Showing papers on "Combined forced and natural convection published in 1988"

Buoyancy-Induced Flows And Transport

Abstract: Contents: Introduction.- General Formulation of Buoyancy-Induced Flows.- External Vertical Thermally Induced Flows.- Vertical Axisymmetric Flows.- Other Than Vertical Flows.- Combined Mass and Thermal Transport.- Unsteady External Flows.- Effects of Variable Fluid Properties.- Transport in Cold Pure and Saline Water.- Mixed Convection.- Instability, Transition and Turbulence.- Turbulent Free-Boundary Buoyant Flows.- Unstably Stratified Fluid Layers.- Transport in Enclosures and Partial Enclosures.- Transport in Saturated Porous Media.- Non-Newtonian Transport.- Some Other Aspects.- Nomenclature.- Appendixes.- Additional References.- Author Index to Additional References.- Author Index.- Subject Index.

Natural convection in enclosures

Abstract: Publisher Summary This chapter discusses the complex nature of the natural convection phenomena in enclosures It discusses the two basic configurations of natural convection— that is, a rectangular cavity and a horizontal circular cylinder In rectangular cavities, consideration is given to the two-dimensional convective motion generated by the buoyancy force on the fluid in a rectangle and to the associated heat transfer The two long sides are vertical boundaries held at different temperatures and the short sides can either be heat conducting or insulated Particular attention is given to the different flow regimes that can occur and the heat transfer across the fluid space between the two plane parallel vertical boundaries Although heat transfer by radiation may not be negligible it is independent of the other types of heat transfer and can be fairly accurately calculated separately To formulate the boundary value problem that describes this phenomena it is assumed that: (a) the motion is two-dimensional and steady, (b) the fluid is incompressible and frictional heating is negligible, and (c) the difference between the hot wall and cold wall temperatures is small relative to the absolute temperatures of the cold wall In horizontal circular cylinder, consideration is given to the large Rayleigh number flow with the Prandtl number large and the Grashof number of unit order of the magnitude

Chaotic particle transport in time-dependent Rayleigh-Bénard convection

Abstract: The transport of passive impurities in nearly two-dimensional, time-periodic Rayleigh-B\'enard convection is studied experimentally and numerically. The transport may be described as a one-dimensional diffusive process with a local effective diffusion constant ${D}^{\mathrm{*}}$(x) that is found to depend linearly on the local amplitude of the roll oscillation. The transport is independent of the molecular diffusion coefficient and is enhanced by 1--3 orders of magnitude over that for steady convective flows. The local amplitude of oscillation shows strong spatial variations, causing ${D}^{\mathrm{*}}$(x) to be highly nonuniform. Computer simulations of a simplified model show that the basic mechanism of transport is chaotic advection in the vicinity of oscillating roll boundaries. Numerical estimates of ${D}^{\mathrm{*}}$ are found to agree semiquantitatively with the experimental results. Chaotic advection is shown to provide a well-defined transition from the slow, diffusion-limited transport of time-independent cellular flows to the rapid transport of turbulent flows.

Mixed Convection in Stagnation Flows Adjacent to Vertical Surfaces

Abstract: Laminar mixed convection in two-dimensional stagnation flows around heated surfaces is analyzed for both cases of an arbitrary wall temperature and arbitrary surface heat flux variations. The two-dimensional Navier-Stokes equations and the energy equation governing the flow and thermal fields are reduced to a dimensionless form by appropriate transformations and the resulting system of ordinary differential equations is solved in the buoyancy assisting and opposing regions. Numerical results are obtained for the special cases for which locally similar solutions exist as a function of the buoyancy parameter. Local wall shear stress and heat transfer rates as well as velocity and temperature distributions are presented. It is found that the local Nusselt number and wall shear stress increase as the value of the buoyancy parameter increases in the buoyancy assisting flow region. A reverse flow region develops in the buoyancy opposing flow region, and dual solutions are found to exist in that flow regime for a certain range of the buoyancy parameter.

Natural convection in vertical enclosures containing simultaneously fluid and porous layers

Abstract: A numerical and experimental study is reported of natural convection in a vertical rectangular fluid enclosure that is partially filled with a fluid-saturated porous medium. Velocities, stresses, temperatures, and heat fluxes are assumed to be continuous across the fluid/porous-medium interface, and the conservation equations for the fluid and the porous regions are combined into a single set of equations for numerical solution. Thermocouples as well as a Mach-Zehnder interferometer are used to measure temperature distributions and infer fluid flow patterns within the fluid and the porous medium. For various test cells, porous-layer configurations and fluid-solid combinations, the model predictions show excellent agreement with the experimental measurements. It is found that the intensity of natural convection is always much stronger in the fluid regions, while the amount of fluid penetrating into the porous medium increases with increasing Darcy and Rayleigh numbers. The degree of penetration of fluid into the porous medium depends strongly on the porous-layer geometry and is less for a horizontal porous layer occupying the lower half of the test cell. If penetration takes place, the flow patterns in the fluid regions are significantly altered and the streamlines show cusps at the fluid/porous-medium interfaces. For a high effective-thermal-conductivity porous medium, natural convection in the medium is suppressed, while the isotherms bend sharply at the fluid/porous-medium interface.

