Showing papers on "Natural convection published in 1975"

The Overall Convective Heat Transfer from Smooth Circular Cylinders

Abstract: Publisher Summary Accurate knowledge of the overall convective heat transfer from circular cylinders is of importance in a number of fields, such as boiler design, hotwire anemometry, and the rating of electrical conductors. The wide dispersion in the published experimental data for the heat transfer from smooth circular cylinders by natural and forced convection is attributed to various factors associated with the experiments. The error due to heat conduction to the supports is particularly important with natural convection, especially where the heat loss and the temperature rise of the cylinder are calculated from the voltage drop across it. A common cause of error is the use of too small a space ratio, so that the temperature and velocity fields are distorted. To reduce this error to less than l%, the space ratio D c /D for natural convection or D T /D for forced convection should exceed 100. The error caused by blockage with wind tunnel measurements can be calculated depending on the type of tunnel. One of the greatest sources of error with forced convection is the failure to allow for the effect of stream turbulence.

On the interaction of two scales of convection in the mantle

Abstract: A system in which convection takes place in the upper mantle on two distinct horizontal length scales is proposed. This is consistent with the existence of the plates themselves, the relatively constant heat flux background in older ocean basins, and the knowledge of convection in fluid layers gained from laboratory and numerical experiments. The large-scale circulation consists of the plates themselves and the return flow necessary to conserve mass. The small-scale flow, analogous to Rayleigh-Benard convection or variants of this, which have been the main target of numerical study, provides the necessary vertical heat transport in the upper mantle that supplies the required heat flux at the base of the lithosphere. The depth of convection is taken to be down to the 650-km seismic discontinuity, and this depth characterizes the horizontal length scale of the small-scale convection. This system is studied by means of a set of laboratory experiments that explore the interaction of the small-scale convection with the large-scale flow. The experiments show the plausibility of convection on two scales. Furthermore, they suggest that beneath fast-moving plates (absolute velocities around 10 cm y−1) the small-scale convection will align itself as rolls in the direction of the large-scale flow in geologically short times. However, beneath very slow moving plates the times required for the alignment of convective rolls are long in comparison with times over which no changes in plate motions are to be expected. Here the convective planform is more likely to take the form of upwelling and downwelling spouts. Thus this simple system of a convecting layer beneath a moving boundary contains the possibility of explaining a wide variety of surface features. Observational tests of the consequences of the two-scale idea are suggested, and the assumptions on which this idea is based are critically discussed.

Sloping convection in a rotating fluid

Abstract: Laboratory experiments on thermal convection in a fluid which rotates about a vertical axis and is subject to a horizontal temperature gradient show that when the rotation rate Ω exceeds a certain critical value ΩR (which depends on the acceleration of gravity, the shape and dimensions of the apparatus, the physical properties of the fluid and the distribution and intensity of the applied differential heating) Coriolis forces inhibit overturning motion in meridian planes and promote a completely different type of flow which has been termed ‘sloping convection’ or ‘baroclinic waves’. The motion is then non-axisymmetric and largely confined to meandering ‘jet streams’, with trajectories of individual fluid elements inclined at only very small (though essentially non-zero) angles to the horizontal. The kinetic energy of the waves derives from the interaction of slight vertical motions with the potential energy field maintained by differential heating, and it is dissipated by friction arising largely...

A General Method of Obtaining Approximate Solutions to Laminar and Turbulent Free Convection Problems

Abstract: Publisher Summary The first part of the chapter focuses on determining equations for the local and mean rate of laminar heat transfer, which are approximately valid for different geometries By use of these equations, several new correlations are obtained for various laminar heat transfer problems, and the results compared with experiments The problems considered involve heat transfer (1) from a cylinder, (2) from a sphere, (3) between concentric cylinders, (4) between concentric and eccentric spheres, (5) between vertical plates, and (6) from a nonisothermal vertical plate Attention is then turned to turbulent free convection heat transfer where the heat transfer from inclined plates and between differentially heated plates is considered A method of solving problems involving both laminar and turbulent convection is then outlined The criterion developed for the regions of applicability of the laminar and turbulent equations is shown to accurately predict the experimentally determined onset of instability of the laminar flow for free convection from an isolated plate A recommendation is then made for correlating heat transfer results in a clearer and more convenient way

Stability characteristics of a single-phase free convection loop

Abstract: Experiments investigating the stability characteristics of a single-phase free convection loop are reported. Results of the study confirm the contention made by previous workers that instabilities near the thermodynamic critical point can occur for ordinary fluids as well as those with unusual behavior in the near-critical region. Such a claim runs counter to traditional beliefs, but it is supported by the observation of such instabilities for water at atmospheric pressure and moderate temperatures in the present work.

