Showing papers on "Combined forced and natural convection published in 1981"

Double-diffusive convection

Abstract: In this paper we present a rather personal view of the important developments in double-diffusive convection, a subject whose evolution has been the result of a close interaction between theoreticians, laboratory experimenters and sea-going oceano-graphers. More recently, applications in astrophysics, engineering and geology have become apparent. In the final section we attempt to draw some general conclusions and suggest that further progress will again depend on a close collaboration between fluid dynamicists and other scientists.

On some consequences and possible causes of layered mantle convection

Abstract: Laboratory and numerical experiments are used to study convection confined to discrete layers. The laboratory experiments, which use the water content of a predominantly glycerine solution as a way of establishing ‘chemical’ density variations, show that convection will remain confined to superimposed layers when the chemical density contrast between layers is greater than the density change associated with the greatest temperature difference within the convecting system. The numerical experiments show a double thermal boundary layer at the interface between layers, a feature that would result in an average temperature increase of about 500°C in the mantle near 700-km depth if the lower mantle is isolated as suggested by recent geochemical models. The possible causes of a layered mantle convection system include major element chemistry variations, the combined effect of major element chemistry and a phase change, or a phase change alone if it has a sufficiently negative Clapeyron slope.

Convection in an imposed magnetic field. Part 1. The development of nonlinear convection

Abstract: Nonlinear two-dimensional magnetoconvection in a Boussinesq fluid has been studied in a series of numerical experiments with values of the Chandrasekhar number Q ≤ 4000 and the ratio ζ of the magnetic to the thermal diffusivity in the range 1 ≥ ζ ≥ 0·025. If the imposed field is strong enough, convection sets in as overstable oscillations which give way to steady convection as the Rayleigh number R is increased. In the dynamical regime that follows, magnetic flux is concentrated into sheets at the sides of the cells, from which the motion is excluded.

Free convection flow through a porous medium bounded by a vertical surface

Abstract: Steady two-dimensional free convection flow through a porous medium bounded by a vertical infinite surface is considered. Expressions for the velocity, temperature and the rate of heat transfer are obtained. Effects of G (Grashof number) and K (permeability parameter) on the velocity and the rate of heat transfer are discussed.

Compressible Convection in a Rotating Spherical Shell

Abstract: Giant cell stellar convection is modeled by solving the fluid equations for a compressible, rotating, spherical, fluid shell. A large part of the motivation is to understand the maintenance of the two major ingredients in solar dynamo theory, that is helicity and differential rotation. An anelastic approximation filters out sound waves but permits the investigation of the effects of large density stratifications in slightly superadiabatic stellar envelopes. Various rotation rates, convection zone depths, density stratifications, boundary conditions, viscosities, and conductivities are considered. The results of first order numerical calculations for the onset of convection are discussed with emphasis on the structure of the most unstable modes. Left (right) handed helical motion dominates in the northern (southern) hemisphere. Also, as the stratification increases, the horizontal dimension of the most unstable modes decreases, the prograde phase velocity increases, and the buoyancy force does more negative work in the upper part of the convection zone. Differential rotation is maintained by the transport of longitudinal momentum and by the coriolis forces acting on the meridional circulation. Second order numerical calculations provide profiles of the differential rotation and meridional circulation induced by the first order perturbations. Results of these calculations for the most unstable modes show that either equatorial acceleration, as observed on the sun, or equatorial deceleration can be maintained depending on the rotation rate, density stratification, viscosity, and conductivity. Small viscous diffusion relative to thermal diffusion is required for equatorial acceleration in rapidly rotating, highly stratified convection zones.

Ion‐neutral momentum coupling near discrete high‐latitude ionospheric features

Abstract: A two-dimensional numerical model is developed to study the momentum coupling between the ionosphere and neutral atmosphere in the vicinity of discrete high-latitude features, such as convection channels and plasma density troughs. Based on generalized magnetohydrodynamic equations the model takes account of global pressure gradients, viscous dissipation, ion drag, the Coriolis force, and electrodynamic drifts. Among the findings of an initial steady state investigation are the following: (1) in convection channels, significant shears and rotations of the thermospheric flow can occur below 200 km if a minimum in the electron density profile is present between the E and F regions; (2) in convection channels, the thermospheric wind decreases with height in the F region owing to the effects of horizontal viscosity; and (3) at low altitudes, the boundaries of convection channels may produce Ekman spirals.

