Showing papers on "Natural convection published in 1976"

An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders

Abstract: An experimental and theoretical-numerical investigation has been carried out to extend existing knowledge of velocity and temperature distributions and local heat-transfer coefficients for naturel convection within a horizontal annulus. A Mach—Zehnder interferometer was used to determine temperature distributions and local heat-transfer coefficients experimentally. Results were obtained using water and air at atmospheric pressure with a ratio of gap width to inner-cylinder diameter of 0·8. The Rayleigh number based on the gap width varied from 2·11 × 104to 9·76 × 105. A finite-difference method was used to solve the governing constant-property equations numerically. The Rayleigh number was changed from 102 to 105 with the influence of Prandtl number and diameter ratio obtained near a Rayleigh number of 104. Comparisons between the present experimental and numerical results under similar conditions show good agreement.

The theory of the transient hot-wire method for measuring thermal conductivity

Abstract: The paper contains a complete, modernized theory of the transient hot-wire method for measuring the thermal conductivity of fluids which can be employed in the form of an absolute instrument and which can be operated with a precision of 0.02% and an accuracy of 0.2%. It is a companion paper for ref. 1. The analysis demonstrates that the instrument can be designed to imitate very closely the behaviour of a finite portion of an infinite line source of constant heat flux, q, which transfers the heat radially into an infinite fluid. Expressions for the corrections are obtained by a general perturbation method which allows us to examine them one or several at a time. The principal corrections discussed in the form of nine subproblems are: finite inner cylinder, composite cylinders, Knudsen effects, radiation, outer cell circumference, compressibility and natural convection, finite cell dimensions, variable fluid properties and heating over a finite length. The last section summarizes the most important corrections for a reader who is interested in using them rather than in following the analysis itself. The main text supplies all data required by the designer of an instrument of this type.

Thermal convection with strongly temperature-dependent viscosity

Abstract: This paper experimentally investigates the heat transport and structure of convection in a high Prandtl number fluid layer whose viscosity varies by up to a factor of 300 between the boundary temperatures. An appropriate definition of the Rayleigh number R uses the viscosity at the average of the top and bottom boundary temperatures. With rigid boundaries and heating from below, the Nusselt number N normalized with the Nusselt number N0 of a constant-viscosity fluid decreases slightly as the viscosity ratio increases. The drop is 12% at a variation of 300. A slight dependence of N/N0 on R is consistent with a decrease in the exponent in the relation N ∝ Rβ from its constant-viscosity value of 0·281 to 0·25 for R [lsim ] 5 × 104. This may be correlated with a transition from three- to two-dimensional flow. At R ∼ 105 and viscosity variation of 150, the cell structure is still dominated by the horizontal wavelength of the marginally stable state. This is true with both free and rigid upper boundaries. The flow is strongly three-dimensional with a free upper boundary, while it is nearly two-dimensional with a rigid upper boundary.

Nonlinear double-diffusive convection

Abstract: The two-dimensional motion of a fluid confined between two long horizontal planes, heated and salted from below, is examined. By a combination of perturbation analysis and direct numerical solution of the governing equations, the possible forms of large-amplitude motion are traced out as a function of the four non-dimensional parameters which specify the problem: the thermal Rayleigh number RT, the saline Rayleigh number ES, the Prandtl number σ and the ratio of the diffusivities τ. A branch of time-dependent asymptotic solutions is found which bifurcates from the linear oscillatory instability point. In general, for fixed σ, τ and RS, as RT increases three further abrupt transitions in the form of motion are found to take place independent of the initial conditions. At the first transition, a rather simple oscillatory motion changes into a more complicated one with different structure, at the second, the motion becomes aperiodic and, at the third, the only asymptotic solutions are time independent. Disordered motions are thus suppressed by increasing RT. The time-independent solutions exist on a branch which, it is conjectured, bifurcates from the time-independent linear instability point. They can occur for values of RT less than that at which the third transition point occurs. Hence for some parameter ranges two different solutions exist and a hysteresis effect occurs if solutions obtained by increasing RT and then decreasing RT are followed. The minimum value of RT for which time-independent motion can occur is calculated for fourteen different values of σ, τ and RS. This minimum value is generally much less than the critical value of time-independent linear theory and for the larger values of σ and RS and the smaller values of τ, is less than the critical value of time-dependent linear theory.

Natural Convection in Enclosed Spaces—A Review of Application to Solar Energy Collection

Abstract: A useful solar-thermal converter requires effective control of heat losses from the hot absorber to the cooler surroundings. Based upon the theory and some experimental measurements it is shown that the spacing between the tilted hot solar absorber and successive glass covers should be in the range 4 to 8 cm to assure minimum gap conductance. Poor choice of spacing can significantly affect thermal conversion efficiency, particularly when the efficiency is low or when selective black absorbers are used. Recommended data for gap Nusselt number are presented as a function of the Rayleigh number for the high aspect ratios of interest in solar collector designs. It is also shown that a rectangular cell structure placed over a solar absorber is an effective device to suppress natural convection, if designed with the proper cell spacing d, height to spacing ratio L/d and width to spacing ratio W/d needed to give a cell Rayleigh number less than the critical value.

