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Showing papers on "Convection published in 1968"


Journal ArticleDOI
TL;DR: In this article, the problem of the onset of convection, induced by buoyancy effects resulting from vertical thermal and solute concentration gradients, in a horizontal layer of a saturated porous medium, is treated by linear perturbation analysis.
Abstract: The problem of the onset of convection, induced by buoyancy effects resulting from vertical thermal and solute concentration gradients, in a horizontal layer of a saturated porous medium, is treated by linear perturbation analysis. It is shown that oscillatory instability may be possible when a strongly stabilizing solute gradient is opposed by a destabilizing thermal gradient, but attention is concentrated on monotonic instability. The eigenvalue equation, which involves a thermal Rayleigh number R and an analogous solute Rayleigh number S, is obtained, by a Fourier series method, for a general set of boundary conditions. Numerical solutions are found for some special limiting cases, extending existing results for the thermal problem. When the thermal and solute boundary conditions are formally identical, the net destabilizing effect is expressed by the sum of R and S.

588 citations


Journal ArticleDOI
TL;DR: The theory of marginal convection in a uniformly rotating, self-gravitating, fluid sphere, of uniform density and containing a uniform distribution of heat sources, is developed to embrace modes of convection which are asymmetric with respect to the axis of rotation.
Abstract: The theory of marginal convection in a uniformly rotating, self-gravitating, fluid sphere, of uniform density and containing a uniform distribution of heat sources, is developed to embrace modes of convection which are asymmetric with respect to the axis of rotation It is shown that these modes are the most unstable, except for the smallest Taylor numbers, T (a measure of the rotation rate); ie for any T and o) (Prandtl number), the lowest Rayleigh number (a measure of the temperature gradients in the sphere) is associated with an asymmetric motion This is demonstrated both by an expansion method suitable for small T, and by asymptotic theory for T oo For large T, the eigenmode most easily excited is small in amplitude everywhere except near a cylindrical surface, of radius about half that of the sphere, and coaxial with the diameter parallel to the angular velocity vector

338 citations


Journal ArticleDOI
TL;DR: The scaling of the equations of motion in the lowest one or two scale heights of the martian atmosphere is discussed in this article, where it is shown that seasonal and diurnal temperature changes can probably be computed with satisfactory precision without taking account of the advection and convection of heat by planetary-scale winds.

251 citations


Journal ArticleDOI
TL;DR: Magnetic field fluctuations in vicinity of magnetopause boundary layer imply substantial transfer of particles and momentum from solar wind to magnetosphere as discussed by the authors, which can be found in Figure 1.
Abstract: Magnetic field fluctuations in vicinity of magnetopause boundary layer imply substantial transfer of particles and momentum from solar wind to magnetosphere

151 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the relationship between the skin friction part of the drag on a natural surface and a simultaneous transfer of mass or heat, and measured the dimensionless transfer coefficients Cd, Cv and Ch for the exchange of (streamwise) momentum, mass, and heat, between a single artificial leaf and the airflow in a wind-tunnel.
Abstract: Investigation of a proposed relationship between the skin friction part of the drag on a natural surface and a simultaneous transfer of mass or (sensible) heat led to measurements of the dimensionless transfer coefficients Cd, Cv and Ch for the exchange of (stream-wise) momentum, mass, and heat, between a single artificial leaf and the airflow in a wind-tunnel. It was shown that Cv, h = C0(D/v, k/v)2/3 where D, k and v are the molecular diffusivities in air of gas or vapour, heat, and momentum, and where C0 is a generalized mass or heat transfer coefficient almost independent of ϕ, the angle of incidence between the leaf and the airflow, Cd, however, made up of a bluff-body or pressure part Cb, in addition to a molecular skin friction part Cf, depended strongly on ϕ. C0 was close to the theoretical skin friction drag coefficient at ϕ = 0 of a thin flat plate with dimensions similar to the leaf. As a general relation between the corresponding coefficients of a natural rough surface CF = βC0, where β lies between 0·1 and unity, depending on the form and inclination (ϕ) of the roughness elements, and on wind speed. C0 was shown experimentally to be proportional to (wind speed)−1/2 in a regime of fully-forced convection. When the evaporation from one side of the leaf was stopped, the transfer coefficient for the removal of vapour from the other side increased by about 30 per cent. An accurate form of the psychrometric constant of the leaf includes the factor (k/D)2/3, which has the value 0·90 for water vapour.