On rotating thermal convection driven by non-uniform heating from below

Abstract: Experiments are described in which a radial temperature gradient is maintained along the lower horizontal boundary of a rotating annulus containing a thermally convecting fluid; the vertical side walls and upper horizontal boundary are nominally insulating. Comparison is made with the non-rotating experiments of Rossby (1965) and the same general asymmetric circulation is observed, i.e. that of a weakly stratified interior of slowly descending fluid occupying most of the annular gap, overlying a thin thermal layer of large vertical temperature gradients, stable over the cold part of the base and statically unstable over the warmer part; the circulation is completed by a narrow region of rising motion at the warm end of the base.A boundary-layer scaling analysis demonstrates the existence of six flow regimes, depending on the magnitude of a quantity Q defined such that Q is the square of the ratio of the (non-rotating) thermal-layer scale to the Ekman-layer scale. For small Q the flow is only weakly modified by rotation but as Q increases past unity rotation tends to thicken the thermal layer. Also presented are some numerical similarity solutions for the special case of a quadratic temperature distribution on the lower boundary and partially covering the range of Q achieved in the experiments, which is zero to ten. Above a certain critical value of Q (for the geometry used here Qc = 3·4) a baroclinic wave regime exists but is not examined in detail here although a brief discussion of an instability problem is given. Throughout comparisons are drawn between the experimental results and theoretical aspects of the problem.It is thought that the essential features of a system thermally driven in this way have their counterparts in natural systems such as the large-scale thermally induced ocean circulation driven by the latitudinal variation of incoming solar radiation.

On the Onset of Free Convection in a Rectangular Channel

Abstract: We study the onset of convection in an infinite channel of rectangular cross section and heated from below; the four boundaries are supposed to be rigid. Three-dimensional transverse rolls are preferred to longitudinal rolls and to finite transverse rolls. We also describe the shape of the convective motion at the critical point. Introduction The study of the onset of convection inside a completely confined region began with Davis in 1967, [1]; this author, considering a fluid maintained in a rectangular parallelepiped heated from below, performed a linear analysis and predicted for a critical thermal gradient the appearance of \"convective finite rolls (rolls with two non-zero velocity components dependent on all three spatial variables) with axes parallel to the shorter sides of the box\". This earlier work, already criticized by Catton [2], regarding the validity of Davis' trial functions, was severely corrected by Davies-Jones [3], who demonstrated that the Davis' finite rolls could never be a solution of the equations that describe the movement of the fluid: the true structure at the onset of convection is purely threedimensional (no component of the fluid velocity vanishes identically). Yet, DaviesJones showed that, although the Davis' finite rolls could not exist, they represent a good approximation of the true, three-dimensional solution. To show the validity of this latest assertion, he calculated tKe stability of the movement of a fluid confined in an infinite channel of rectangular cross section, heated from below, and maintained between two \"free\" horizontal boundaries, which allows very simple — and exact — solutions of the equations but does not permit the comparison with experiments. The aim of this paper is a complete inquiry of the onset of convection in a \"reasonable\" apparatus (i.e. allowing comparison with experiments) — with rigid horizontal boundaries — and especially the investigation of the differences between the \"finite rolls\" approach and the real, three-dimensional convective structure. 0340-0204/81/0006-0141 $02.00 © Copyright by Walter de Gruyter & Co. Berlin New York 142 J. M. Luijkx, J. K. Platten 1. Basic equations A fluid is confined in an infinite channel of rectangular cross section (see Fig. 1). The horizontal boundaries (z = ± a) supposed to be rigid and perfectly heat-conducting are maintained at different temperatures. The lateral boundaries (y = ± b) are also rigid and perfectly heat-insulating. Fig. 1: System of coordinates. The boundary conditions are: = v(z=.±a) = and dy y=± = 0. (1) (2)

A numerical study of transient mixed convection flows in a thermal storage tank

Abstract: Transient, two-dimensional, mixed convection flows in a thermal storage tank have been studied using a previously developed numerical technique based on the marker and cell method. The governing equations are the conservation equations for laminar, natural convection flow based on the Boussinesq approximation. Forced convection flow is superimposed through the use of appropriate boundary conditions (inflow and outflow conditions). The transient heat transfer and fluid flow characteristics are examined for different boundary conditions. Typical transient temperature and velocity distributions are presented. The effect of inflow and outflow configurations on the storage tank thermal performance is also investigated. It is found that the device can store energy at a faster rate when hot water is discharged into the tank from the top and colder water is extracted from the bottom. However, the discharge direction into and from the tank, which can be either vertical or horizontal, is found to have negligible effect on the thermal storage efficiency.

