Showing papers on "Combined forced and natural convection published in 1971"
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
87 citations
86 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
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.)
70 citations
68 citations
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.
64 citations
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, the authors considered the instability of a horizontal fluid layer with a univariant phase transition and found that the layer can be unstable even when the less dense phase lies above the dense phase and can be stable in the opposite case.
Abstract: The gravitational instability of a horizontal fluid layer with a univariant phase transition is considered It is found that the layer can be unstable even when the less dense phase lies above the dense phase and can be stable in the opposite case Applications of the theory to convection with phase transitions in astrophysical and geophysical problems are briefly discussed
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 article, the authors report an experimental study of heat transfer from fine horizontal wires of various lengths to fluids having various Prandtl numbers and determine transport characteristics for the full spectrum of processes from natural, through mixed, to forced convection.
Abstract: This paper is the report of an experimental study of heat transfer from fine horizontal wires of various lengths to fluids having various Prandtl numbers. Transport characteristics were determined for the full spectrum of processes from natural, through mixed, to forced convection. The experimental results are compared with those of past analysis and with correlations. The very high level of accuracy and reproducibility of the data makes possible the detection of very small effects. The influence of cylinder length on transport is shown for both of the asymptotic rgimes of natural and of forced convection. Transport in the mixed-convection rgime is determined and limits of that rgime are estimated.
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 paper, the authors present a linear stability analysis of Benard convection of a Boussinesq fluid in a thin rotating annulus for modest Taylor numbers T ([les ] 104] ).
Abstract: We present a linear stability analysis, to second order in initial amplitude, of Benard convection of a Boussinesq fluid in a thin rotating annulus for modest Taylor numbers T ([les ] 104). The work is motivated in part by the desire to study further a mechanism for maintaining, through horizontal Reynolds stresses induced in the convection, the sun's ‘equatorial acceleration’, which has been demonstrated for a rotating convecting spherical shell by Busse & Durney. The annulus is assumed to have stress free, perfectly conducting top and bottom (which allows separation of the equations) and non-conducting non-slip sides. A laboratory experiment which fulfills these conditions (except perhaps the free bottom) is being developed with H. Snyder.We study primarily annuli with gap-width to depth ratios a of order unity. The close, non-slip side-walls produce a number of effects not present in the infinite plane case, including overstability at high Prandtl numbers P, and multiple minima in Rayleigh number R on the stability boundary. The latter may give rise to vacillation. The eigenfunctions for stationary convection for a = 2, T [lsim ] 2000 clearly show momentum of the same sense as the rotation is transported from the inner to the outer half of the annulus, corresponding to transport toward equatorial latitudes on the sphere. The complete second-order solutions for the induced circulations indeed give faster rotation in the outer half, except for large P (> 102), in which case thermal stresses dominate. At all P, this differential rotation is qualitatively a thermal wind. Overstable convective cells, and stationary cells at higher T, induce more complicated differential rotations.
TL;DR: In this paper, the dynamics of thermal convection through a shallow layer with vertical shear was examined using an idealized numerical model, where convection is assumed to take the form of two-dimensional rolls.
Abstract: The dynamics of thermal convection through a shallow layer with vertical shear is examined using an idealized numerical model. The convection is assumed to take the form of two-dimensional rolls. The mean shear flow and the unstable temperature gradient are maintained by no-slip, conducting boundary conditions applied at the upper and lower boundaries of the model. When the convective rolls are transverse to the mean current, the flow approaches a steady state with time for the cases of primary interest. In agreement with previous numerical studies the shear has a stabilizing influence on the convection: the transformation of potential energy into disturbance kinetic energy is reduced, and disturbance kinetic energy is transformed into basic kinetic energy. A new result, in agreement with linear stability theory, is that shear can significantly increase the horizontal distance between disturbances over that expected with no shear. Steady-state results were also obtained when the rolls are paralle...
TL;DR: In this article, a simplified Nusselt number based on superposed free and forced convection for air for a horizontal cylinder in which the forced and free convection forces act in the same direction is considered.
Abstract: An analytical correlation of superposed free and forced convection for air for a horizontal cylinder in which the forced convection and free convection forces act in the same direction is considered. A simplified method by which the ordinary formulas for forced convection and for free convection can be used together to give the Nusselt number is presented. The method proposed herein can easily be modified to work for other combinations of free and forced flow systems. The method, therefore, may have wide application because standard formulas for simple systems are easily combined to obtain formulas which are valid for complicated systems.
TL;DR: In this paper, it is shown that the flow can be expected to become turbulent before the outer vorticity region of the laminar boundary layer is fully established, and the results are generalized to the isothermal plate case.
Abstract: Expansions are obtained for the large Prandtl number structure of the laminar natural convection boundary layer, together with its linear stability characteristics, for the case of a uniform-heat-flux semi-infinite vertical plate. The primary source of instability is shown to arise from a temperature-coupling effect associated with the inner heated region of the boundary layer. Based upon an empirical correlation between the results of linear stability theory and experimentally determined regimes of the turbulent-transition process, it is shown that the flow can be expected to become turbulent before the outer vorticity region of the laminar boundary layer is fully established. The results are generalized to the isothermal plate case.
TL;DR: In this article, the influence of free convection on a thermal explosion was considered and it was indicated that the pa ramete r 6 chara ter ing the l imits of thermal self-ignit ion should depend on a pa ramese variable variable of the intensity of natural convection, i.e., on the Rayleigh (Ra) c r i t e r ion.
Abstract: The question of the need to consider the influence of free convection on a thermal explosion was f i rs t posed in [i], where it was indicated that the pa ramete r 6 charac ter iz ing the l imits of thermal self-ignit ion should depend on a pa rame te r charac te r iz ing the intensity of natural convection, i .e. , on the Rayleigh (Ra) c r i t e r ion (for gases the Ra c r i te r ion equals the Grashof cr i ter ion). The assumption has been expressed that the influence of convection on a thermal explosion for gases s tar ts to be manifest for values of Ra >_104. The appearance of convective effects at considerably lower values of the Ra c r i te r ion (Ra ~ 600) has been detected in [2] by means of an experimental investigation of the tempera ture distribution in vesse ls with a react ing gas.
TL;DR: In this paper, an experimental study has been made of ionic mass transfer where both forced and free convective mechanisms contribute to the over-all transfer rate, and criteria are proposed for the dominance of both forms of pure flow, and also for the occurrence of the point of minimum mass-transfer rate.