study simulates a practical system such as air-cooled electronic equipment with heated components. Emphasis is placed on the influence of the location and the height of the divider, as well as the locations of the source and the outflow opening. The developed mathematical model is governed by the coupled equations of stream Junction, vorticity transport, and energy and is solved by employing the cubic spline collocation scheme. The computation is carried out for wide ranges of Reynolds and Grashof numbers. The results indicate that the average Nusselt number and the dimensionless surface temperature on the heat source strongly depend on the location and the height of the divider. The basic nature of the resulting interaction be...