Showing papers on "Combined forced and natural convection published in 1979"

Fast viscous bénard convection

Abstract: We have previously described a method for the precise study of steady two-dimensional convection problems in the asymptotic limit of large Rayleigh number R, assuming a very viscous fluid with the ...

Nonlinear properties of convection rolls in a horizontal layer rotating about a vertical axis

Abstract: Steady finite amplitude two-dimensional solutions are obtained for the problem of convection in a horizontal fluid layer heated from below and rotating about its vertical axis. Rigid boundaries with prescribed constant temperatures are assumed and the solutions are obtained numerically by the Galerkin method. The existence of steady subcritical finite amplitude solutions is demonstrated for Prandtl numbers P < 1. A stability analysis of the finite amplitude solutions is performed by superimposing arbitrary three-dimensional disturbances. A strong reduction in the domain of stable rolls occurs as the rotation rate is increased. The reduction is most pronounced at low Prandtl numbers. The numerical analysis confirms the small amplitude results of Kuppers & Lortz (1969) that all two-dimensional solutions become unstable when the dimensionless rotation rate Ω exceeds a value of about 27 at P ≃ ∞. A brief discussion is given of the three-dimensional time-dependent forms of convection which are realized at rotation rates exceeding the critical value.

Combined heat and mass transfer in natural convection on inclined surfaces

Abstract: The combined heat and mass transfer characteristics of natural convection flow along inclined surfaces are studied analytically. The buoyancy forces arise from both temperature and concentration variations in the fluid. In the analysis, the diffusion-thermo and thermo-diffusion effects are neglected, as are the interfacial velocities resulting from mass diffusion. The surfaces are either maintained at a uniform temperature/concentration or subjected to a uniform heat/mass flux. The important parameters of the problem include Prandtl and Schmidt numbers, thermal and concentration Grashof numbers, the relative buoyancy force effect between species and thermal diffusion, and the angle of inclination from the vertical. Numerical results are presented for diffusion of common species into air and water. For both heating/diffusing conditions, the wall shear stress and the local Nusselt number are found to increase and decrease as the buoyancy force from species diffusion assists and opposes, respectively, the th...

Note on Gill's solution for free convection in a vertical enclosure

Abstract: This paper develops an alternative approach to evaluating the arbitrary constants found in Gill's solution for the boundary-layer free-convection regime in a vertical rectangular enclosure. The new method consists of calculating the net upward flow of energy through the enclosure and setting it equal to zero near the top and bottom boundaries of the cavity. The present method takes into account the impermeable and adiabatic properties of the horizontal end walls. The overall Nusselt number derived on this new basis is shown to agree well with available experimental and numerical heat-transfer correlations.

Mixed Convection on Inclined Surfaces

Abstract: An analysis is performed to study the effects of buoyancy force on the heat transfer characteristics of laminar forced convection flow over an inclined flat surface which is either maintained at a uniform temperature or subjected to a uniform heat flux. Numerical results are presented for Prandtl numbers of 0.7 and 7 over a wide range of values of the buoyancy force parameters, with the angle of inclination ranging from 0 to 90 deg from the vertical. In general, it is found that for both surface heating conditions, the local friction factor and the local Nusselt number increase with increasing buoyancy force for assisting flow and decrease with increasing buoyancy force for opposing flow. In addition, the effects of the buoyancy force on these two quantities are found to diminish as the angle of inclination increases. A comparison is also made of the results between the case of uniform wall temperature and the case of uniform surface heat flux.

Free Convection Effects on the Flow Past an Infinite Vertical Oscillating Plate

Abstract: The motion of a semi-infinite incompressible viscous fluid, caused by the oscillation of a plane vertical plate, has been studied, taking into account the presence of free convection currents. Closed form solutions to the velocity, temperature and the penetration distance through which the leading edge effect propagates have been derived on neglecting the transient part. Velocity profiles are shown forGr>0 (Grashof number) (cooling of the plate by the free convection currents),Gr<0 (heating of the plate) on graph. Also the penetration distance has been shown on graphs for different values ofP, the Prandtl number. It has been observed that for ωt=3π/2, greater cooling of the plate may cause the flow to become unstable. Also, the penetration distance is not found to be affected by the frequency of the oscillating vertical plate.

An experimental investigation of natural convection in the melted region around a heated horizontal cylinder

Abstract: Melting from an electrically heated horizontal cylinder embedded in a paraffin (n-octadecane, fusion temperature 301·3 °K) has been studied experimentally. The shape of the solid-liquid interface has been determined photographically, and the local heat transfer coefficients have been measured using a shadowgraph technique. The experiments provide conclusive evidence of the important role played by natural convection in melting a solid due to an embedded cylindrical heat source. The four distinct pieces of quantitative evidence which contribute to this conclusion are the melt shape, surface temperature, local and average heat transfer coefficients and their variation with time.The experimental findings prove the importance of natural convection in phase change problems involving melting and indicate that continued practice of neglecting the effects in the analysis of such problems does not appear reasonable. Natural convection should be considered in analysis and design of systems involving phase change.

