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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: Turbulent convection exemplifies many of the startling aspects of turbulent flows that have been uncovered in the past two decades, but frequently exhibits a novel twist as discussed by the authors, as in the case of free shear flows, convection can organize into large-scale vortical structures, but these then react back in subtle ways on the boundary layers which ultimately sustain them.
Abstract: Turbulent convection exemplifies many of the startling aspects of turbulent flows that have been uncovered in the past two decades, but frequently exhibits a novel twist. Thus, as in the case of free shear flows, convection can organize into large-scale vortical structures, but these then react back in subtle ways on the boundary layers which ultimately sustain them. Thermal plumes are a coherent mode of heat transport, analogous to boundary layer bursts, yet their overall effect can be surprisingly close to the structureless predictions of mixing length theory. Convection cells are closed, which facilitates their experimental control, but fluctuations never exit and there is a dynamically determined bulk forcing. While the single pass mode characteristic of wind tunnel experiments seems simpler, the convection cell is, in ways to be discussed, more constrained. This review aims to familiarize the turbulence researcher with con vergent lines of investigation in convection and also to remind those working in convection that turbulence is not a new subject. To situate convection within the gamut of other turbulent flows, let us by way of introduction contrast the directions in which convection has developed with research on the turbulent boundary layer. From the onset of convection up to Rayleigh numbers Ra � 1 0 times critical, there is a great wealth of information about flow structures (which can be visualized from above), and their relative stabilities (Busse 198 1 ) . Turbulence, in the sense of many coupled modes, and not just sensitive dependence on initial conditions, can arise for low Ra in large aspect ratio
633 citations
TL;DR: In this paper, the authors performed two-dimensional numerical calculations of convection in a domain containing a divariant phase change and found that the critical value of the negative Clapeyron slope, which must be surpassed in order to induce layered convection, decreases in magnitude with increasing Rayleigh number Ra in the range 104 ≤ Ra ≤ 2×106.
Abstract: We report a systematic study on the conditions under which an endothermic phase transition can enforce layered convection. Two-dimensional numerical calculations of convection in a domain containing a divariant phase change were performed in the framework of the “extended Boussinesq approximation,” i.e., considering the effects of adiabatic gradient, latent heat, and frictional heating in the energy equation. We find that the critical value of the negative Clapeyron slope, which must be surpassed in order to induce layered convection, decreases in magnitude with increasing Rayleigh number Ra in the range 104 ≤ Ra ≤ 2×106. Near the critical Clapeyron slope, vacillations between double- and single-layer convection or strongly leaking double-layer convection are possible. The breakdown into layers is influenced very little by the latent heat release but depends solely on the phase boundary deflection caused by lateral temperature differences. The value of the critical Clapeyron slope also seems little affected by the width of the transition zone or by its depth. A possible superplastic rheology within the transition zone would tend to favor layered convection. Scaling the model results to the 670-km discontinuity in the earth's mantle as a possible endothermic phase boundary, we estimate the critical Clapeyron slope to be in the range of −4 to −8 MPa/K (−40 to −80 bar/K). The possibility that the spinel → perovskite + periclase transition is within this range appears to be remote but certainly cannot be neglected.
628 citations
TL;DR: In this paper, an experimental study has been undertaken concerning natural convection heat transfer of a nanofluid in vertical square enclosures of different sizes, whose dimensions, width, height, and length (mm) are 25, 25, 30, 60, 40, 80, 90, and 120, respectively.
615 citations
TL;DR: In this paper, a solution was obtained for steady, cellular convection when the Rayleigh number and the Prandtl number are large, and the theory was used to test the hypothesis of large scale convective cells in the earth's mantle.
Abstract: A solution is obtained for steady, cellular convection when the Rayleigh number and the Prandtl number are large. The core of each two-dimensional cell contains a highly viscous, isothermal flow. Adjacent to the horizontal boundaries are thin thermal boundary layers. On the vertical boundaries between cells thin thermal plumes drive the viscous flow. The non-dimensional velocities and heat transfer between the horizontal boundaries are found to be functions only of the Rayleigh number. The theory is used to test the hypothesis of large scale convective cells in the earth's mantle. Using accepted values of the Rayleigh number for the earth's mantle the theory predicts the generally accepted velocity associated with continental drift. The theory also predicts values for the heat flux to the earth's surface which are in good agreement with measurements carried out on the ocean floors.
611 citations
TL;DR: In this article, an upper limit to the heat transport is found subject to the constraint that some minimum eddy size exists which is effective in this transport, and the spectrum of convecting motions, the mean thermal gradients at each point and the eddy conductivity are then determined in terms of the minimum edddy size.
Abstract: In this paper a theoretical investigation is made of various properties of the steady-state inhomogeneous turbulent convection of heat in a fluid between horizontal conducting surfaces. An upper limit to the heat transport is found subject to the constraint that some minimum eddy size exists which is effective in this transport. The spectrum of convecting motions, the mean thermal gradients at each point and the eddy conductivity are then determined in terms of the minimum eddy size. The relation between the boundary conditions and eddy size is studied by an extension of the work of Pellew & Southwell using the mean thermal gradients deduced when n 0 modes of motion are present to establish the Rayleigh number at which the ( n 0 +1)th mode first becomes unstable. In a final section the spectra and mean-square values of the fluctuating velocity and temperature fields are estimated from the Boussinesq form of the hydrodynamic equations. The previously reported experimental heat transports are within 10% of those predicted. The discrete transitions are within the error limits of the observations. However, further data must be mgathered to justify the use of minimum eddy size as a defining parameter in situations of geophysical scale.
607 citations