Showing papers on "Natural convection published in 1973"

Natural convection in a sloping porous layer

Abstract: This paper describes an experimental and theoretical study of thermal convection in a sloping porous layer. The saturated layer is bounded by two parallel impermeable planes maintained at different temperatures. Several types of flows were observed: a unicellular movement and a juxtaposition of longitudinal coils or of polyhedral cells.A theoretical analysis has been made using the standard bases of the linear theory of stability and by taking into account some assumptions suggested by experimental observations. The critical conditions for the transition between unicellular and polycellular flows has been determined. For flow in longitudinal coils or with polyhedral cells the average heat transfer depends mainly on the filtration Rayleigh number and on the slope of the layer.The experimental study was made in a Rayleigh number range 0–800 and for various slopes (0–90°). For both the transition criterion and the heat transfer, a good fit was observed between the experimental and theoretical results. For maximum slope, i.e. 90°, a correlation which connects the Nusselt number with both the Rayleigh number and the vertical extent of the model is proposed.

A Review of Mesoscale Cellular Convection

Abstract: A brief review of the classical theory for convective instability is presented, with primary emphasis on the more recent theoretical and experimental findings that pertain to mesoscale cellular convection in the atmosphere. Important physical and geometrical features of three-dimensional patterns of free convection commonly observed over the oceans are discussed, especially those features that point to distinct differences when compared to laboratory convection. Some suggestions for future study are offered with particular reference to the AMTEX program being planned by the Japanese Committee for GARP.

Free convection effects on the oscillatory flow past an infinite, vertical, porous plate with constant suction. I

Abstract: An analysis of the two-dimensional flow of an incompressible, viscous fluid past an infinite porous plate is presented under the following conditions: (i) the suction velocity normal to the plate is constant, (ii) the free stream velocity oscillates in time about a constant mean, (iii) the plate temperature is constant, (iv) the difference between the temperature of the plate and the free stream is moderately large causing the free convection currents. Approximate solutions for the coupled nonlinear equations are obtained for velocity and temperature field. Expressions for the mean velocity, the mean temperature and the mean skin-friction are derived in part I. The mean velocity, the mean temperature are shown on graphs and the numerical values of the skin friction are entered in table 1. The effects of $G$ (the Grashof number), $P$ (the Prandtl number) and $E$ (the Eckert number), on the mean motion of air and water are described during the course of discussion. Some of the important observations are as follows. There is a reverse flow of the mean velocity profile of fluids, with small Prandtl number, in the boundary layer close to a plate which is being heated by the free convection currents. The mean skin friction increases with more cooling of the plate and decreases with more heating of the plate. In part II of the paper, the fluctuating flow is described.

Velocity and heat transfer measurements in thermal convection

Abstract: Measurements were taken of the heat transport and vertical component of the fluid velocity in a horizontal layer of water heated from below. The heat transfer results were well correlated by a simple power law relationship and indicated the possibility of flow transitions even at relatively high Rayleigh numbers. The velocity measurements were obtained optically and compared to predictions of Kraichnan.

Inversion Rise Model Based on Penetrative Convection

Abstract: A mathematical model to describe the height changes and other characteristics of an inversion base under the influence of surface convection and general subsidence is developed. Inversion interface dynamics and entrainment rates are formulated based on an unstable boundary layer environment of well-organized, plume-like, penetrative convection. The use of unstable boundary layer scaling velocities in describing the convection leads to a natural inclusion of the relevant parameters associated with inversions into this model. It is found that the model does accurately predict realistic rates of inversion rise and of temperature changes for conditions where organized free convection is prevalent.

A note on free convection

Abstract: The limiting condition of µ*, →0 in the unstable atmospheric boundary layer is usually referred to as ‘free convection’. Some of the similarity laws that are proposed for this condition do not agree with experiment. A mechanism is proposed in this paper to show why the asymptotic free convection condition is never completely reached near the surface. It is shown that local turbulent shear production plays an important role in shaping the temperature profile even when the average velocity is zero.

Convection in the Earth's Mantle

Abstract: The computer is used to solve for thermal convection within the earth's mantle. A review of the knowledge of surface displacements and of the present understanding of the mantle and its relevant physical and chemical properties is contained in the paper. Applicable equations assume a Newtonian fluid layer heated from below and within, with gravity acting downward. The numerical method employs finite differences and was constructed with a view toward the faithful simulation of coupling mechanisms. It enables surveying the effect of a parameter using a relatively coarse computing mesh. Some of the results obtained are presented.