142 citations


Journal ArticleDOI
TL;DR: In this paper, the Boussinesq equations are expanded in two parameters: η, and the amplitude e.g., the direction of the motion depends upon the sign of η.
Abstract: When a horizontal layer of fluid is heated from below and cooled from above with the mean temperature and physical parameters of the fluid constant, the two-dimensional roll is known to be the stable solution near the critical Rayleigh number. In this study, with the mean temperature changing steadily at a rate η, the Rayleigh number and the velocity and temperature fields governed by the Boussinesq equations are expanded in two parameters: η, and the amplitude e. Hexagons are shown to be the stable solution near the critical Rayleigh number. The direction of the motion depends upon the sign of η. A finite amplitude instability is possible with an associated hysteresis in the heat flux as the critical Rayleigh number is approached from below or from above.

142 citations


Journal ArticleDOI
TL;DR: In this paper, a method for calculating convection coefficients for thin broad leaves of arbitrary shape, using existing equations for rectangular flat plates, is described, and experimental data from long, narrow leaf models show that convection in flow perpendicular to the leaf surface may be almost double the value for parallel flow.

120 citations


Journal ArticleDOI
01 Oct 1968-Nature
TL;DR: In this article, a model for convection in the upper mantle of the Earth comprising two flows, one of percolating melt fluid (which need a small volume fraction in the intergranular channels of coherent solid matter), the other a solid plastic flow, avoids some paradoxical features of other models for mantle convection.
Abstract: A model for convection in the upper mantle of the Earth comprising two flows, one of percolating melt fluid (which need be no more than a small volume fraction in the intergranular channels of coherent solid matter), the other a solid plastic flow, avoids some paradoxical features of other models for mantle convection. This model leads to a reasonably consistent account of the processes of continental drift.

90 citations


Journal ArticleDOI
TL;DR: In the presence of a large restoring force, an oscillating convective motion is possible in a thin layer of an elasticoviscous liquid as mentioned in this paper, where the restoring force is large.
Abstract: In the presence of a large restoring force, an oscillating convective motion is possible in a thin layer of an elasticoviscous liquid.

84 citations


Journal ArticleDOI
TL;DR: In this paper, Krishnamurti et al. showed that when the mean temperature of a fluid layer is changing at a constant rate η, hexagonal flows are stable in a range of Rayleigh numbers near the critical point.
Abstract: It has been found in part 1 (Krishnamurti 1968) that when the mean temperature of a fluid layer is changing at a constant rate η, hexagonal flows are stable in a range of Rayleigh numbers near the critical. The direction of flow depends upon the sign of η. The static state is unstable to finite amplitude disturbances at Rayleigh numbers below the critical point predicted by linear theory. The validity of this theory is tested in an experiment in which the heat flux is measured as a function of η and Rayleigh number. The horizontal plan form is determined from the side by continuously exposing a photographic film moving in a vertical direction as tracers in different regions of the fluid are illuminated. Finite amplitude instability and hexagonal cells are indeed observed.

76 citations


Journal ArticleDOI
TL;DR: In this article, the operating characteristics of an atmospheric pressure, rf plasma torch and its associated 30kW power oscillator are inferred from available instrumentation and calorimetric heat balance measurements with various working fluids in torches of two diameters.
Abstract: Operating characteristics of an atmospheric‐pressure, rf plasma torch and of its associated 30‐kW power oscillator are inferred from available instrumentation and calorimetric heat balance measurements with various working fluids in torches of two diameters. The governing equations for the arc, neglecting convection, are derived and solved analytically for the crude channel‐model approximation. Material functions for argon and nitrogen are then used to predict operating characteristics for these fluids. Fair agreement indicates that at least some of the essential physical phenomena of the discharge have been resolved. The analysis serves to explain much of the ``art of operation'' with special emphasis on the concepts of coupling and impedance matching.


