Showing papers on "Combined forced and natural convection published in 1992"

Laminar flow and convective transport processes : scaling principles and asymptotic analysis

Abstract: Basic Principles Unidirectional Flows Creeping Flows Further Results in the Creeping Flow Limit Asymptotic Approximations for Unidirectional, One-Dimensional, and Nearly Unidirectional Flows Thin Films, Lubrication, and Related Problems Weak Convection Effects Strong Convection Effects in Heat and Mass Transfer at Low Reynolds Number Laminar Boundary-Layer theory Thermal Boundary-Layer Theory at Large Reynolds Number Natural and Mixed Convection Flows.

Three-dimensional convection in a horizontal fluid layer subjected to a constant shear

Abstract: Rayleigh-Be'nard convection in the presence of a plane Couette flow is investigated by numerical computations. From earlier work it is well known that longitudinal rolls are preferred at the onset of convection and that at Prandtl numbers of the order unity or less these rolls become unstable with respect to the wavy instability which introduces wavy distortions perpendicular to the axis of the rolls. In the present analysis the three-dimensional flows arising from these distortions are studied and their stability is considered. A main result is the subcritical existence of three-dimensional flows at Rayleigh numbers far below the critical value for onset of convection.

Chaos in models of double convection

Abstract: In certain parameter regimes, it is possible to derive third-order sets of ordinary differential equations that are asymptotically exact descriptions of weakly nonlinear double convection and that exhibit chaotic behaviour. This paper presents a unified approach to deriving such models for two-dimensional convection in a horizontal layer of Boussinesq fluid with lateral constraints. Four situations are considered: thermosolutal convection, convection in an imposed vertical or horizontal magnetic field, and convection in a fluid layer rotating uniformly about a vertical axis. Thermosolutal convection and convection in an imposed horizontal magnetic field are shown here to be governed by the same sets of model equations, which exhibit the period-doubling cascades and chaotic solutions that are associated with the Shil'nikov bifurcation (Proctor & Weiss 1990). This establishes, for the first time, the existence of chaotic solutions of the equations governing two-dimensional magneto-convection. Moreover, in the limit of tall thin rolls, convection in an imposed vertical magnetic field and convection in a rotating fluid layer are both modelled by a new third-order set of ordinary differential equations, which is shown here to have chaotic solutions that are created in a homoclinic explosion, in the same manner as the chaotic solutions of the Lorenz equations. Unlike the Lorenz equations, however, this model provides an accurate description of convection in the parameter regime where the chaotic solutions appear.

Laminar flow analysis

Abstract: Preface 1. Derivation of the Navier-Stokes equations 2. Exact solutions of the Navier-Stokes equations 3. Boundary layer theory 4. Thermal boundary layers - forced convection 5. Thermal boundary layers - free convection 6. Compressible boundary layers Appendices.