Mantle convection with spherical effects

Abstract: Results of a similarity theory for spherical mantle convection are presented. The single-mode mean field equations are analyzed for convection which is so vigorous that temperature disturbances become localized in thin thermal boundary layers. Our purpose is to study effects of spherical geometry, density interfaces, heat source distribution, and cell size. Steady state solutions are found for isoviscous spherical shells in which the field of motion is spatially periodic in a single spherical harmonic degree. Calculations are carried out over the range 2 ≤ l ≤ 40 and for various fractions of internal versus base heating. Three configurations are examined: (1) convection in a single layer of cells extending through the whole mantle, (2) convection in two layers, separated by a density interface at 670-km depth, and (3) convection in a single layer terminating at 670 km. Results of these calculations are used to give estimates of surface horizontal velocities in terms of the heat loss, viscosity stratification, amount of internal heating, and depth of circulation. The surface velocity is most strongly affected by the thickness of the convecting shell. Deep mantle convection can achieve surface velocities which agree with observed plate speeds, while convection restricted to the upper mantle does not, at least on the scale of the major plates. The temperature distribution is strongly affected by the spherical geometry and by the presence of density interfaces. The principal difference between convection in one and two layers is that the latter produces a ‘hot’ lower mantle, while the former produces a ‘warm’ one.

The large-scale structure of compressible convection

Abstract: We study convection of small but finite amplitude in a plane-parallel layer of perfect gas. The conductivity is assumed constant, hence the static state is polytropic. The heat flux on the boundaries is held fixed. When the polytropic index is not too large, the critical horizontal wave number for the onset of convection is zero and there is finite-amplitude instability. The finite-amplitude instability persists into the thin-layer limit provided that there are no geometrical limits to the horizontal scale of the convection. This result contradicts conclusions drawn from the strict Boussinesq approximation and it suggests that results based on that approximation are not generic for convection with flux prescribed on the boundaries. For all the Rayleigh numbers and layer thicknesses accessible to our amplitude expansions, convection with very large horizontal extent is expected to be prevalent at significant amplitudes. We suggest ways in which the nonlinear solutions found here may be useful in the interpretation of large-scale solar convection.

Dual solutions in mixed convection

Abstract: Dual similarity solutions in the context of mixed convection are presented. In contrast to the Falkner–Skan solutions the bifurcation point is found to be distinct from the point of vanishing skin friction. The eigenvalue problem arising out of a stability analysis of these solutions is examined numerically. The numerical evidence would seem to indicate that the margin of stability is associated with the onset of reverse flow as opposed to the bifurcation point, as conjectured by Banks and Drazin in 1973.

Heat transfer by natural convection across vertical air layers

Abstract: Finite-difference predictions of natural convection in vertical air layers are reported for a wide range of Rayleigh numbers and aspect ratios. Calculations were carried out for both perfectly conducting and adiabatic boundaries at the top and bottom ends of the layer. Comparisons between the predictions and measurements show that the calculated heat transfer rates are valid only over a limited range of parameters, and that the points of departure correlate closely with predicted points of instability.

Free convection and mass transfer effects on the hydro-magnetic oscillatory flow past an infinite vertical porous plate

Abstract: Two-dimensional unsteady free convection and mass transfer, flow of an incompressible viscous dissipative and electrically conducting fluid, past an infinite, vertical porous plate, is considered, when the flow, is subjected in the action of uniform transverse magnetic field. The magnetic Reynolds number is taken to be small enough so that the induced magnetic field is negligible. The solution of the problem is obtained in the form of power series of Eckert numberE, which is very small for incompressible fluids. Analytical expressions for the velocity field and temperature field are given, as well as for the skin friction and the rate of heat transfer for the case of the mean steady flow and for the unsteady one. The influence of the magnetic parameter,M, modified Grashof numberG c , Schmidt numberS c and frequency ω, on the flow field, is discussed with the help of graphs, when the plate is being cooled, by the free convection currents (G r ,E>0), or heated (G r ,E<0). A comparative study with hydrodynamic case (M=0) and the hydromagnetic one (M≠0) is also made whenever necessary.

Transient hydromagnetic convective flow in a rotating channel with porous boundaries

Abstract: The paper studies the combined free and forced convection in a rotating, viscous, incompressible fluid confined between two parallel porous plates. Assuming that the temperature varies linearly along the plates and the pressure gradient maintained uniform over the planes parallel to the plates, the velocity, temperature and the stresses are calculated analytically. Their behaviours for different values of the parameters viz., the Hartmann number, the Grashoff number and the suction parameter etc., are discussed graphically giving out the interplay between the various forces.