The seasonal thermal structure of deep temperate lakes

Abstract: A theoretical description is given of the seasonal variation of the thermal structure of deep, temperate lakes. The influence of the unsteady and nonlinear interaction between the wind-induced turbulence and the stable buoyancy gradients due to surface heating on the thermal eddy diffusivities is assumed to be given by a product of the eddy diffusivities under conditions of neutral stability and an appropriate function of a stratification parameter, which, in this case, is taken to be the gradient Richardson number. An implicit account is taken of the interaction between the current and thermal structures within the lake, and free convection is also included implicitly during the cooling portion of the annual cycle. The basic equation, which is integrated by finite difference means, is an unsteady, nonlinear diffusion equation describing the vertical temperature structure. The boundary condition on the heat exchange at the lake surface is formulated in terms of the concept of an equilibrium temperature. The seasonal stratification cycle of a lake is determined as the response of the lake to certain imposed “external parameters” which specify the exchange of mechanical and thermal energies between the lake and the environment. The results of calculations of the vertical thermal structure using this model agree with the observed qualitative features of the stratification cycle. For the one case in which quantitative comparisons are made, good agreement with observations is obtained. A brief discussion comparing the features of the present theory with those of other existing theories is also given. DOI: 10.1111/j.2153-3490.1973.tb01602.x

Natural Convection Flows and Stability

Abstract: Publisher Summary This chapter discusses laminar and transition flows, external and free boundary flows, and boundary layer regimes. It presents general equations of the natural convection flow and introduces approximations in terms of their physical significance to yield the conventional equations of analysis. The boundary layer simplifications for two-dimensional vertical flows are also discussed followed by the equations for vertical axisymmetric flows. For steady laminar boundary layers arising from the temperature induced buoyancy, known solutions for the vertical and axisymmetric flows are reviewed, including plumes. The combined mass transport and thermally induced buoyancy is treated, consideration is given to laminar transients. The chapter also reviews how laminar flows become unstable and how disturbances amplify to lead the flow toward transition. Vertical flows adjacent to surfaces and in plumes are considered. The nature of transition and turbulent flow are treated. The general question of instability in buoyancy induced flows is also treated. The question of separation in natural convection flow is reviewed and distinctions are drawn relative to the forced flow separation.

Transpiration and natural convection: the vertical-flat-plate problem

Abstract: A study is made of the natural convective flow which is induced in an infinite expanse of gas by the presence of a vertical hot flat plate from which hot gas of the same chemical type is being blown. The transpiration rate is assumed to be such that a self-similar boundary-layer type of solution is available. It differs from previous analyses in the following respects. Most important, the density is not assumed to be constant a t any stage in the description of the flow field. Also the form of the induced flow in the outer domain is calculated and proves to be substantially independent of the blowing rate in this case; the induced outer flow is found to be of large lateral extent. Finally, the variable-gas-property problem is carried to second order and solutions are obtained by using an ‘exact’ form of Howarth-Dorodnitsyn variable. The opportunity is taken t o make some comments about the comparison between theory and experiment for finite flat plates without transpiration.

Free convection effects on the oscillatory flow past an infinite, vertical, porous plate with constant suction. II

Abstract: An analysis of a two-dimensional flow of an incompressible, viscous fluid is presented here for the unsteady flow. The mathematical analysis having been presented in part I, only the solutions for the transient velocity profiles, transient temperature profiles, the amplitude and the phase of the skin friction and the rate of heat transfer are presented in this paper. They are shown graphically. The effects of heating or cooling the plate $(G\lessgtr 0)$ the Eckert number (E), the Prandtl number (P), and the frequency $(\omega)$ are discussed. It has been observed that a reversed type of flow occurs when the plate is heated by the free convection currents. The amplitude of the skin friction is not affected significantly by the free convection currents when the frequency is large. In the case of air, the phase of the skin friction is more, when the plate is cooled than that when it is heated, by the free convection currents. Also, owing to greater viscous dissipative heat for G > 0, or to greater cooling of the plate, the amplitude of the skin friction increases, whereas owing to greater viscous dissipative heat for G < 0 or to greater heating of the plate, the amplitude of the skin friction decreases. But the amplitude of the rate of heat transfer increases owing to greater heating or cooling of the plate. However, it is more when the plate is cooled than that when the plate is heated.