Thermoconvective instabilities in a horizontal porous layer

Abstract: Experimental investigations of natural convection in a porous layer placed between two horizontal and isothermal plane surfaces have revealed a new type of convection as the Rayleigh number Ra* increases: fluctuating convection. A numerical study carried out on a two-dimensional model in order to simulate this phenomenon shows that, apart from the influence of the Rayleigh number, the aspect ratio A (length/height) of a vortical cell is the most important parameter for the occurrence of this type of convection. These quasi-periodic fluctuations induce important variations in the temperature field and in the streamlines. The total heat transport, as defined by the Nusselt number Nu*, varies within limits which may be separated by 80% of the mean value. Using the Galerkin method it is possible to deduce the conditions for the onset of convection from a state of pure conduction and also to define the critical conditions for the development of fluctuating convection from another perturbed state. A physical interpretation of the results is given for each type of convection. The results seem to agree with the experimental and numerical results obtained by different authors.

Free convection in low-temperature gaseous helium

Abstract: Free convection has been studied in gaseous helium at low temperatures in a cylindrical vessel of aspect ratio (diameterlheight) 2·5. Compared with measurements in fluids at room temperature the present arrangement has the advantages of small size, a short time constant and improved accuracy. As the Rayleigh number was varied from 60 to 2 × 109, the Nusselt number rose from 1 to 69, obeying the relation Nu = 0·173Ra0·2800±0·0005 over the upper four decades of Ra. The critical Rayleigh number was 1630, but the conditions of the experiment did not allow reliable measurements at such low values of Ra. The very high sensitivity within a given experiment showed the presence of several ‘discrete transitions’, which were often step like and not merely a change of gradient as reported by other workers. The largest of these, at Ra = 3 · 105, involved a drop in heat flux of some 6% and was somewhat hysteretic. The temperature fluctuations increased markedly as the step was crossed.

Nonlinear Thermal Convection

Abstract: The topic of this. review article is thermal convection in thin horizontal fluid layers, uniformly heated from below and/or cooled from above. If the temperature difference between the two horizontal boundaries is sufficiently small, the heat will be transferred through the fluid by conduction alone. For greater temperature differences the conduction state becomes unstable and a convective motion is set up. The first experimental investigations on thermal convection date back to Thomson (1881) and Benard ( 1900). The experiments by Benard in particular have attracted great attention and are today considered classical in fluid mechanics. This is essentially due to the surprising and fascinating pattern of very regular hexagonal cells obtained for large values of time in his experiments. Benard studied convective motion in a very shallow layer of viscous fluid (molten spermaceti) and made the motion visible by graphite or aluminum powder. The theory of thermal convection was initiated by Rayleigh ( 1916). He assumed that the amplitude of the motion was infinitesimal such that the equations could be linearized. He thus derived the critical temperature gradient (or in modern language, the critical Rayleigh number) for the onset of convection together with the wavenumber for the marginal stable mode. The resemblance of the cell pattern in the Rayleigh theory to certain cloud forms was early noticed by meteorologists. For example, it was pointed out that often the observed ratio between the vertical height and the lateral extent in cumulus clouds is the same as found in the theory for hexagonal cells. The theory on cloud formation is perhaps best applied to the convective motion set up in an altostratus layer when it breaks up into altocumulus clouds because of radiative cooling at the top of the layer. This application is, however, obscured by the effect of the release of latent heat, which is not accounted for in the theory. The theory on thermal convection has become very important in the study of motion in the earth's interior (see Turcotte & Oxburgh 1972) and also in some branches of astrophysics (Spiegel 1971 , 1972). The great interest shown to the theory for the last 10--15 years is partly due to these and other applications. The main

Natural convection in a porous medium - Effects of confinement, variable permeability, and thermal boundary conditions

Abstract: Two-dimensional numerical calculations are reported for natural convection of a fluid in a porous, horizontal layer heated from below. Effects of the following parameters are examined: rigid (impermeable) and constant-pressure (permeable) upper boundaries; isothermal and uniform heat flux at the lower boundary; and permeabilities which are constant, or which vary with depth to simulate compaction of a porous medium or property variations of real fluids within the medium. Steady-state results are presented for the heat flux distribution on the upper surface, as well as for flow and temperature fields in the interior.

Numerical simulation of two-dimensional compressible convection

Abstract: A procedure for obtaining numerical solutions to the equations describing thermal convection in a compressible fluid is outlined. The method is applied to the case of a perfect gas with constant viscosity and thermal conductivity. The fluid is considered to be confined in a rectangular region by fixed slippery boundaries and motions are restricted to two dimensions. The upper and lower boundaries are maintained at fixed temperatures and the side boundaries are thermally insulating. The resulting convection problem can be characterized by six dimension-less parameters. The onset of convection has been studied both by obtaining solutions to the nonlinear equations in the neighbourhood of the critical Rayleigh number Rc and by solving the linear stability problem. Solutions have been obtained for values of the Rayleigh number up to 100Rc and for pressure variations of a factor of 300 within the fluid. In some cases the fluid velocity is comparable to the local sound speed. The Nusselt number increases with decreasing Prandtl number for moderate values of the depth parameter. Steady finite amplitude solutions have been found in all the cases considered. As the horizontal dimension A of the rectangle is increased, the length of time needed to reach a steady state also increases. For large values of A the solution consists of a number of rolls. Even for small values of A, no solutions have been found where one roll is vertically above another.

