Showing papers on "Natural convection published in 1969"

The Anelastic Approximation for Thermal Convection

Abstract: A formal scale analysis of the equations of motion in a plane parallel atmosphere is made, assuming conditions to be such that relative fluctuations in density and temperature are small. It is found that an energetically consistent set of approximate equations can be derived which preclude the existence of acoustic motions. Such equations can be used to describe subsonic convection or internal gravity waves. Under certain conditions the analysis can be generalized to include vertical pulsations of the atmosphere.

Convection and stress propagation in the upper mantle.

Abstract: Dynamic processes in upper earth mantle, discussing thermal convection currents and stress propagation

Effect of modulation on the onset of thermal convection

Abstract: The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the walls of the layer, a time-dependent sinusoidal perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The effects of the oscillating temperature field are treated by a perturbation expansion in powers of the amplitude of the applied field. The shift in the critical Rayleigh number is calculated as a function of frequency, and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures.

Thermocapillary convection in a horizontal layer of liquid

Abstract: An exact solution is found for the equations for free convection in a planar horizontal layer of liquid with a constant temperature gradient at the boundaries. Two cases of boundary conditions for the velocity are considered: 1) the liquid is bounded by two solid planes, 2) the upper surface of the liquid is free, and the surface tension is a function of temperature.

Stability of natural convection in a vertical slot

Abstract: The stability of natural convection of a viscous fluid in a vertical slot having isothermal side walls of different temperatures is investigated analytically. Both the conduction and boundary-layer regimes are found to be unstable with respect to stationary disturbances in the form of multicellular secondary flows. Theoretical predictions of the critical Rayleigh number and of the form of the secondary flow are verified by experimental measurements.

Natural convection above unconfined horizontal surfaces

Abstract: The paper discusses free convective flows above a horizontal plate, both theoretically and on the basis of experiments which yield quantitative data. The theory is applicable to the semi-infinite plate and is extended to cover the complete range of Prandtl number values including Pr → 0 and Pr → ∞. Experiments were carried out to demonstrate the existence of a laminar boundary layer above a horizontal plate at intermediate Grashof (respectively Rayleigh) numbers, and its extent along the plate. This layer breaks down into large-eddy instability some distance from the leading edge. The value of the critical Rayleigh number for this to occur, obtained experimentally using semi-focusing colour-Schlieren photography is in reasonable qualitative agreement with previously known data (Tritton 1963a,b).

An Experimental Study of Turbulent Natural Convection Boundary Layers

Abstract: An experimental investigation on turbulent natural convection boundary layers has been conducted with water on a vertical plate of constant heat flux. Local heat transfer data are presented for laminar, transition, and turbulent natural convection, with the emphasis on the turbulent regime. The data extend to a modified Rayleigh number of 1016 for a threefold range in Prandtl number. The results indicate that natural transition occurs in the range 1012 < Ra* < 1014 ; i.e., fully developed turbulent flow occurs by Ra* = 104 . This latter value can be as low as 2 × 1013 with the use of a trip rod. The physical structure of the turbulent boundary-layer flow was studied using the combined time-streak marker hydrogen bubble method. Temperature data and temperature corrected velocity data obtained by hot-film sensors are presented for Ra* values between 8.7 × 1013 and 7.1 × 1014 . For the range of variables investigated, the major conclusions are (a) the local heat transfer coefficient exhibits a slight decrease with length, (b) confirmation that the vortex street layer in the transition region decays into a longitudinal-vortex-type structure, and (c) the outer portion of the thermal and velocity fields can be approximated by power profiles that fit almost all the data available to date.

Viscous dissipation in external natural convection flows

Abstract: The effects of viscous dissipation are considered for external natural convection flow over a surface. A class of similar boundary-layer solutions is given and numerical results are presented for a wide range of the dissipation and Prandtl numbers. Several general aspects of similarity conditions for flow over surfaces and in convection plumes are discussed and their special characteristics considered. The general equations including the dissipation effect are given for the non-similar power law surface condition.

Numerical study of natural convection in an enclosure with localized heating from below—creeping flow to the onset of laminar instability

Abstract: An analytical study was made of the natural convection induced in an enclosure by a small hot spot centrally located on the floor. The enclosure was a circular cylinder, vertically oriented, with height equal to radius. A Prandtl number of 0.7 (air) was assumed; the Grashof number (Gr) was based on cylinder height and hot spot temperature. The equations of fluid flow in axisymmetric cylindrical co-ordinates were simplified with the Boussinesq approximation. The equations were solved numerically with a computationally stable, explicit method. The computation, starting from quiescent conditions, proceeded through the initial transient to the fully developed flow. Solutions were obtained for Gr from 4 × 104 to 4 × 1010. The theoretical flows are in excellent agreement with experimentally observed laminar flows (Gr [lsim ] 1.2 × 109) which are discussed in a companion paper, Torrance, Orloff & Rockett (1969). Turbulence was observed experimentally for Gr [gsim ] 1.2 × 109. When the theoretical calculations were extended to Gr = 4 × 1010, a periodic vortex shedding developed, suggestive of the onset of laminar instability. The theoretical results reveal a √Gr scaling for the initial flow transients and, at large Gr, the velocities and heat transfer rates.

