Showing papers on "Natural convection published in 1971"
TL;DR: In this article, a set of Boussinesq approximations were shown to have solutions of similarity form for combined buoyancy effects, for vertical flows adjacent to surfaces and in plumes, and the resulting equations were integrated for air and water for various practical values of the Schmidt number.
553 citations
TL;DR: In this article, the conservation of Reynolds shear stress and the two components of heat flux (velocity-temperature covariance) in the homogeneous atmospheric surface layer are derived.
Abstract: Equations for the conservation of Reynolds shear stress and the two components of heat flux (velocity-temperature covariance) in the homogeneous atmospheric surface layer are derived. The behavior of the production and turbulent transport (flux divergence) terms in each budget is determined directly from measurements obtained over a wide range of stability conditions during the 1968 Kansas field program of AFCRL. The data are presented in the dimensionless form suggested by Monin-Obukhoy similarity theory, and follow universal functions quite well. The theory is extended to the “local free convection” regime which exists under very unstable conditions, and specific power law forms are predicted. Several of these are verified and values are given for the proportionality factors in the power laws. The flux divergence terms are small, implying that in each budget the local production and destruction rates are in balance. The third moments which represent the vertical fluxes of stress and heat flux a...
504 citations
TL;DR: In this paper, the stability of convection rolls with varying wave-number was investigated and the results confirmed the theoretical predictions by Busse (1967a) and showed two distinct types of instability in the form of nonoscillatory disturbances.
Abstract: An experiment on the stability of convection rolls with varying wave-number is described in extension of the earlier work by Chen & Whitehead (1968). The results agree with the theoretical predictions by Busse (1967a) and show two distinct types of instability in the form of non-oscillatory disturbances. The ‘zigzag instability’ corresponds to a bending of the original rolls; in the ‘cross-roll instability’ rolls emerge at right angles to the original rolls. At Rayleigh numbers above 23,000 rolls are unstable for all wave-numbers and are replaced by a three-dimensional form of stationary convection for which the name ‘bimodal convection’ is proposed.
289 citations
TL;DR: The influence of large variations of viscosity on convection in a layer of fluid heated from below has been investigated in this paper, where solutions for the flow and temperature fields were obtained numerically assuming infinite Prandtl number, free-surface boundary conditions, and two-dimensional motion of fixed horizontal wavelength.
Abstract: The influence of large variations of viscosity on convection in a layer of fluid heated from below has been investigated. Solutions for the flow and temperature fields were obtained numerically assuming infinite Prandtl number, free-surface boundary conditions, and two-dimensional motion of fixed horizontal wavelength. The effects of a temperature-dependent and a depth-dependent viscosity were each studied; calculations were also carried out using a temperature- and depth-dependent viscosity model appropriate to the earth's mantle.
221 citations
TL;DR: In this paper, the authors studied the behavior of the flow field induced by lateral heating in a stably stratified fluid of constant gradient and found that the critical Rayleigh number above which cellular convection occurs has been experimentally determined to be 15000 ± 2500.
171 citations
TL;DR: In this paper, the authors describe the behavior of thermodynamic and transport properties near the critical point and examine the equations of continuity, momentum, and energy with a view to revealing the effect of variable properties and deciding whether the same simplifications can be made as are common with a constant property fluid.
Abstract: Publisher Summary This chapter describes the behavior of thermodynamic and transport properties near the critical point. The near-critical region may be thought of as that region, in which boiling and convection merge. When the pressure is sufficiently subcritical or supercritical, the problem tends toward either a boiling problem or a constant property convection problem. Under such conditions, existing theoretical and empirical methods are generally adequate. The chapter concentrates on the region rather close to the critical point where the property variations are severe and where there are very significant heat transfer effects. The equations of continuity, momentum, and energy are examined with a view to revealing the effect of variable properties and deciding whether the same simplifications can be made as are common with a constant property fluid. Various modes of heat transfer are also discussed, particular attention being given to the interaction between forced and free convection.
158 citations
TL;DR: In this paper, the effect of ionic migration on free convection and free convective limiting currents is investigated, and the presence of supporting electrolyte lowers the electric field, as in stagnant or forced convective systems.
Abstract: Free convection and ionic migration effects are reviewed. Electrolytic free convection is treated theoretically for solutions and for solutions without added electrolyte and with additions of or . The effect of ionic migration on limiting currents is investigated. The presence of supporting electrolyte lowers the electric field, as in stagnant or forced convective systems. In addition, the concentration distributions of added electrolytes affect the density distribution, hence, the velocity profile in free convection, and, indirectly, the value of the calculated limiting currents.
