Showing papers on "Natural convection published in 1988"

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

Onset of Finger Convection in a Horizontal Porous Layer Underlying a Fluid Layer

Abstract: The problem of the onset of finger convection in a porous layer underlying a fluid layer is considered using linear stability analysis. The linear stability equations for the porous layer are formulated for temperature and salinity gradients existing in both layers. The eigenvalue problem is solved by a shooting method. The solution method and associated computer program are validated by comparison with the results of Sun (1973) for the thermal convection case. Results are also presented for the onset of salt-finger convection.

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.

Free Convection Flow of Non-Newtonian Fluids Along a Vertical Plate Embedded in a Porous Medium

Abstract: The problem of free convection flow of a non-Newtonian power law fluid along an isothermal vertical flat plate embedded in the porous medium is considered in the present study. The physical coordinate system is shown schematically in Fig 1. In the present study, it is assumed that the modified Darcy law and the boundary layer approximation are applicable. This implies that the present solutions are valid at a high Rayleigh number. With these simplifications, the governing partial nonlinear differential equations can be transformed into a set of coupled ordinary differential equations which can be solved by the fourth-order Runge-Kutta method. Algebraic equations for heat transfer rate and boundary layer thickness as a function of the prescribed wall temperature and physical properties of liquid-porous medium are obtained. The similarity solutions can be applied to problems in geophysics and engineering. The primary purpose of the present study is to predict the characteristics of steady natural convection heat transfer using the model of the flow of a non-Newtonian power law fluid in a porous medium given by Dharmadhikari and Kale (1985). Secondly, the effects of the new power law index n on heat transfer are investigated.

Three‐Dimensional Flow Effects in Silicon CVD in Horizontal Reactors

Abstract: Numerical modeling of Si homoepitaxial deposition from in the horizontal reactor has been undertaken employing the steady‐state, fully parabolic flow approximation for the heat, momentum, and mass‐transfer equations. Reactants are assumed to be dilute in their carrier gas. The resulting set of partial differential equations are discretized using finite elements and solved using the method of lines. The effect of a third dimension, the side temperature boundary conditions, and natural convection are explored. Given recent kinetics data on the silane decomposition and silylene insertion reactions, it is shown that a quasi‐thermodynamic equilibrium exists in the heated region above the surface, at least for hydrogen gas ambients. The combination of a fast silylene surface reaction and a slow silane surface reaction implies that the effective surface reaction rate is governed by the homogeneous thermodynamic equilibrium in the gas phase and diffusion through a thin mass‐transfer boundary layer near the surface. Examples of how tilting the susceptor contributes to growth uniformity are presented, and the effectiveness of similarity solution models at predicting this enhanced axial uniformity is tested.

The infinite candle and its stability—A paradigm for flickering diffusion flames

Abstract: Large diffusion flames are known to flicker at a frequency (∼12Hz) that is remarkably insensitive to flow rate, burner size, or gas composition. We have confirmed this phenomenon and propose a theoretical explanation. We note that, in addition to the forced convection associated with a tube-burner diffusion flame, there is strong natural convection generated by the hot gases. This bouyancy-induced flow surrounds the forced component and depends only on the thermomechanical properties of the hot and cold gas, together with g , the gravitational acceleration. We argue that it is the instability (of modified Kelvin-Helmholtz type) of this annular flow that is responsible for the flickering. A paradigm for this flow is defined by the infinite candle , an ideal plane diffusion flame in which the flow field is induced solely by buoyancy. The infinite candle admits a similarity solution. An inviscid, parallel flow stability analysis of this flow-field yields a frequency for which the spatial growth of the disturbance is a maximum. This is within a factor of 2 of the observed frequency.

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.

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.

On the numerical modelling of heat transfer during solidification processes

Abstract: An extensive amount of work has been published on the treatment of heat transfer associated with phase change. A few recent advances are discussed in this paper with some emphasis on the phase change of metals. The apparent capacity, effective capacity, enthalpy, post iterative, source based and semi-analytical methods are discussed and relative advantages and disadvantages of each are analysed. Recent developments in nodelling the flow during pouring and natural convection with applications of two widely used convective liffusive codes, the Los Alamos MAC and the Imperial College TEACH, are presented. An alternative tream function–vorticity approach is also discussed. Applications of these methods to turbulent convection during mould filling and continuous casting are presented. Areas of interest for further research work are identified as modelling of turbulence in liquid metals, flow through mushy regions and improvement of the performance of weak methods in multidimensional problems when the ratio of latent heat to sensible heat is large.