Traveling-wave convection in an annulus

Abstract: We report experimental observations of traveling-wave convection in a binary fluid mixture in an annular container---a flow which approximates a large, one-dimensional dynamical system. In this geometry, the convective rolls align themselves radially and propagate azimuthally. We observe competition between several non- equilibrium states. This leads to a rich variety of dynamical behavior, including coexisting regions of conduction and convection, sources and sinks of convective rolls, and more complex spatiotemporal defects.

Role of the lithosphere in mantle convection

Abstract: Plate geometry and kinematics generally reflect the mechanical properties of the solid lithosphere rather than those of the fluid mantle underneath, and plate formation and subduction account for most of the heat transport from the Earth's interior. Correspondingly, mantle convection models must incorporate a stiff but mobile boundary layer, like the lithosphere, before they can reproduce the main features of mantle convection. A relatively easy way to accomplish this in numerical models is to combine a temperature-dependent viscosity with an imposed, piecewise constant surface velocity boundary condition. It is shown how surface heat flux, topography, gravity, and geoid (but not plate velocities or stresses) can then be derived. Numerical models confirm that a lithosphere has a first-order effect on the underlying flow structure. For internally heated models, approx-imating the case of whole mantle convection, the calculated surface signatures are in first-order agreement with observations, a level of empirical success which hitherto has not been approached by models of mantle convection. Companion papers exploit the observations more fully to constrain the main features of mantle convection.

Heat transfer in turbulent mixed convection

Abstract: The contents of this book are: Basic Equations of Convective Heat Transfer; Basic Information on the Theory of Turbulent Heat Transfer in Flow Near Walls; Heat Transfer in Laminar Mixed Convection; Turbulent Mixed Convection in Boundary Layers; Turbulent Flow and Heat Transfer in Horizontal Channels; Turbulent Flow and Heat Transfer in Vertical Channels; and Gravitational Effects on Heat Transfer in a Single-Phase Fluid Near the Critical Point.

The dependence of convection planform on mode of heating

Abstract: A fundamental property of a convecting fluid is its planform—the distribution in the horizontal plane of hot rising regions and cold sinking regions. For the Earth's mantle the planform might he visualized as a map of subduction zones, hotspots and possibly ocean ridges. Here I report numerical experiments of convection at high Rayleigh number which show a strong dependence of planform on heating mode. When heat generation is distributed uniformly through the box the preferred planform consists of an ensemble of time-dependent cold axial sinkers distributed in a hot diffuse upward flow. When half of the heat is generated within the box and the other half is input through the base, the preferred planform consists of an array of hot axial plumes and elongated cold sheets. In the former case the mean horizontal wavelength is about equal to the layer depth; for the latter it is about twice the layer depth.

Numerically Predicted Transient Temperature and Velocity Profiles During Natural Convection Heating of Canned Liquid Foods

Abstract: Numerically predicted transient flow patterns and temperature profiles during natural convection heat transfer of a liquid in a uniformly heated cylindrical can were presented for the first time. A recirculating flow pattern was predicted inside the cylindrical container. The liquid was found to be stratified inside the container with increasing temperatures towards the top. The slowest heating location in the fluid was a donut-shaped region close to the bottom of the can at about one-tenth the can height.

Fluid Flow and Mixed Convection Transport From a Moving Plate in Rolling and Extrusion Processes

Abstract: The heat transfer arising due to the movement of a continuous heated plate in processes such as hot rolling and hot extrusion has been studied. Of particular interest were the resulting temperature distribution in the solid and the proper imposition of the boundary conditions at the location where the material emerges from a furnace or die. These considerations are important in the simulation and design of practical systems. A numerical study of the thermal transport process has been carried out, assuming a two-dimensional steady circumstance. The boundary layer equations, as well as full governing equations including buoyancey effects, are solved employing finite difference techniques. The effect of various physical parameters, which determine the temperature and flow fields, is studied in detail. The significance of these results in actual manufacturing processes is discussed.

