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Showing papers on "Natural convection published in 1979"


Journal ArticleDOI
TL;DR: In this paper, the floating constants in Weber's boundary layer solution for free convection in a differentially heated vertical porous slab are reevaluated with a new approach, which uses Weber's solution to calculate the net vertical heat flux which is equated to zero near the top and bottom ends of the enclosure.

224 citations


Journal ArticleDOI
TL;DR: In this article, the vertical turbulent diffusivities over Thetford Forest, U.K., were analyzed to find values of vertical turbulent diffusion at a reference heightzR, nine roughness lengths above the zero-plane displacementd.
Abstract: Simultaneous profile and eddy correlation flux data gathered over Thetford Forest, U.K., have been analysed to find values of the vertical turbulent diffusivitiesKM,KH andKE (for momentum, heat and water vapour transfer, respectively) at a reference heightzR, nine roughness lengths above the zero-plane displacementd. The results show: (i), that values ofKM over the forest are not significantly different from these predicted by semiempirical diabatic influence functions appropriate to much smoother surfaces such as short grass; and (ii), thatKH andKE exceed their values predicted from the semiempirical functions by an average factor of 2 or more in unstable, near neutral and slightly stable conditions. These conclusions are strongly dependent on the assumed behaviour ofd, here taken as 0.76 tree heights, independent of both property and stability. Consideration is given to an alternative analysis procedure, in which values of the zero-plane displacementsdH anddE for heat and water vapour respectively, are obtained from the data by assumingKH andKE to be given by semiempirical diabatic influence functions; this procedure is shown to be unacceptable on both practical and physical grounds. To account for the anomalies inKH andKE, a mechanism is proposed in which the horizontally inhomogeneous temperature structure of the canopy causes free convection to be maintained by discrete; localized heat sources and/or sinks, effectively enhancing turbulent transport processes even in nearneutral conditions.

216 citations


Journal ArticleDOI
TL;DR: In this article, a parabolic-cylindrical solar collector with a circular receiver tube, with a suitable selective coating, is enclosed by a concentric glass envelope and situated along the focal line of a parabolized trough reflector, where the heat transfer processes which occur in the annular space between the receiver tube and the glass envelope are important in determining the overall heat loss from the tube.
Abstract: An effective device for the collection of solar energy which has received widespread attention is the so called parabolic-cylindrical solar collector. In this design a circular receiver tube, with a suitable selective coating, is enclosed by a concentric glass envelope and situated along the focal line of a parabolic trough reflector. The heat transfer processes which occur in the annular space between the receiver tube and the glass envelope are important in determining the overall heat loss from the receiver tube. In typical high temperature receiver tube designs the rate of energy loss by combined thermal conduction and natural convection is of the same order of magnitude as that due to thermal radiation, and can amount to approximately 6 percent of the total rate at which energy is absorbed by the solar collector. The elimination of conduction and natural convection losses can significantly improve the performance of a large collector field. Several techniques useful for the reduction of energy loss by thermal conduction and natural convection are considered. The receiver configuration chosen for study is typical of those used in the Solar Total Energy System at Sandia Laboratories. The receiver tube has a ''black chrome'' selective coating and is 2.54 more » cm in outside diameter. The inside diameter of the glass envelope is approximately 4.4 cm. Typical operating temperatures of the receiver tube and glass envelope are approximately 300/sup 0/C and 100/sup 0/C, respectively. « less

137 citations



Journal ArticleDOI
TL;DR: In this paper, it is shown that the fully developed turbulent boundary layer must be treated in two parts: an outer region consisting of most of the boundary layer and an inner region in which the mean convection terms are negligible.

124 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of buoyancy forces on the steady, laminar, plane flow over a horizontal plate is investigated within the framework of a first-order boundary layer theory, taking into account the hydrostatic pressure variation normal to the plate.

104 citations



Journal ArticleDOI
TL;DR: In this article, a method for the precise study of steady two-dimensional convection problems in the asymptotic limit of large Rayleigh number R was described, assuming a very viscous fluid with the...
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 ...

99 citations


Journal ArticleDOI
TL;DR: In this article, the existence of subcritical finite amplitude solutions for convection in a horizontal fluid layer heated from below and rotating about its vertical axis is demonstrated for Prandtl numbers P < 1.
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.

94 citations


Journal ArticleDOI
TL;DR: In this paper, the results of an analytical investigation of natural convection in porous media completely enclosed by concentric spheres and horizontal cylinders have been reported, showing that a maximum value of the heat transfer occurs for the spherical and cylindrical geometries dependent solely upon the radius ratio for each geometry.