Magma convection, temperature distribution, and differentiation

Abstract: Normal heat fluxes from the Earth are sufficient to cause magma convection in plutons greater than 15 m for magma viscosities to 10 (super -8) poise. Convection increases markedly with size of the magma chamber and becomes the dominant method of heat transfer within the magma. Large solidifying intrusions have an approximately isothermal temperature distribution during part of the crystallization history. Natural convection also redistributes settling crystals. The population distribution (differentiation) of crystals in the vertical direction depends on the settling and convective back diffusion fluxes. An equation for population distribution is derived, and calculations made for olivine and quartz crystals in ultramafic and granitic magmas are in agreement with observed distribution of these minerals in corresponding solidified intrusions.

Longitudinal vortices in natural convection flow on inclined plates

Abstract: Experiments are performed to demonstrate the occurrence and explore the characteristics of a secondary flow superposed upon the natural convection main flow on an inclined plate A flow visualization technique is employed whereby the flow pattern is made visible by local changes of colour of the fluid itself, the colour change being brought about by a change in pH The secondary flow consists of longitudinal vortices or rolls distributed more or less periodically across the width of the plate The number of such vortices increases with the temperature difference between the surface and the ambient fluid, but appears to be relatively insensitive to the inclination angle of the plate The secondary flow results from the destabilizing effect of the buoyancy force component, which acts normal to the plate surface The longitudinal vortices are the first stage of the laminarturbulent transition process This is in contrast to the case of natural convection on a vertical plate, where the first stage of transition is Tollmien-Schlichting waves

Convection Heat Transfer in Rotating Systems

Abstract: Publisher Summary Because the convective heat transfer phenomena in rotating systems are intimately related to the flow characteristics, they too are quite complex and offer challenges to theoreticians as well as experimenters. Heat transfer by convection to or from bodies of revolution spinning about their axes of symmetry in an otherwise undisturbed fluid has been studied analytically and experimentally by numerous authors. This chapter summarizes results of more recent investigations. The flow and heat transfer characteristics of spinning bodies of revolution in a forced flow field are important for projectiles or re-entry missiles with spin as well as for certain other engineering problems. The fluid-mechanical phenomena of enclosed rotating disks and of parallel corotating disks are distinctly different from those of disks rotating in an infinite environment. In general, the results for convection heat transfer of a disk rotating in an infinite environment can, therefore, not be applied to shrouded or corotating disks. When a quiescent horizontal layer of fluid is heated from below, the fluid at the bottom becomes lighter than the fluid at the top and convection currents are set into motion. The chapter deals with convection in fluids that are set in motion principally by rotating bounding surfaces, but that do not have an independent axial flow. It also deals with heat transfer by convection in systems in which the fluids also have an independent axial motion superimposed on the rotating motion.

Natural Convection between Concentric Vertical Cylinders

Abstract: The motion of a fluid in the closed annular cavity formed by two concentric vertical cylinders and two horizontal planes has been analyzed by a numerical solution of the equations of motion and energy using a high‐speed digital computer. The motion is generated by a radial density gradient caused by the thermal boundary conditions which are, typically: inner cylinder at a (dimensionless) temperature of unity; outer cylinder at a temperature of zero; horizontal boundaries adiabatic. The fluid is assumed to have constant thermodynamic and transport properties except for the density, which is temperature‐dependent in the buoyancy term of the equation of vertical motion (the Boussinesq approximation); the flow is assumed to be axisymmetric. The equations of time‐dependent motion have been solved, so that both transient and steady‐state solutions are obtained. The parameters of the problem, and the respective ranges of values which have been considered, are: Rayleigh number (based on gap width) up to 2 × 105; Prandtl number 0.5 to 5; radius ratio 1 to 4; aspect ratio (cavity height/gap) 1 to 20. At moderate Rayleigh numbers the motion consists of a single cell (i.e., torus), while at higher Rayleigh numbers the onset of a multicellular motion is observed. The local and average Nusselt numbers, of interest in determining the insulating value of an annular cavity, have been obtained.

Centrifugally driven thermal convection in a rotating cylinder

Abstract: Thermally induced convection in a rotating cylinder of fluid heated from above and strongly influenced by centrifugal accelerations is treated using boundary-layer methods. As in the theory of homogeneous rotating fluids, the horizontal Ekman layers control the inviscid axial flow. The solution also largely depends upon the thermal conditions assumed at the side wall, and if these be insulated, consideration of the side-wall boundary layers is necessary for complete specification of the problem. For perfectly conducting side walls, the side layers do not influence the zeroth-order flow, but contribute a second-order correction, which would be absent if the lateral boundaries were ignored. The critical parameters governing the solutions in both cases are found to be γ and the group σβe−½, where γ is the aspect ratio, σ the Prandtl number, e the Ekman number, and β the thermal Rossby number for the flow. Boundary-layer solutions are given for a wide range of parameters, and gravity is seen to have at most only a local effect on the flow near the side walls.