Three-dimensional natural convection in a confined porous medium heated from below

Abstract: Previous analyses of natural convection in a porous medium have drawn seemingly contradictory conclusions as to whether the motion is two- or three-dimensional. This investigation uses numerical results to show the relationship between previous contending observations, and demonstrates that there exists more than one mode of convection for any particular physical configuration and Rayleigh number. In some cases, a particular flow situation may be stable even though it does not maximize the energy transfer across the system. The methods used are based on the efficient numerical solution of the governing equations, formulated with the definition of a vector potential. This approach is shown to be superior to formulating the equations in terms of pressure. For a cubic region the flow pattern at a particular value of the Rayleigh number is not unique and is determined by the initial conditions. In some cases there exist four alternatives, two- and three-dimensional, steady and unsteady.

Moving lithospheric plates and mantle convection

Abstract: Summary. The coupling between a rigidly moving lithospheric plate and a convecting mantle is investigated using a simple two-dimensional numerical model that incorporates a horizontally moving upper boundary, simulating the effect of a moving plate, over a fluid layer heated from below. The moving boundary strongly controls the horizontal length scale of convection cells when its velocity is greater than the free convective velocity (i.e. the velocity with which the fluid would convect under a stationary boundary). In a box of aspect ratio 4 (width/depth), a transition in flow structure occurs from several equidimensional convection cells under a slowly moving boundary to a single long convection cell under a rapidly moving boundary. The flow structure transition occurs approximately when Pe/RaW3 = 0.04, where the Peclet number, Pe, measures the (prescribed) velocity of the upper boundary, and the Rayleigh number, Ra, measures the heating of the fluid layer. Near the transition, the flow tends to be unsteady; this behaviour can be well understood in terms of the instability of the thermal boundary layers, which can be characterized by a local Rayleigh number. Using conventional estimates of mantle parameters, the mantle is either near or above the transition to single-cell convection, whether upper-mantle or whole-mantle convection is assumed. The net tangential force exerted by the fluid on the upper boundary varies approximately linearly with the boundary velocity above the transition, and it is positive (driving) for boundary velocities ranging from the value at the transition to about three times the transition

Nonstationary Convection in a Rotating System

Abstract: Since Kuppersand Lortz (1969) have demonstrated that all small amplitude stationary solutions for convection in a layer heated from below and rotating about a vertical axis are unstable, the problem of the realized form of convection has remained unsolved. By considering simple examples, it is demonstrated that a time-dependent form of convection is likely to be physically realized which not only depends on the initial conditions, but on the continuous presence of experimental noise as well. In this respect, the problem exhibits a characteristic property of turbulent fluid system.

An experimental determination of transition limits in a vertical natural convection flow adjacent to a surface

Abstract: This paper reports the results of an experimental investigation to determine transition mechanisms and limits in gases at high pressure levels. We sought also to refine further the parameters for transition, in particular the role of kinematic viscosity. In flow adjacent to a vertical uniform-flux surface in nitrogen, pressures to 16 atm were used. Both mean and disturbance quantities for the temperature and velocity fields were measured for various values of the heat flux, downstream location and ambient pressure level. Hot-wire and fine thermocouple probes were used. We found that the velocity and thermal fields remain closely coupled. Velocity, or fluid-dynamic, transition is immediately followed by thermal transition. Each was detected as a decrease in the rate of increase of both the maximum velocity and the overall temperature difference, respectively, from the laminar downstream trends. Also, the ends of transition for the velocity and the thermal fields, respectively, signalled by no further appreciable change in the intermittency distributions, were simultaneous. These results re-affirm the finding that the events of transition are not correlated by the Grashof number alone. An additional dependence on both downstream location and pressure level arises. A fixed value of the parameter , where Q is the fifth root of the local non-dimensional total heat convected in the boundary region. A re-examination of other transition studies, in both gases and liquids, supports these correlations, although many such data were not determined with fast response to local sensors. There remains a small level of uncertainty in establishing exact limits for transition, since the apparently proper standards for determining them are very difficult to apply precisely in experiments. However, such limits are very important in separating regimes of different transport mechanisms.

Laminar natural convection boundary layers on horizontal circular discs

Abstract: A first-order boundary-layer analysis, including variable properties effects, is given for laminar natural convection on a horizontal circular disc. It is shown that the result for the Nusselt number is very close to that for a square plate.

The dynamic effect of flux ropes on Rayleigh-Bénard convection

Abstract: The interaction between magnetic fields and convection in a fluid heated from below is investigated in an axisymmetric cylindrical geometry. When Rm, the magnetic Reynolds number, is large the field is concentrated into a thin rope on the axis of the cylinder. For weak magnetic fields a larger Rayleigh number is necessary to produce a flux rope than that needed for infinitesimal convection. For larger total fluxes, however, the opposite is true and the system is subcritically unstable to steady motions. The results are contrasted with those found by Busse (1975) for the corresponding two-dimensional roll problem.