89 citations


Journal ArticleDOI
TL;DR: In this article, a linear stability analysis of the critical Rayleigh number of a vertical fracture or fault in which the temperature increases with depth is performed, and it is shown that the critical number is time dependent.
Abstract: Natural convection of water contained in a vertical fracture or fault in which the temperature increases with depth is strongly influenced by the heat transport processes not only within the water itself but also by the heat transferred to and from the surrounding rock mass. The results of a linear stability analysis indicate that the critical Rayleigh number R* is time dependent. For spontaneous neutral stability, R* (t=0) approx. =10(h/a) /sup 2/, where h and a are the fault height and aperture, respectively. Since h>>a, R* (0) is several orders of magnitude greater than the value 4..pi../sup 2/ that would pertain to the same situation without the influence of the surrounding rock masses, e.g., a porous bed with large horizontal dimensions. The resultant cell motion consists of rolls about axes parallel to the aperture. These rolls are of height h and closely spaced in the strike direction. Cases of spontaneous instabilities in fractures or faults are expected to be infrequent, but initially subcritical convection could be fostered by other means such as tectonic displacements at the fault. Because R* diminishes as time /sup -1/2/, eventually, this subcritical convection becomes unstable, and exponential growth ensues. As the heat of the surroundingmore » rock is depleted and an isothermal state is approached, the convection eventually dampens until a period of thermal recovery allows its resumption.« less


Journal ArticleDOI
TL;DR: In this paper, the problem of laminar, natural convection flow over a vertical frustum of a cone is treated, and the governing differential equations are solved by a combination of quasilinearization and finite-difference methods.
Abstract: The problem of laminar, natural convection flow over a vertical frustum of a cone is treated in this paper. The thermal boundary condition at the wall include both the constant wall temperature and the constant wall heat flux cases. The governing differential equations are solved by a combination of quasilinearization and finite-difference methods. Numerical solutions are obtained for a range of Prandtl numbers. The solutions are found to approach to the solutions for a full cone if the flow is far downstream or the radius of the cross-section at the leading edge is very small.



Journal ArticleDOI
TL;DR: In this article, the combined heat and mass transfer characteristics of natural convection flow along inclined surfaces are studied analytically, where the surfaces are either maintained at a uniform temperature/concentration or subjected to a uniform heat/mass flux.
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...

Journal ArticleDOI
TL;DR: In this article, an alternative approach to evaluate the arbitrary constants found in Gill's solution for the boundary-layer free-convection regime in a vertical rectangular enclosure was developed. But this method only takes into account the impermeable and adiabatic properties of the horizontal end walls.
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.

Journal ArticleDOI
TL;DR: In this paper, 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.
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.


Journal ArticleDOI
TL;DR: In this paper, the equations of energy, continuity, and momentum are solved to give axial and radial values of temperature, pressure, and axial-and radial velocity for vertical arcs stabilized by natural convection.
Abstract: The equations of energy, continuity, and momentum are solved to give axial and radial values of temperature, pressure, and axial and radial velocity for vertical arcs stabilized by natural convection. It is assumed that the electric field is purely axial and magnetic forces are neglected. For a free‐burning arc of 10 A in air, calculated temperature and velocity profiles are in good agreement with published experimental results. For an arc in an enclosed vertical tube of mercury vapor, results of central velocities as a function of axial position for a 2.9‐A arc are in good agreement with the experimental results of Kenty. Comparisons are made of the differing properties predicted for free‐burning arcs of 10 A in air, sulfur hexafluoride, and hydrogen. Removal of the maxima in the thermal conductivity has a negligible effect on the degree of predicted arc constriction in SF6. Convective flow in all calculations is assumed to be laminar. The influence of radial pressure variations is found to be almost negligible.

Journal ArticleDOI
TL;DR: In this paper, the shape of the solid-liquid interface has been determined photographically, and the local heat transfer coefficients have been measured using a shadowgraph technique, showing 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.
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.

Journal ArticleDOI
TL;DR: In this paper, experiments were performed for freezing under conditions where the liquid phase is either above or at the fusion temperature (i.e., superheated or nonsuperheated liquid).
Abstract: Experiments were performed for freezing under conditions where the liquid phase is either above or at the fusion temperature (i.e., superheated or nonsuperheated liquid). The liquid was housed in a cylindrical containment vessel whose surface was maintained at a uniform, time-invariant temperature during a data run, and the freezing occurred on a cooled vertical tube positioned along the axis of the vessel. The phase change medium was n-eicosane, a paraffin which freezes at about 36/sup 0/C (97/sup 0/F). In the presence of liquid superheating, the freezing process is drastically slowed and ultimately terminated by the natural convection in the liquid. The terminal size of the frozen layer an the time at which freezing terminates can be controlled by setting the temperature parameters which govern the intensity of the natural convection. The stronger the natural convection, the thinner the frozen layer an the shorter the freezing time. In the absence of liquid superheating, a cylindrical frozen layer grows continuously as predicted by theory, but the growth rate is higher than the predictions because of the presence of whisker-like dendrites on the freezing surface.

Journal ArticleDOI
TL;DR: An exact analysis of the effects of mass transfer and free convection currents on MHD Stokes' (Rayleigh's) problem for the flow of an electrically conducting, incompressible, viscous fluid past an impulsively started vertical plate, under the action of a transversely applied magnetic field is made in this article.



Journal ArticleDOI
TL;DR: In this paper, mass transfer at a vertical gas sparged electrode with and without superimposed electrolyte flow has been investigated and the results can be represented by an analogous correlation in which the Grashof number, characteristic for free convection, is replaced by a modified Archimedes number: Sh = 0.19(Sc.Ar ∗ ) 1 3.

Journal ArticleDOI
TL;DR: In this paper, the authors used numerical results to show the relationship between previous contending observations, and demonstrate that there exists more than one mode of convection for any particular physical configuration and Rayleigh number.
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.


Journal ArticleDOI
TL;DR: In this paper, 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.
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