Journal ArticleDOI
TL;DR: In this article, an analysis of axisymmetric poloidal circulation in a rotating compressible sphere was conducted, and it was shown that convection of heat is the only important nonlinear term.
Abstract: The external nonhydrostatic gravity field must be maintained by flow within the mantle. An analysis of axisymmetric poloidal circulation in a rotating compressible sphere shows it to be more important than was previously believed. However, such flow is probably unable to produce the observed nonhydrostatic equatorial bulge. The basic equations are nonlinear, but can be solved if the viscosity is sufficiently large. The conditions which must be satisfied before this approximation is valid are examined in some detail because of their relevance to convection in the mantle. The horizontal temperature differences between oceans and continents must also drive convection currents, though such flow can only be of local importance at present. Two-dimensional convection driven by horizontal temperature variations can successfully account for most of the phenomena which are believed to be the surface expressions of flow in the mantle. The only exception is the gravity anomaly over the rising current, which is positive in the model. Though this linear theory is not self consistent, it does show that convection of heat is the only important nonlinear term. Further understanding of the problem will require numerical analysis.


Journal ArticleDOI
TL;DR: When an insulating paramagnetic fluid such as gaseous oxygen is subjected to combined thermal and magnetic field gradients, a magnetic body force is shown to exist which is analogous to that of gravity as discussed by the authors.
Abstract: When an insulating paramagnetic fluid such as gaseous oxygen is subjected to combined thermal and magnetic field gradients, a magnetic body force is shown to exist which is analogous to that of gravity. It is shown both theoretically and experimentally that this magnetic body force can be larger in magnitude than that due to gravity for gaseous oxygen for even modest values of the magnetic field strength‐gradient product. The possibility of magnetic control of thermal convection is discussed for several instances. The application of this effect to control thermal convection during crystal growth from paramagnetic liquids is discussed in detail.

Journal ArticleDOI
TL;DR: In this paper, an analytical procedure is developed to investigate the interaction or coupling of radiation with the conduction and convection mechanism in a nonisothermal, nongray gas flowing in the entrance region of a tube with isothermal, black walls.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the Nusselt number for liquid metals in the Reynolds number range 3 × 104 to 3 × 105 is distorted by a superimposed free convection effect up to Reynolds numbers of at least 50000.

Journal ArticleDOI
H. L. Kuo1
TL;DR: In this article, the authors investigated the thermal interaction between the atmosphere and the underlying earth, as related to the diurnal heat wave, through the use of a modified virtual conduction model in which the influences of turbulence and thermal convection are simulated by diffusion while the influence of terrestrial radiation is approximated partly by diffusion and partly by a Newtonian cooling, the ratio between the two parts increasing from summer to winter.
Abstract: The thermal interaction between the atmosphere and the underlying earth, as related to the diurnal heat wave, is investigated through the use of a modified virtual conduction model in which the influences of turbulence and thermal convection are simulated by diffusion while the influence of terrestrial radiation is approximated partly by diffusion and partly by a Newtonian cooling, the ratio between the two parts increasing from summer to winter. The virtual thermal diffusivity is assumed to vary both in time and in space in order to represent the various physical processes involved in accomplishing the actual heat transfer. It is shown that a mean upward transport of heat is maintained through the diurnal variation of the transfer process although the mean lapse rate is stable, thereby removing a long-standing difficulty in evalutating the turbulent heat flux from the mean potential temperature distribution. The solar energy received at the surface is found to be partitioned into the two media a...