The Effect of Large-Scale Convergence on the Generation and Maintenance of Deep Moist Convection

Abstract: The effect of large-scale convergence on the generation and maintenance of deep moist convection is examined with a numerical cloud model. The term large-scale is defused as a scale an order of magnitude greater than the convective scale. Convergence is included in the model by imposing a momentum forcing at the lowest levels of the domain. The simulations are initialized with the linear response to this forcing. It is shown that large-scale convergence has an important effect both before and after the generation of convection. Before convection commences, the convergence lifts the atmosphere to saturation, or close to saturation, over a wide region. This means that once convection begins, the air entering the system requires little further lifting and it is demonstrated that this allows the system to maintain itself without the additional lifting that evaporative cooling produces. This is in contrast to a system which is generated in an unsaturated environment by an initial warm bubble perturbat...

Analysis of combined buoyancy effects of thermal and mass diffusion on laminar forced convection heat transfer in a vertical tube

Abstract: This study investigates the role of vaporization of a thin liquid film onthe tube wall in laminar mixed convection flows under the combined buoyancy effects of thermal and mass diffusion. Results are specifically presented for an air-water system under various conditions. The effects of the liquid film temperature, the Reynolds number, and the relative humidity of the moist air in the ambient on the momentum, heat, and mass transfer in the flow are examined in great detail.

Time-dependent thermal convection - a possible explanation for a multiscale flow in the Earth's mantle

Abstract: SUMMARY The temporal evolution of thermal convection in stress-free, base-heated boxes is investigated by means of a finite-element model. It is shown that the aspect ratio and also the initial conditions have a tremendous influence on the evolution. In boxes of aspect ratio A, significantly greater than unity (1.8 < A < 3), the onset of time-dependence occurs at much lower values of the Rayleigh number Ra than predicted from studies which assumed square boxes (A = 1). While steady-state solutions can be obtained by a particular choice of initial conditions, stationary convection breaks down for less restrictive conditions. It is also demonstrated, that the long held view, that convection cells with A = 1 would break down into smaller units, is not valid. At Ra = lo6 elongated convection cells of A=3 with superimposed boundary-layer instabilities are found in the long-term range of the temporal evolution. Regarding the Earth’s mantle, the model of a time-dependent multiscale flow can basically explain the coexistence of different scales of convection in the mantle.

Forced flow near a heated rotating disk: a similarity solution

Abstract: This paper presents an analysis of the flow and heat transfer between two parallel infinite disks that are separated by a distance L. One of the disks is solid, heated, and rotated; the other disk is porous, unheated, and stationary. Fluid is injected through the porous disk normal to its surface and toward the rotating disk. The three-dimensional Navier-Stokes and energy equations have been reduced to a system of ordinary differential equations by means of a similarity transformation and have been solved over a range of values of the two Reynolds numbers Reωequals; L2ω/νL and Reν = LU/νL, for two values of the temperature ratio Tr = (Ts - TL)/TL, of 0.001 (constant property flow) and 2.33. For Tr = 0.001 the velocity profiles are independent of the temperature profile which is determined for Pr = 0.67; for Tr = 2.33, the velocity and temperature profiles are determined for helium. The assumptions made in the analysis are shown to be valid provided that the mixed convection parameter , is small. Velocity ...

An analysis on forced convection in a channel filled with a Brinkman-Darcy porous medium: exact and approximate solutions

Abstract: An analysis was made to investigate non-Darcian fully developed flow and heat transfer in a porous channel bounded by two parallel walls subjected to uniform heat flux. The Brinkmanextended Darcy model was employed to study the effect of the boundary viscous frictional drag on hydrodynamic and heat transfer characteristics. An exact expression has been derived for the Nusselt number under the uniform wall heat flux condition. Approximate results were also obtained by exploiting a momentum integral relation and an auxiliary relation implicit in the Brinkmanextended Darcy model. Excellent agreement was confirmed between the approximate and exact solutions even in details of velocity and temperature profiles.

Engineering Heat Transfer

Abstract: Introduction to conduction, convection, radiation the equations of heat conduction one-dimensional steady state conduction two-dimensional steady state conduction transient conduction forced convection - boundary layer principles forced convection - Reynolds analogy and dimensional analysis natural convection separated flow convection convection with phase change extended surfaces heat exchanges the laws of black and grey body radiation.

Analysis of fully developed opposing mixed convection between inclined parallel plates

Abstract: An exact solution is presented of fully developed, laminar flow between inclined parallel plates with a uniform wall heat flux boundary condition. The flow is downward and the heat flux is into the channel, so that natural convection opposes the forced flow. The solution depends on the two parametersP1=Gr sinθ/Re andP2=Gr cosθ/Re2Pr. Four different flow reversal regimes are observed: 1) no reversal, 2) top reversal, 3) bottom reversal, and 4) top and bottom reversal. Velocity profiles, temperature profiles, wall friction, and Nusselt numbers are presented. Despite the simplicity of the problem which has been analyzed, it does display some features which have been observed in real mixed convection flows, such as flow reversal and nonmonotonic dependence on tilt angle.