The oceanography of winter leads

Abstract: Leads in pack ice have long been considered important to the thermodynamics of the polar regions. A winter lead affects the ocean around it because it is a density source. As the surface freezes, salt is rejected and forms more dense water which sinks under the lead. This sets up a circulation with freshwater flowing in from the sides near the surface and dense water flowing away from the lead at the base of the mixed layer. If the mixed layer is fully turbulent, this pattern may not occur; rather, the salt rejected at the surface may simply mix into the surface boundary layer. In either event the instability produced at the surface of leads is the primary source of unstable buoyancy flux and, as such, exerts a strong influence on the mixed layer. Here as many as possible of the disparate and almost anecdotal observations of lead oceanography are assembled and combined with theoretical arguments to predict the form and scale of oceanographic disturbances caused by winter leads. The experimental data suggest the velocity disturbances associated with lead convection are about 1–5 cm s−1. These appear as jets near the surface and the base of the mixed layer when ice velocities across the lead are less than about 5 cm s−1. The salinity disturbances are about 0.01 to 0.05 psu. Scaling arguments suggest that the geostrophic currents set up by the lead density disturbances are also of the order of 1–5 cm s−1. The disturbances are most obvious when freezing is rapid and ice velocity is low because the salinity and velocity disturbances in the upper ocean are not smeared out by turbulence. In this vein, lead convection may be characterized at one extreme as free convection in which the density disturbance forces the circulation. At the other extreme, lead convection may be characterized as forced convection in which the density disturbance is mixed rapidly by boundary layer turbulence. The lead number Lo, which is the ratio of the pressure term to the turbulence term in the momentum equation, and the turbulent lead number Lot, which is the ratio of buoyant production to shear production in the turbulent kinetic energy equation, define the boundary between the free and forced regimes. For Lo and Lot less than one, both the large-scale circulation and the turbulence are forced by surface stress. For Lo and Lot greater than one, both the large-scale circulation and the turbulence are forced by the buoyancy flux. The magnitudes of velocity and salinity disturbances from a model developed elsewhere, suitable to free convection, agree with what few observations we have. The results of a forced convection model, developed here, suggest salinity disturbances of the order of 0.01–0.02 practical salinity units, with the maximum occurring at the surface of the lead and decreasing substantially below 5–10 m. This unstable gradient is a unique characteristic of lead convection. Though the salinity disturbances may be small when ice velocities are large, the buoyancy flux in leads has a major effect on the boundary layer turbulence.

Transition to a periodic regime in mixed convection in a square cavity

Abstract: This work describes the transition from a steady, laminar regime to a periodic regime in an air-filled, two-dimensional cavity subjected to localized heating The interaction of the buoyancy induced flow with a cold air stream that flows through leads to steady flow and thermal fields only for values of the Grashof number that are lower then a certain critical value Gr cr As Gr cr is exceeded, an unstable situation arises and, after an initial transient, the results show a very regular, periodic, almost sinusoidal behavior Similar previous works on natural convective flows in cavities have discovered such a periodic behavior, as a form of travelling wave instability, having the characteristics of a Hopf bifurcation The present problem is also governed by the Reynolds number and its effect on the results is studied as well The observed instability was found to be of thermal origin

Experiments on convection in rotating hemispherical shells: Transition to a quasi‐periodic state

Abstract: Convection driven by thermal buoyancy in the presence of the Coriolis force occurs in planetary atmospheres and interiors. In order to model convection subject to nearly spherically symmetric distributions of gravity and temperature, a hemisphere has been constructed which can be rotated about its axis of symmetry. The angular velocity is selected such that the paraboloidal surfaces of equal potential match closely surfaces of constant radius within the hemispherical fluid shell. While the baroclinicity of the fluid state is still noticeable, quantitative measurements can be obtained which can be compared with the theoretical calculations for the spherically symmetric case. The drift of the convection columns has been measured and a transition from the singly periodic state of convection to a modulated state has been visualized and determined quantitatively.

Laminar Mixed Convection from a Uniform Heat Flux Horizontal Cylinder in a Crossflow

Abstract: An analysis of combined forced and natural convection (mixed convection) heat transfer from a horizontal cylinder dissipating a uniform heat flux is conducted by solving the full two-dimensional steady-state Navier Stokes and energy equations. For Pr = 0.7, flowfields and transport results are determined in the ranges of Reynolds numbers 1 < ReD < 60 and the modified Grashof numbers 0 < Gr£ < 1.6 x 10. The results are presented as local and average values of the Nusselt number, the vorticity, the pressure distribution and the coefficient of drag around the cylinder. Correlation for the average Nusselt number and the coefficient of drag around the cylinder in the forced convection regime is suggested. Comparison with theoretical and experimental correlations is established. It was established that the Nusselt number as well as drag coefficient increase with the buoyancy parameter. It was also shown that uniform heat flux horizontal cylinder has higher Nusselt number than a cylinder under uniform surface temperature.

