Showing papers on "Natural convection published in 1978"

Non-linear properties of thermal convection

Abstract: Thermal convection in a layer heated form below is an exemplary case for the study of non-linear fluid dynamics and the transition to turbulence. An outline is given of the present knowledge of the simplest realisation of convection in a layer of fluid satisfying the Oberbeck-Boussinesq approximation. Non-linear properties such as the dependence of the heat transport on Rayleigh and Prandtl numbers and the stability properties of convection rolls are emphasised in the discussion. Whenever possible, theoretical results are compared with experimental observations. A section on convection in rotating systems has been included, but the influence of other additional physical effects such as magnetic fields, side wall geometry, etc., has not been considered.

Instability of steady natural convection in a vertical fluid layer

Abstract: The instability of steady natural convection of a stably stratified fluid between vertical surfaces maintained at different temperatures is analysed. The linear stability theory is employed to obtain the critical Grashof and Rayleigh numbers, for widely varying levels of the stable background stratification, for Prandtl numbers ranging from 0·73 to 1000 and for the limiting case of infinite Prandtl number. The energetics of the critical disturbance modes also are investigated. The numerical results show that, if the value of the Prandtl number is in the low to moderate range, there is a transition from stationary to travelling-wave instability if the stratification exceeds a certain magnitude. However, if the Prandtl number is large, the transition, with increasing stratification, is from travelling-wave to stationary instability. The theoretical predictions are in excellent agreement with the experimental observations of Elder (1965) and of Vest & Arpaci (1969), for stationary instability, and in fair to good agreement with the experimental results of Hart (1971), for travelling-wave instability.

Thermal convection with spatially periodic boundary conditions: resonant wavelength excitation

Abstract: Thermal convection in a fluid contained between two rigid walls with different mean temperatures is considered when either spatially periodic temperatures are prescribed at the walls or surface corrugations exist. The amplitudes of the spatial non-uniformities are assumed to be small, and the wavelength is set equal to the critical wavelength for the onset of Rayleigh-Benard convection. For values of the mean Rayleigh number below the classical critical value, the mean Nusselt number and the mean flow are found as functions of Rayleigh number, Prandtl number, and modulation amplitude. For values of the Rayleigh number close to the classical critical value, the effects of the non-uniformities are greatly amplified, and the amplitude of convection is then governed by a cubic equation. This equation yields three supercritical states, but only the state linked to a subcritical state is found to be stable.

Critical effects in Rayleigh-Benard convection

Abstract: 2014 The properties of the convection Rayleigh-Bénard phenomenon near its critical threshold of instability are shown to be closely related to those of a second order phase transition. A theory is developed in the framework of the Landau-Hopf hypothesis, and all its predictions are verified by experimental results. Tome 39 N° 7 JUILLET Classification Physics Abstracts 47 . 25Q

Free convective heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall

Abstract: Analyses of fluid flow over a wavy wall are of interest because of their applications to the physical problems mentioned in § 1. The authors have therefore devoted their attention to the effect of waviness of one of the walls on the flow and heat-transfer characteristics of an incompressible viscous fluid confined between two long vertical walls and set in motion by a difference in the wall temperatures. The equations governing the fluid flow and heat transfer have been solved subject to the relevant boundary conditions by assuming that the solution consists of two parts: a mean part and a disturbance or perturbed part. To obtain the perturbed part of the solution use has been made of the long-wave approximation. The mean (zeroth-order) part of the solution has been found to be in good agreement with that of Ostrach (1952) after certain modifications resulting from the different non-dimensionalizations employed by Ostrach and the present authors respectively. The perturbed part of the solution is the contribution from the waviness of the wall. The zeroth-order, the first-order and the total solution of the problem have been evaluated numerically for several sets of values of the various parameters entering the problem. Certain qualitatively interesting properties of the flow and heat transfer, along with the changes in the fluid pressure on the wavy and flat wall, are recorded in §§ 5 and 6.

Visual observation of natural convective flow in a narrow vertical cavity

Abstract: Experimental visualization of natural convective flow was carried out by using several kinds of fluid contained in a narrow vertical rectangular cavity with one vertical wall heated, the opposing vertical wall cooled and the upper and lower walls insulated. The effects of the Prandtl number Pr of the working fluid and the width of the cavity W on the flow pattern are discussed qualitatively in the present paper. The occurrence of flow patterns consisting of unicellular flow, steady secondary flow, tertiary flow and transition (from laminar to turbulent) flow is categorically demonstrated by the photographs taken. Moreover, experimental measurements of the net heat transfer through the vertical fluid layer are given for aspect ratios of 6-30 and Prandtl numbers of 4-12 500.