88 citations
87 citations
TL;DR: In this article, an exact solution for the problem of fully developed, radiating, laminar convective flow in a vertical heated channel was obtained for the case of a convective gas.
Abstract: An exact solution is obtained for the problem of fully-developed, radiating, laminar convective flow in a vertical heated channel. The effect of radiation is to decrease the temperature difference between the gas and the wall, thereby reducing the influence of natural convection. Thus, the reduction in velocity occurring in a heated upflow is less for a radiating gas. Graphs are presented for the dimensionless velocity and temperature profiles and for the volume and heat fluxes.
87 citations
TL;DR: In this article, the authors demonstrate the feasibility of using numerical calculations to determine the structure of convection cells within the mantle and demonstrate that large flow velocities and small temperature differences are associated with ascending convection and significant flows extend to a depth of 300 km.
Abstract: This paper demonstrates the feasibility of using numerical calculations to determine the structure of convection cells within the mantle. A temperature and depth-dependent viscosity appropriate for diffusion creep is employed. The upper boundary is a rigid surface moving at constant speed; this boundary condition is compatible with plate tectonics. It is found that large flow velocities and small temperature differences are associated with ascending convection, and significant flows extend to a depth of 300 km. The surface heat flow and topography are determined and are in reasonable agreement with observations.
85 citations
01 Apr 1971
TL;DR: In this paper, an approximate analysis is presented to describe the flow field in molten steel held in a ladle, as caused by natural convection, and it is shown that a thick slag layer is required to suppress extensive vertical mixing within the ladle.
Abstract: An approximate analysis is presented to describe the flow field in molten steel held in a ladle, as caused by natural convection. It is shown that a thick (say 8 to 14 in.) slag layer is required to suppress extensive vertical mixing within the ladle. It is also shown that natural convection caused by the contact of the metal with the cold ladle walls may produce mass flow rates of the order of 2 to 3 tons per min for typical 100 to 150 ton ladles. If ladles are tapped at comparable rates, then this pehnomenon can effectively prevent mixing in the bulk. The resultant stratification may be desirable in tundish temperature control.
TL;DR: In this article, an experimental study of thermal convection in a horizontal porous layer bounded by isothermal planes has been performed with and without a mean flow of the saturating fluid phase.
Abstract: An experimental study of thermal convection in a horizontal porous layer bounded by isothermal planes has been performed with and without a mean flow of the saturating fluid phase. The temperature distribution and heat transfer resulting from convection have been determined. The theoretical criterion for the onset of convection (Rayleigh number NDRaU > 4piU2D) has been verified. For low values of NDRaU (<260) a regular pattern of convection cells has been observed which may be motionless or moving depending on the experimental conditions. For NDRaU values higher than 260, another convective state has been found that is mainly unstable. Numerical computations have been worked out that confirm the experimental results on the heat transfer and size of convective cells. (23 refs.)
TL;DR: In this paper, linear stability theory is applied to the natural convection boundary layer arising from a vertical plate dissipating a uniform heat flux, and computer solutions are obtained for a much larger range of the Grashof number (G).
Abstract: Linear stability theory is applied to the natural convection boundary layer arising from a vertical plate dissipating a uniform heat flux. By using a numerical procedure which is much simpler than those previously employed on this problem, computer solutions are obtained for a much larger range of the Grashof number (G). For a Prandtl number (σ) of 0·733, it is found that, as G → ∞: the effect of temperature coupling vanishes more rapidly than that of viscosity; the upper branch of the neutral curve is oscillatory but does approach a finite non-zero inviscid asymptote. For moderate and large values of σ, a loop appears in the neutral stability curve as a result of the merging of two unstable modes. As σ → ∞, the mode associated with the uncoupled (i.e. Orr–Sommerfeld) problem rapidly becomes less unstable than that arising from the temperature coupling, with the stability characteristics being independent of the thermal capacity of the plate. For small values of σ, only one unstable mode is found to exist with the coupling effect being negligible in the case of large thermal capacity plates but markedly destabilizing when the thermal capacity is small.By obtaining numerical results out to G ≈ 1010 for the cases σ = 0·733 and 6·7, it becomes possible to attempt to directly relate the theory to the actual observance of turbulent transition. Based upon comparison with available experimental data, empirical correlations are obtained between the linear stability theory and the regimes in which: (i) the boundary layer is first noticeably oscillatory; (ii) the mean (temporal) flow quantities first deviate significantly from those of laminar flow.
TL;DR: In this paper, the authors determined the solutions of the energy equation which satisfy certain fundamental boundary conditions, and these fundamental solutions can be superposed to satisfy a wide variety of boundary conditions.