Natural Convection With Radiation in a Cavity With Open Top End

Abstract: The heat transfer by natural convection and radiation in a two-dimensional cavity with one side heated, one side and bottom insulated, and the top open was investigated numerically The first part of the study focused on natural convection alone, and concluded with closed-form correlations for the heat transfer from each of the side walls It was found that the fluid rises along both side walls in the boundary layer regime In the second part of the study, the natural convection correlations were incorporated into a seven-equation model for combined convection and radiation The procedure needed for calculating the floating temperature of the insulated wall was illustrated numerically The individual effects of the dimensions of the cavity, the temperature of the heated wall, and the emissivities of the two side walls were also documented numerically

Strongly chaotic non-newtonian mantle convection

Abstract: We have studied the problem of strongly time-dependent, two-dimensional, incompressible, infinite Prandtl number thermal convection in an aspect-ratio five box for a non-Newtonian power-law rheology and a heated from below configuration, as applied to mantle dynamics. The convection equations are solved by means of a characteristics-based method with a Lagrangian formulation of the total derivative in the energy equation. Iterations are required at each time step for solving the nonlinear momentum equation. Bicubic splines are used for the spatial discretization. The transition from mildly time-dependent to the strongly chaotic or turbulent regime, in which the plumes become disconnected, occurs at much lower Nusselt numbers (Nu), between 20 and 25, than for Newtonian rheology. TheNu versus Rayleigh number(Ra) relationship displays a kink at this transition. Rising non-Newtonian plumes exhibit much greater curvature in their ascent than Newtonian ones and are strongly attracted by descending curr...

An experimental approach to thermochemical convection in the Earth's core

Abstract: Both thermal and compositional buoyancy affect convection in the Earth's liquid outer core. We report preliminary experiments on the structure of thermochemical convection in a rotating sphere with the geometry of the Earth's core. Fully-developed thermochemical convection in a rapidly rotating sphere is driven by buoyant ribbon-shaped plumes concentrated in the equatorial region. Curtains of fluid aligned parallel to the rotation axis and extending across the sphere move with the plumes. The motion is turbulent in planes parallel to the equator. The convection generates a secondary, large scale zonal flow which is primarily retrograde (westward). The main difference between chemically-dominated and thermally-dominated convection is the smaller scales of motion present when compositional buoyancy drives the flow. In cases when both are present simultaneously, the probable situation in the outer core, we find the structure of the motion is similar to purely thermal convection.

Reversed Flow Structure and Heat Transfer Measurements for Buoyancy-Assisted Convection in a Heated Vertical Duct

Abstract: Buoyancy-assisted convection flow and heat transfer processes in a heated vertical channel are studied experimentally for situations where the buoyancy Parameter Gr/Re[sup 2] is relatively large. The channel wall is made of two parallel plates, with one wall heated uniformly and the opposite wall insulated. A uniform air flow is made to enter the channel from the bottom. The reversed flow is visualized, which occurs initially near the channel exit for the case when Gr/Re[sup 2] is greater than a threshold value. The cold reversed flow enters the channel from the outside and forms a V-shaped recirculating flow region in the downstream part of the duct. This region gradually propagates upstream as the buoyancy parameter Gr/Re[sub 2] increases. The counterflow motion, leading to mixing between the heated buoyant fluid and the V-shaped recirculation, is shown to be highly unstable and characterized by generation of eddies and vortices when the value of Gr/Re[sup 2] is large. An increase in Re has the effect of pushing the reversed flow downstream and making the recirculating region wider. Temperature fluctuations are measured to provide insight into the complex phenomena being -studied. The penetration depth of the reversed flow is measured and compared with predictionmore » based on a simple model. Local and average Nusselt numbers are also measured and presented.28 refs., 11 figs.« less

Convection within the inner‐core and thermal implications

Abstract: Estimation of the Rayleigh numbers of the inner-core leads to the conclusion that, even with low internal heating rates, this region of the Earth is convecting. This work presents an axisymmetrical model able to investigate convection in a sphere and its applications to the Earth's inner-core. Rayleigh numbers ranging from the critical (onset of the convection) to ten thousand times the critical have been explored. The thermal implications of a convecting inner-core have been pointed out: in all the cases the temperature profiles are very close to the adiabat, leading to the possibility of a partially molten regions in the inner-core. Indeed, the most important effects appear in the first tens of kilometers, just below the inner-core surface and could be at the origin of the low quality factors Qα and Qβ revealed by seismological studies.