Experimental study of the velocity field in Rayleigh-Benard convection

Abstract: Local velocity measurements performed in a convecting layer of fluid show that the velocity field can be described by a dominant fundamental velocity mode mixed with an increasing proportion of second and third harmonics as e, the reduced distance to the convective threshold Rc, is increased from 0 to ∼ 10. The spatial and thermal dependences of the amplitudes of these different modes are reported and compared with theoretical predictions.

Three-dimensional natural convection motion in a confined porous medium

Abstract: Weakly nonlinear analysis is used to calculate the possible two‐ and three‐dimensional convection patterns in a rectangular parallelepiped of saturated porous media when the horizontal dimensions are integral multiples of the vertical dimension. A two‐term expansion for the Nusselt number is found for values of the Rayleigh number close to the critical values. It is shown that the two‐dimensional roll configurations transfer heat more effectively than does the three‐dimensional pattern of motion when the Rayleigh number is just above the critical value.

Heat transfer and fluid flow phenomena in electroslag refining

Abstract: A mathematical formulation has been developed to represent the electromagnetic force field, fluid flow and heat transfer in ESR units. In the formulation, allowance has been made for both electromagnetically driven flows and natural convection; furthermore, in considering heat transfer the effect of the moving droplets has been taken into account. The computed results have shown that the electromagnetic force field appears to be the more important driving force for fluid motion, although natural convection does affect the circulation pattern. The movement of the liquid droplets through the slag plays an important role in transporting thermal energy from the slag to the molten metal pool, although the droplets are unlikely to contribute appreciably to slag-metal mass transfer The for-formulation presented here enables the prediction of thermal and fluid flow phenomena in ESR units and may be used to calculate the electrode melting rates from first principles. While a detailed comparison has not yet been made between the predictions based on the model and actual plant scale measurements, it is thought that the theoretical predictions are consistent with the plant-scale data that are available.

Natural Convection in a Horizontal Porous Medium Subjected to an End-to-End Temperature Difference

Abstract: Natural convection in a porous medium filling a slender horizontal space with an end-to-end temperature difference is studied analytically. The end-to-end temperature difference gives rise to a horizontal counterflow pattern augmenting the heat transfer rate through the porous medium. Two basic geometries are considered: horizontal layer confined between 2 adiabatic and impermeable parallel plates, and horizontal cylinder surrounded by an adiabatic and impermeable cylindrical surface. Nusselt number relations are derived in terms of the Rayleigh number and the cavity aspect ratio. The end-wall permeability is shown to affect the heat transfer rate through the medium. (12 refs.)

Natural Convection in a Square Enclosure by a Finite-Element, Penalty Function Method Using Primitive Fluid Variables

Abstract: Numerical solutions for the problem of laminar natural convection in a square enclosure using the penalty function, finite-element method are presented. Solutions are obtained for values of the Rayleigh number up to 107 using primitive fluid variables, and the efficacy of the method is demonstrated through a qualitative and quantitative evaluation of the results. The simplicity and general applicability of the method are shown especially in the context of extensions to three-dimensional geometries and irregular computational grids.

Natural convection in an infinite porous medium with a concentrated heat source

Abstract: summary of what is presented below, the mathematical problem is formu- lated in $2. The transient flow and temperature patterns are derived analytically in $3. A solution for the steady-state temperature and flow distributions around the source is presented in $ 4. Finally, in $ 5 we conclude the study by reviewing the asymptotic character of the solutions and the limitations of the Darcy flow model. 2. Problem statement Consider the spherical polar co-ordinate system (r, 8,$) shown in figure 1. A point source of strength q (watts) is situated at the origin with the 8 = 0 axis pointing vertically upwards. Since the problem is symmetric in the angular direction 4 around the vertical axis, neither 4 nor the 4 velocity component w appears in the analysis. The fluid saturating the porous medium is Boussinesq-incompressible, its density p varying slightly as a result of temperature changes: in which P is the volumetric coefficient of thermal expansion, T the temperature and the subscript

Further thoughts on convective heat transport in a variable-viscosity fluid

Abstract: In a previous paper (Booker 1976) we found experimentally that the convective heat transport in a fluid with temperature-dependent viscosity decreased significantly as the ratio of the viscosities at the top and bottom boundaries increased. In this note, we show that this decrease in heat transport can be entirely accounted for by an increase in the critical Rayleigh number with variable viscosity.