An experimental study of natural convection in a vertical cavity with discrete heat sources

Abstract: Natural convection heat transfer in a tall vertical cavity (aspect ratio = 16.5), with one isothermal vertical cold wall, and eleven alternately unheated and flush-heated sections of equal height on the opposing vertical wall, is experimentally investigated. The flow visualization pictures for the ethylene glycol-filled cavity reveal a flow pattern consisting of primary, secondary, and tertiary flows. The heat transfer data and the flow visualization photographs indicate that the stratification is the primary factor influencing the temperature of the heated sections. This behavior persists for all the runs where the secondary flow cells cover a large vertical extend of the cavity. Based on the analysis of the photographs it is suggested that the turbulent flow should be expected when the local modified Rayleigh number is in the range of 9.3 {times} 10 {sup 11} to 1.9 {times} 10{sup 12}. It is found that discrete flush-mounted heating in the enclosure results in local Nusselt numbers that are nearly the same as those reported for a wide flush-mounted heater on a vertical plate. This is believed to be due to the fact that the present problems in inherently unstable, and the smallest temperature difference between a heated section and the cold wallmore » results in the onset of convection motion.« less

Unsteady hydromagnetic free-convection flow with radiative heat transfer in a rotating fluid

Abstract: We study the unsteady free-convection flow near a moving infinite flat plate in a totating medium by imposing a time-dependent perturbation on a constant plate temperature. The temperatures involved are assumed to be very large so that radiative heat transfer is significant, which renders the problem very nonlinear even on the assumption of a differential approximation for the radiative flux. When the perturbation is small, the transient flow is tackled by the Laplace transform technique. Complete first-order solutions are deduced for an impulsive motion.

Natural Convection Along Slender Vertical Cylinders With Variable Surface Temperature

Abstract: Natural convection in laminar boundary layers along slender vertical cylinders is analyzed for the situation in which the wall temperature T{sub w}(x) varies arbitrarily with the axial coordinate x. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a nonsimilar transformation and the resulting system of equations is then solved by a finite difference method in conjunction with the cubic spline interpolation technique. As an example, numerical results were obtained for the case of T{sub w}(x) = T{infinity} + ax{sup n}, a power-law wall temperature variation. They cover Prandtl numbers of 0.1, 0.7, 7, and 100 over a wide range of values of the surface curvature parameter. Representative local Nusselt number as well as velocity and temperature profiles are presented. Correlation equations for the local and average Nusselt numbers are also given.

Natural convection in a long vertical cylinder under gravity modulation

Abstract: This study is devoted to the onset of convection in differentially heated cylinders under gravity modulation. It specifically concerns the case of a vertical cylinder of infinite length, when a negative temperature gradient is maintained in the upward direction. The effect of modulation on the stability limits given by linear theory in the standard steady case is analysed. A method based on Floquet theory is proposed in the case of small values of the modulation amplitude e, for a fixed value of the frequency ω. A general technique, called matrix method, which can easily be adapted to various kinds of geometries and boundary conditions, has been developed. Analytical approaches have been derived in some cases. Finally, an asymptotic analysis is presented for large ω, under very general boundary conditions and periodic constraints, for finite e. An asymptotic relation is established for the onset of convection under periodic gravity modulation for large ω values, when e [Lt ] ω; the mathematical and physical foundations of this inequality are discussed.

Stability and finite amplitude natural convection in a shallow cavity with insulated top and bottom and heated from a side

Abstract: The stability of laminar natural convection in a shallow cavity has been studied theoretically. The flow is driven by a horizontal temperature gradient between isothermal vertical sidewalls of the cavity, the top and bottom of which are insulated. It was found that for a Prandtl number (Pr) less than 0.033, shear instability causes stationary transverse cells to be formed in the flow. For larger values of Prandtl number the instability sets in as oscillating longitudinal rolls in the range 0.033

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.

Analysis of laminar natural convection in a triangular enclosure

Abstract: The Galerkin finite-element method is used in conjunction with a stream function-vorticity-temperature formulation of the steady-stale governing equations to calculate laminar two-dimensional natural convection of air within a triangular enclosure. Isosceles triangles with horizontal bases are considered. All possible combinations of cold, hot, and adiabatic walls are studied for different Grashof numbers and aspect ratios. Flow patterns and isotherms are presented. Convective Nusselt numbers are also calculated. Comparison is made with published experimental data.