TL;DR: In this paper, the effects of free convection on laminar flow of water in horizontal circular tubes having essentially constant heat flux at the tube wall were investigated and a visual and quantitative study was performed utilizing electrically heated glass tubing.
TL;DR: In this article, boundary-layer solutions are given for free convection in laminar three-dimensional systems driven by a temperature-dependent or composition-dependent density, and the results of Acrivos [1] for power-law fluids are generalized.
TL;DR: In this paper, the authors show that surface roughness has a particular effect on forced convection heat transfer to supercritical fluid and that the wall temperature profiles obtained in the experiments and also in those of previous investigators can be explained fairly well by the theory assuming normal mode turbulent convection.
TL;DR: In this paper, the incompressible thermal boundary layer equations for a vertical tube open at both ends and heated at the wall were solved by a finite difference method for conditions of constant wall temperature and constant wall heat flux.
TL;DR: In this paper, numerical integration of the rigid-boundary Boussinesq equations in two and three space dimensions is investigated by numerical integration with experimental data in an effort to explain the observed increase of cell wavelength with Rayleigh number.
Abstract: The finite‐amplitude Benard convection problem is investigated by numerical integration of the rigid‐boundary Boussinesq equations in two and three space dimensions. Solutions are obtained for a wide range of Prandtl numbers and at moderate Rayleigh numbers for which the flow is observed to approach a two‐dimensional steady state. Detailed quantitative comparisons are made with experimental data in an effort to explain the observed increase of cell wavelength with Rayleigh number and to determine the effect of changing cell size on the heat transport. The three‐dimensional model shows good evidence of being able to yield realistic values of the cell wavelength, while the two‐dimensional models yield wavelengths that are much too short. These results strongly suggest that the increase in wavelength is determined by a three‐dimensional transient process, while the convection tends to a two‐dimensional steady state. The increase in cell size is shown to be responsible for a substantial part of the discrepancy between previous theoretical‐numerical and experimental determinations of Nusselt number. It also provides a plausible explanation for the experimentally observed dependence of heat transport on Prandtl number.
TL;DR: In this paper, a Mach-Zehnder interferometer was used to study the role of convection currents in the formation of ice, and the critical Rayleigh number for freezing from below is about 480.
TL;DR: In this article, combined free and forced convection heat transfer from a horizontal circular cylinder to a transverse flow is analyzed for the case when the forced flow is either in the direction of the free convection flow (parallel flow) or in the opposite to it (counter flow), and a coordinate perturbation method is used to transform the governing set of partial differential equations into a system of ordinary differential equations.
Abstract: Combined free and forced convection heat transfer from a horizontal circular cylinder to a transverse flow is analysed for the case when the forced flow is either in the direction of the free convection flow (parallel flow) or in the direction opposite to it (counter flow). The problem is solved for two cases: (1) a specified surface temperature variation and (2) a specified wall heat flux variation along the circumference. A coordinate perturbation method is used to transform the governing set of partial differential equations into a system of ordinary differential equations, which are solved by numerical methods. The numerical work is done for the boundary conditions of constant surface temperature and constant wall heat flux. The variation of local heat transfer coefficient and wall shear stress along the circumference up to the point of separation and velocity and temperature profiles in the boundary layer are obtained for varying values of the governing parameters Gr/Re 2 in the constant temperature case (or Gr/Re 2 in the constant heat flux case) and Pr.
TL;DR: In this article, an analysis for transient laminar natural convection in a rectangular cavity containing either one fluid or two immiscible liquids is presented, and the resultant differential equations are integrated numerically and computed results are presented for the transient streamline patterns and for the isotherms, for a variety of conditions including high, low and intermediate values of the Prandtl number.
TL;DR: In this article, an array of rectangular cells, properly shaped with highly reflecting specular walls absorbing to infrared radiation, is shown to be an effective device to limit heat losses when placed over a solar absorber.
TL;DR: In this paper, the problem of beam-induced thermal modifications of a high powered cw laser beam is considered and the extent and type of modification depend principally upon the nature of the medium (liquid or air) and whether an external flow field is present.
Abstract: The problem of beam-induced thermal modifications of a high powered cw laser beam is considered. The extent and type of modification depend principally upon the nature of the medium (liquid or air) and whether an external flow field is present. These conditions determine the dominant heat loss mechanism operating the fluid: forced convection, free convection, and diffusion and, thus, the beam distortions. All three cases are analyzed and figures presented, showing the type of distortion expected as determined within the framework of geometric optics.
TL;DR: The behavior of the vapor wake is highly dependent upon the manner in which vapor is being formed on the forward portion of the sphere as discussed by the authors, and it is shown that film and transition boiling are as effective as nucleate boiling over the velocity range, 9.6-20.0 fps, in highly subcooled water.