Convection in a rotating cylindrical annulus Part 3. Vacillating and spatially modulated flows

Abstract: The problem of convection driven by radial buoyancy in a rotating cylindrical annulus with conical end surfaces represents one of the basic models of rotating fluid dynamics with applications to convection in planets and stars Although only two-dimensional equations govern the flow in the limit of high rotation rates, a surprising variety of different states of motion can be found In this paper earlier numerical work is extended by the consideration of rigid boundary conditions at the cylindrical walls and by a study of spatially modulated convection

Conjugate conduction and laminar mixed convection in vertical pipes for upward flow and uniform wall heat flux

Abstract: This paper presents the results of a numerical investigation of conjugate conduction and laminar mixed convection in vertical pipes for upward flow and uniform wall heat flux. The Prandtl number was fixed at 5; the Grashof number, based on heat flux, was set at 5000; and Reynolds numbers of 1 and 10 were used. Results are presented for four different values of solid-to-fluid thermal conductivity ratio K and three different values of wall thickness-to-pipe diameter ratio Δ. The effects of axial conduction in the pipe wall are quite pronounced when K and Δ are high and Re is low. In one case, upstream axial wall conduction distorted the parabolic velocity profile at the entrance of an upstream section to the point that the centerline velocity was negative at the entrance of the heated section, which established a zone of recirculation. Experimental flow visualization results and corresponding numerical predictions of these recirculation zones are also presented.

Mass and heat transport in strongly time-dependent thermal convection at infinite prandtl number

Abstract: We have studied heat and mass transport in two-dimensional, infinite Prandtl number, incompressible thermal convection for a range of Rayleigh numbers (Ra), between 106 and 108, and two different aspect-ratio boxes, between 1·8 and 10. This study has been motivated by recent developments in studying the transition from weak to strong turbulence in thermal convection. We have employed a two-dimensional finite element method in solving the time-dependent convection equations. Passive tracers, up to 900, have been put into the flow fields for monitoring the style and pattern of mass transport. At Ra around 106 convection does not take place in a strictly cellular mode. Thermals are ejected from the hot and cold boundary layers. These boundary-layer instabilities enhance the mass transport in the interior of individual cells. The fate of these instabilities is determined ultimately by the large-scale circulation. The persistent large-scale circulation gives rise to a significant decrease of the heat ...

Liquid Immersion Cooling of a Longitudinal Array of Discrete Heat Sources in Protruding Substrates: I—Single-Phase Convection

Abstract: Experiments have been performed using water and FC-77 to investigate heat transfer from an in-line 1 x 10 array of discrete heat sources, flush mounted to protruding substrates located on the bottom wall of a horizontal flow channel. The data encompass flow regimes ranging from mixed convection to laminar and turbulent forced convection. Buoyancy-induced secondary flows enhanced heat transfer at downstream heater locations and provided heat transfer coefficients comparable to upstream values. Upstream heating extended enhancement on the downstream heaters to larger Reynolds numbers. Higher Prandtl number fluids also extended heat transfer enhancement to larger Reynolds numbers, while a reduction in channel height suppressed buoyancy driven flows, thereby reducing enhancement. The protrusions enhanced the transition to turbulent forced convection, causing the critical Reynolds number to decrease with increasing row number. The transition region was characterized by large heater-to-heater variations in the average Nusselt number.