Journal ArticleDOI
TL;DR: In this article, it was observed that during the melting of small ice particles supported in a vertical wind tunnel, strong convection currents developed in the melt water and bubbles released from the ice during melting were swept up by the currents and rapidly transferred to the surface where they burst.
Abstract: It was observed that during the melting of small ice particles supported in a vertical wind tunnel, strong convection currents developed in the melt water. Bubbles released from the ice during melting were swept up by the currents and rapidly transferred to the surface where they burst. The separation of electric charge accompanying the bursting of the bubbles was highly dependent on the convection currents in the water. The observed charging effects are not entirely consistent with theories based on the disruption of an electric double layer. In particular, the separation of charge is considerably increased if the air contains high concentrations of CO2. It is shown that the observed values of charge separation are sufficient to account completely for the presence of the lower pocket of positive charge found below the melting level in many thunderstorms.

Journal ArticleDOI
TL;DR: In this article, convective and radiative heat transfer to entry vehicles protected by ablation heat shield, obtaining absorption coefficients, is described. But the authors do not consider the effect of the temperature of the vehicles.
Abstract: Convective and radiative heat transfer to entry vehicles protected by ablation heat shield, obtaining absorption coefficients

Journal ArticleDOI
TL;DR: In this article, the problem of the onset of thermal instability in heated layers of fluid is investigated in a linear approximation, assuming the confining planes to be surfaces of constant heat flux, and it is shown that in the absence of time dependence, a limiting point of the neutral stability curve can be obtained exactly by analytical methods.
Abstract: The problem of the onset of thermal instability in heated layers of fluid is investigated in a linear approximation, assuming the confining planes to be surfaces of constant heat flux. It is shown that in the absence of time dependence a limiting point of the neutral stability curve can be obtained exactly by analytical methods. This point is evaluated for a variety of boundary conditions on the fluid motion, and it is verified that the results give criteria for the onset of instability as stationary convection. Similar calculations are made for an idealized fluid in the time‐dependent case, and it is established that the combined effects of buoyancy and surface‐tension gradients may lead to overstable oscillations in certain circumstances.

Journal ArticleDOI
TL;DR: In this paper, the axisymmetric flow of liquid in a rigidly bounded annular container of height H, rotating with angular velocity Ω and subjected to a temperature difference ΔT between its vertical cylindrical perfectly conducting side walls, whose distance apart is L, is analyzed in the boundary-layer approximation for small Ekman number v/2ΩL2, with gαΔTHv/4Ω2L2K ∼ 1.
Abstract: The axisymmetric flow of liquid in a rigidly bounded annular container of height H, rotating with angular velocity Ω and subjected to a temperature difference ΔT between its vertical cylindrical perfectly conducting side walls, whose distance apart is L, is analysed in the boundary-layer approximation for small Ekman number v/2ΩL2, with gαΔTHv/4Ω2L2K ∼ 1. The heat transfer across the annulus is then convection-dominated, as is characteristic of the experimentally observed ‘upper symmetric regime’. The Prandtl number v/k is assumed large, and H is restricted to be less than about 2L. The side wall boundary-layer equations are the same as in (non-rotating) convection in a rectangular cavity. The horizontal boundary layers are Ekman layers and the four boundary layers, together with certain spatial averages in the interior, are determined independently of the interior flow details. The determination of the latter comprises a ‘secondary’ problem in which viscosity and heat conduction are important throughout the interior; the meridional streamlines are not necessarily parallel to the isotherms. The secondary problem is discussed qualitatively but not solved. The theory agrees fairly well with an available numerical experiment in the upper symmetric regime, for v/k [bumpe ] 7, after finite-Ekmannumber effects such as finite boundary-layer thickness are allowed for heuris-tically.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the onset of haline convection induced by the freezing of sea water and derived the time necessary for the manifest convective behavior and horizontal spacing of the convection cells for various manners of increasing the salinity at the top surfaces.
Abstract: The onset of haline convection induced by the freezing of sea water is investigated. The linear analysis appropriate to the onset of thermal convection is applied to haline convection by replacing the temperature variables in the equations with salinity variables. Expressions for the time necessary for the onset of manifest convective behavior and the horizontal spacing of the convection cells are derived for various manners of increasing the salinity at the top surfaces. For molecular coefficients of viscosity and diffusion and cooling conditions that may be appropriate for the freezing season in the Antarctic it is found that the initial horizontal spacing of convection cells is about 0.3 cm.