Laminar plume interactions

Abstract: Interactions between laminar thermal natural convection plumes generated by line and concentrated heat sources were experimentally investigated with a Mach-Zehnder interferometer. Adjacent plane plumes were found to interact more strongly than axisymmetric plumes a t the same spacing. These flows with nominally free boundaries were also found to be affected by nearby surfaces which interfered with the supply of entrainment fluid. Several types of interference with plume entrainment were investigated. The nature of the interacting flows suggests a model which is successful in interpreting the mechanism. An application of the effects of plume interaction is discussed.

Numerical models of convection in the upper mantle

Abstract: Two-dimensional numerical models of steady state convection show that convection cells of aspect ratio as large as 8.6 are possible for variable viscosity convection in the upper mantle. Our models include the effects of variable viscosity, viscous dissipation, internal heating, heat flow through the bottom, and the adiabatic gradient. The large aspect ratio of the convection cells is primarily due to the large viscosity contrast between the lithosphere and the asthenosphere. It appears possible for multiple convection cells to occur in a low-viscosity zone while the surface velocities give the appearance of a single cell. The details of the viscosity law relevant to mantle materials and conditions are presently uncertain but are of crucial importance; temperature, viscosity, and flow patterns are inextricably entwined. Convection decreases the overall temperature gradient; consequently, generally accepted temperatures for most of the mantle are too high. The controversies over plate-mantle decoupling and passive versus active plates are probably due to oversimplifications that disregard hydrodynamic concepts.

Further investigations of combustion of free droplets in a freely falling chamber including moving droplets

Abstract: For the further investigation of the combustion of free droplets under a zero-gravity condition in a freely falling chamber, the experimental apparatus and technique were improved as follows: Increased duration of zero-gravity condition; observation of moving droplets as well as stationary droplets; and schlieren system to observe the hot gas zone. In addition to n -heptane, ethyl alcohol and benzene were also used as fuels. The effects of the initial droplet diameter on the evaporation constant and the variation of the flame/droplet diameter ratio were found to be completely consistent with predictions based on the authors' previous experiment. The influence of the relative velocity of moving droplets on their combustion characteristics such as the evaporation constant, flame shape and behavior of the hot gas zone were investigated, and the combustion of fuel droplets in weak forced convection, not disturbed by natural convection, has been studied for the first time.

Temperature profile in the molecular sublayer near the interface of a fluid in turbulent motion

Abstract: The molecular sublayers adjacent to the air-sea interface are assumed to undergo cyclic growth and destruction in order to explain the exponential temperature profiles measured by Khundzhua and Andreyev. The duration of such cycles is taken to be randomly distributed in forced convection and a constant period is used to determine the temperature profile in free convection.

Pressure- and buoyancy-driven thermal convection in a rectangular enclosure

Abstract: Results are presented for unsteady laminar thermal convection in compressible fluids at various reduced levels of gravity in a rectangular enclosure which is heated on one side and cooled on the opposite side. The results were obtained by solving numerically the equations of conservation for a viscous, compressible, heat-conducting, ideal gas in the presence of a gravitational body force. The formulation differs from the Boussinesq simplification in that the effects of variable density are completely retained. A conservative, explicit, time-dependent, finite-difference technique was used and good agreement was found for the limited cases where direct comparison with previous investigations was possible. The solutions show that the thermally induced motion is acoustic in nature at low levels of gravity and that the unsteady-state rate of heat transfer is thereby greatly enhanced relative to pure conduction. The nonlinear variable density profile skews the streamlines towards the cooler walls but is shown to have little effect on the steady-state isotherms.

Turbulent Natural Convection on Upward and Downward Facing Inclined Constant Heat Flux Surfaces

Abstract: Local heat transfer data were obtained for turbulent natural convection on vertical and inclined upward and downward facing surfaces. The test surface consisted of a 1.83 m (6 ft) wide × 7.32 m (24 ft) high plate with a constant heat flux obtained by electrical resistive heating of a metal foil on the surface. The tests were conducted in air for modified Grashof numbers up to 1015 . Measurements were made of the local surface temperature for this constant heat flux condition, for the plate inclined at angles from 30 deg to the vertical (upward facing, unstable) through the vertical to 80 deg to the vertical (downward facing, stable). The results show the location of the transition to be a function of the plate angle. For the unstable case, the transition length decreases as the plate angle increases from the vertical while for the stable case the position of transition increases with the angle from the vertical. The laminar data for both orientations are correlated as: Nux = 0.55 (Grx*Pr)0.20 in which the gravity is the component along the surface, g cos θ. The turbulent natural convection data are correlated quite well by the relation: Nux = 0.17 (Grx*Pr)0.25 In the turbulent case the correlation is independent of angle for the unstable case, whereas for the stable case the data correlate best when the gravity is modified by cos2 θ, where θ is measured from the vertical. Thus, there is a significant influence of angle on the convective heat transfer for the stable turbulent region.

Heat Flow and Convection Experiments aboard Apollo 17.

Abstract: Experiments conducted aboard Apollo 17 showed that in uncovered liquids, convection driven by surface tension can occur at lower temperature gradients in low gravity than in 1 g. In completely confined fluids (no liquid-gas interface), vibrations caused by spacecraft and astronaut movements increased the heat transfer considerably over the pure conduction case.