Effects of ultrasonic vibrations on heat transfer to liquids by natural convection and by boiling

Abstract: The effects of ultrasonic vibrations on heat transfer to water and methanol by natural convection and by boiling were measured at three ultrasonic energy levels with frequency ranging from 20.6 to 306 kcycles/sec., using electrically heated platinum wires of diameters 0.007 and 0.010 in. Up to an eight-fold increase in heat transfer coefficient was obtained in natural convection, but the effects diminished with increased temperature difference and became negligible in the well-developed nucleate boiling region. High-speed photographs showed that the increase was due to the motion of cavitation bubbles on the wire surface. The heat transfer results were correlated by local cavitation activity values measured by a technique developed for this work.

Experiments on natural convection in enclosures with localized heating from below

Abstract: An experimental study was made of the steady-state natural convection induced in enclosures by a small hot spot centrally located on the floor. Enclosures of rectangular and circular floor plan were employed, with height equal to one-half the major dimension of the floor plan. The movement of air within the chambers was made visible by adding metaldehyde dust particles and illuminating them with an intense light beam. The Grashof number (Gr) based on hot-spot temperature and enclosure height ranged from 8 × 105 to 1 × 1010. Laminar flows were observed for Gr [lsim ] 1.2 × 109. The experimental flows in the circular chamber are compared in a companion paper with theoretically calculated flows (Torrance & Rockett 1969). In the region of laminar flows the agreement was excellent. The present paper notes certain similarities in the flows in rectangular and circular geometries. The disturbing effect of a slight heating of one wall of the rectangular enclosure was also investigated. Measurements were made of heat transfer from the hot spot to the air in the chamber.

Convection electric fields and the diffusion of trapped magnetospheric radiation.

Abstract: We explore here the possible importance of time-dependent convection electric fields as an agent for diffusing trapped magnetospheric radiation inward toward the earth. By using a formalism (Birmingham, Northrop, and Falthammar, 1967) based on first principles, and by adopting a simple model for the magnetosphere and its electric field, we succeed in deriving a one-dimensional diffusion equation to describe statistically the loss-free motion of mirroring particles with arbitrary but conserved values of the first two adiabatic invariants M and J. Solution of this equation bears out the fact that reasonable electric field strengths, correlated in time for no longer than the azimuthal drift period of an average particle, move particles toward the earth at a rate at least an order of magnitude faster than electric fields whose source is a fluctuating current on the magnetopause.

Mixed convection from a sphere at small Reynolds and Grashof numbers

Abstract: Consideration is given to the effects of gravity which arise when a heated sphere, maintained at a steady uniform temperature, is located in a vertical uniform stream. Restricting analysis to a medium of unit Prandtl number (σ), the method of matched asymptotic expansions is employed in obtaining solutions for the velocity, temperature and pressure fields in the limit: G = o(R2), R ↓ 0 (G and R being, respectively, the Grashof and Reynolds numbers). Based on these results, conjectures are formed about the corresponding pure natural convection problem.

Free convection at low Prandtl numbers

Abstract: In this paper it is shown that the free convection boundary layer approaches a singular character if the Prandtl number tends to zero. The method of matched asymptotic expansions is used to integrate the equations for this extreme case. An expression is derived for the Nusselt—Grashof relation and the results are compared with those of previous investigations which attack the problem in a different way.

Numerical Study of Natural Convection in a Vertical Rectangular Enclosure

Abstract: The steady‐state natural convection of a fluid in a vertical rectangular cavity with isothermal side walls and adiabatic top and bottom walls is considered for 6 × 104 ≤ Ra ≤ 3.6 × 105 with Pr = 1, 6, 2000, and at an aspect ratio of 5.0. The governing nonlinear fourth‐order equation in the stream function and the coupled second‐order energy equation are solved numerically by a stable and rapidly converging iteration scheme. The computed flow distributions, including the appearance of multicellular flows, the temperature profiles, and the heat transfer predictions compare favorably with experimental results and with other numerical studies.

Effect of Vortices Induced by Corona Discharge on Free-Convection Heat Transfer From a Vertical Plate

Abstract: Experimental results are presented to show that columnar, counterrotating, vertical vortices can be produced on a heated, vertical, flat plate under free-convection conditions in air using a high-voltage d-c electric field. The vortices result from the corona discharge on 0.002-in.-dia parallel wires of alternate high voltage and ground potential placed vertically on the surface of a phenolic laminate plate. Heat-transfer rates are measured using an energy-balance method, and the thermal boundary layer is made visible using a Mach-Zehnder interferometer. Experimental curves are presented to illustrate the increase in the heat-transfer rate with increase in the electric-field power. Interference photographs and frames from a motion picture show the effects of the vortices on the thermal boundary layer. The convective part of the heat transfer from the 10 × 10 in. plate is more than doubled before the electric-field power becomes as large as 5 percent of the increase in the heat-transfer rate. Local heat-transfer rates are highest at the high-voltage wires and lowest at the grounded wires.