Journal ArticleDOI
TL;DR: In this paper, an attempt is made to calculate the length of the ice-free reach that develops during the winter below a thermal pollution site on a river, where a differential equation for the steady-state heat balance of a volume element of a river is developed.
Abstract: An attempt is made to calculate the length of the ice-free reach that develops during the winter below a thermal pollution site on a river. A differential equation for the steady-state heat balance of a volume element of a river is developed, which leads to the expression x=Cx∫TwoTwxdTw/Q* where x is distance downstream from the pollution site to the cross section where the water temperature equals Twx, Two is water temperature at x equals zero, Q* is rate of heat loss from the water surface, and Cx is a constant that includes flow velocity and depth. The value of x at Twx equals 0°C is taken as the length of the ice-free reach. Q* is the sum of heat losses due to evaporation, convection, long- and short-wave radiation, and other processes, each of which is evaluated by an empirical or theoretical expression. The two principal limitations in accurately calculating downstream temperature changes are related to difficulties in evaluating the degree of lateral mixing in natural rivers and the convective and evaporative heat losses under unstable atmospheric conditions. Observations of lengths of ice-free reaches on the Mississippi River are in good agreement with the calculated values. Significant portions of the St, Lawrence Seaway can be kept ice-free by the installation of nuclear reactors at appropriate locations.

Journal ArticleDOI
TL;DR: The critical points for the onset of convection for the systems benzene-carbon tetra-chloride and chlorobenzene-car tetrachloride were determined in this article.

Journal ArticleDOI
TL;DR: The onset of convection in a layer of water formed continuously by melting ice from below, has been determined experimentally as mentioned in this paper, and the critical Rayleigh number Rac for a fluid undergoing phase change and density inversion is correlated empirically as a function of warm plate temperature T8.
Abstract: The onset of convection, or the critical Rayleigh number in a layer of water formed continuously by melting ice from below, has been determined experimentally. Homogeneous, bubble‐free ice was prepared, and used in all the experiments. The critical Rayleigh number Rac for a fluid undergoing phase change and density inversion is not a single value but may be correlated empirically as a function of warm plate temperature T8 by Rac = 14 200 exp (−6.64 × 10−2T8). This relation is valid for T8 varying from 6.72‐25.50°C. The initial ice sample temperature T0 was varied from −4.8 to −22.00°C. The effect of T0 was found to be insignificant.

01 Aug 1968
TL;DR: Magnetospheric convection patterns inferred from high latitude ionospheric currents - use and limitations of convection models as mentioned in this paper, using a convection model from high-latitude ionosphere currents.
Abstract: Magnetospheric convection patterns inferred from high latitude ionospheric currents - use and limitations of convection models

Journal ArticleDOI
TL;DR: In this paper, an analysis of the heat and vapor diffusion from the walls of the chamber indicates that the counter does indeed develop the supersaturations predicted by thermodynamics in the absence of dropwise condensation and that the natural sensitive time is of the order of 0.3 sec.
Abstract: The measurement of the temperature drop in a dry Pollak condensation nucleus counter by Israel and Nix has been interpreted as an indication that the expansion process does not yield as high a supersaturation as predicted by thermodynamics. An analysis of the heat and vapor diffusion from the walls of the chamber indicates that the counter does indeed develop the supersaturations predicted by thermodynamics in the absence of dropwise condensation and that the natural sensitive time is of the order of 0.3 sec. The measurements of Israel and Nix can be explained in terms of a thermal analysis of the thermocouple itself. The seemingly rapid response of the thermocouple is an indication of the attainment of the steady-state heat flow from the thermocouple and is not an indication that the thermocouple is reading the temperature of the ambient gas accurately. Moreover, the anomalous temperature drop observed about 1 sec after the expansion marks the point at which convection currents sweep away the he...