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Rayleigh number
About: Rayleigh number is a research topic. Over the lifetime, 15164 publications have been published within this topic receiving 367799 citations.
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TL;DR: In this paper, the complex nature of the natural convection phenomena in enclosures is discussed and the boundary value problem is formulated, assuming that the motion is 2D and steady, the fluid is incompressible and frictional heating is negligible, and the difference between the hot wall and cold wall temperatures is small relative to the absolute temperatures of the cold wall.
Abstract: Publisher Summary This chapter discusses the complex nature of the natural convection phenomena in enclosures It discusses the two basic configurations of natural convection— that is, a rectangular cavity and a horizontal circular cylinder In rectangular cavities, consideration is given to the two-dimensional convective motion generated by the buoyancy force on the fluid in a rectangle and to the associated heat transfer The two long sides are vertical boundaries held at different temperatures and the short sides can either be heat conducting or insulated Particular attention is given to the different flow regimes that can occur and the heat transfer across the fluid space between the two plane parallel vertical boundaries Although heat transfer by radiation may not be negligible it is independent of the other types of heat transfer and can be fairly accurately calculated separately To formulate the boundary value problem that describes this phenomena it is assumed that: (a) the motion is two-dimensional and steady, (b) the fluid is incompressible and frictional heating is negligible, and (c) the difference between the hot wall and cold wall temperatures is small relative to the absolute temperatures of the cold wall In horizontal circular cylinder, consideration is given to the large Rayleigh number flow with the Prandtl number large and the Grashof number of unit order of the magnitude
973 citations
TL;DR: In this article, an experimental study of Rayleigh-Benard convection in helium gas at roughly 5 K is performed in a cell with aspect ratio 1.65 and 1.5.
Abstract: An experimental study of Rayleigh-Benard convection in helium gas at roughly 5 K is performed in a cell with aspect ratio 1. Data are analysed in a ‘hard turbulence’ region (4 × 107 < Ra < 6 × 1012) in which the Prandtl number remains between 0.65 and 1.5. The main observation is a simple scaling behaviour over this entire range of Ra. However the results are not the same as in previous theories. For example, a classical result gives the dimensionless heat flux, Nu, proportional to . A new scaling theory is described. This new approach suggests scaling indices very close to the observed ones. The new approach is based upon the assumption that the boundary layer remains in existence even though its Rayleigh number is considerably greater than unity and is, in fact, diverging. A stability analysis of the boundary layer is performed which indicates that the boundary layer may be stabilized by the interaction of buoyancy driven effects and a fluctuating wind.
899 citations
TL;DR: In this paper, the authors present the present knowledge of the simplest realisation of convection in a layer of fluid satisfying the Oberbeck-Boussinesq approximation, and compare theoretical results with experimental observations.
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.
803 citations
TL;DR: In this paper, it was shown that the minimum temperature gradient for which convection can occur is approximately 4π2h2μ/kgρ0α D2, where h2 is the thermal diffusivity, g is the acceleration of gravity, μ is the viscosity, k is the permeability, α is the coefficient of cubical expansion, ρ 0 is the density at zero temperature, and D is the thickness of the layer; this exceeds the limiting gradient found by Rayleigh for a simple fluid by a factor of 16D2/27π2
Abstract: The problem is considered of the convection of a fluid through a permeable medium as the result of a vertical temperature‐gradient, the medium being in the shape of a flat layer bounded above and below by perfectly conducting media. It appears that the minimum temperature‐gradient for which convection can occur is approximately 4π2h2μ/kgρ0α D2, where h2 is the thermal diffusivity, g is the acceleration of gravity, μ is the viscosity, k is the permeability, α is the coefficient of cubical expansion, ρ0 is the density at zero temperature, and D is the thickness of the layer; this exceeds the limiting gradient found by Rayleigh for a simple fluid by a factor of 16D2/27π2kρ0. A numerical computation of this gradient, based upon the data now available, indicates that convection currents should not occur in such a geological formation as the Woodbine sand of East Texas (west of the Mexia Fault zone); in view of the fact, however, that the distribution of NaCl in this formation seems to require the existence of ...
796 citations
TL;DR: In this paper, it was shown that 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.
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.
761 citations