Studies of finite amplitude non‐Newtonian thermal convection with application to convection in the Earth's mantle

Abstract: Studies of non-Newtonian thermal convection have been made to determine the importance of non-Newtonian viscosity on flow in the earth's mantle. Finite difference solutions have been obtained with a viscosity law representing the sum of deformation rates due to diffusion and dislocation creep. Non-Newtonian flow structures differ only slightly from corresponding Newtonian flows. The principal effect of the non-Newtonian viscosity is to increase the effective Rayleigh number. An effective Rayleigh number based on a strain rate squared averaged viscosity provides a good correlation between Newtonian and non-Newtonian flows over a wide range of Rayleigh numbers.

The Effect of Heater Size, Location, Aspect Ratio, and Boundary Conditions on Two-Dimensional, Laminar, Natural Convection in Rectangular Channels

Abstract: The effect of localized heating in rectangular channels was studied by solving the partial differential equations for the conservation of mass, momentum, and energy numerically using an unsteady state formulation and the alternating-direction-implicit method. The heating element was a long, horizontal, isothermal strip located in one, otherwise-insulated vertical wall. The opposing wall was maintained at a lower uniform temperature and the upper and lower surfaces were insulated or maintained at the lower temperature. Computations were carried out for Pr = 0.7, 0 less than or equal to Ra less than or equal to 10/sup 5/, a complete range of heater widths and locations and a wide range of aspect ratios. Flow visualization studies and comparison with prior computed results for a limiting case confirm the validity of the computed values. The computed rates of heat transfer and circulation provide guidance for locating heaters or coolers.

Thermoconvective instabilities in a porous medium bounded by two concentric horizontal cylinders

Abstract: The study of natural convection in a saturated porous medium bounded by two concentric, horizontal, isothermal cylinders reveals different types of evolution according to the experimental conditions and the geometrical configuration of the model. At small Rayleigh numbers the state of the system corresponds to a regime of pseudo-conduction. The isotherms are coaxial with the cylinders. At larger Rayleigh numbers a regime of steady two-dimensional convection sets in between the two cylinders. Finally, for Rayleigh numbers above the critical Rayleigh number Ra*c the phenomena become three-dimensional and fluctuating. The appearance of these different regimes depends, moreover, on the geometry considered and, in particular, on two numbers: R, the ratio of the radii of the cylinders, and A, the ratio of the length of the cylinders to the radius of the inner one. In order to approach these experimental observations and to obtain realistic theoretical models, several methods of solving the equations have been used.The perturbation method yields information about the thermal field and the heat transfer between the cylinders under conditions close to the equilibrium state.A numerical two-dimensional model enables us to extend the range of investigation and to represent properly the phenomena when steady convection appreciably modifies the temperature distribution and the velocities within the porous layer.Neither of these models allows account to be taken of the instabilities observed experimentally above a critical Rayleigh number Ra*c. For this reason, a study of stability has been carried out using a Galerkin method based on equations corresponding to an initial state of steady convection. The results obtained show the importance of three-dimensional effects for the onset of fluctuating convection. The critical transition Rayleigh number Ra*c is thus determined in terms of the ratio of the radii R by solving an eigenvalue problem.A numerical three-dimensional model based on the method of finite elements has thus been developed in order to point out the different types of evolution with time. Steady two-dimensional convection and fluctuating three-dimensional convection have been actually found by calculation. The solution of the system of equations by the method of finite elements is briefly described.The experimental and theoretical results are then compared and a general physical interpretation is given.

Laboratory simulation of thermal convection in rotating planets and stars.

Abstract: Because of dynamical constraints in a rotating system, the component of gravity perpendicular to the axis of rotation is the dominant driving force of convection in liquid planetary cores and in stars. Except for the sign, the centrifugal force closely resembles the perpendicular component of gravity. Convection processes in stars and planets can therefore be modeled in laboratory experiments by using the centrifugal force with a reversed temperature gradient.

Onset of Convection in a Porous Medium With Internal Heat Generation

Abstract: The conditions leading to the onset of thermal convection in a horizontal porous layer are determined analytically using the method of linear stability of small disturbances. The lower boundary is treated as a rigid surface and the upper boundary as a free surface. The critical internal and external Rayleigh numbers are determined for both stabilizing and destabilizing boundary temperatures. The predicted critical external Rayleigh number in the limit of no heat generation is in agreement with the critical number predicted for a porous medium heated from below. (16 refs.)

Natural Convection From a Vertical Surface to a Thermally Stratified Fluid

Abstract: Results are presented of a study of natural convection from an isothermal finite plate immersed in a stable thermally stratified fluid. An analytical solution to the problem is obtained by using the local nonsimilarity method. Theoretical local and overall heat transfer coefficients are given for Pr = 0.7 and 6.0. Velocity and temperature profiles are given for Pr = 6.0. The actual experimental configuration was a vertical copper cylinder enclosed in a cube with rigid walls. Heat transfer data are correlated with the measured ambient thermal gradient. Visual studies of the flow field are also discussed. Excellent agreement is achieved between analysis and experiment.

Transient combined laminar free convection and radiation in a rectangular enclosure

Abstract: The mass, momentum and energy-transfer equations are solved to determine the response of a rectangular enclosure to a fire or other high-temperature heat source. The effects of non-participating radiation, wall heat conduction, and laminar natural convection are examined. The results indicate that radiation dominates the heat transfer in the enclosure and alters the convective flow patterns significantly. At a dimensionless time of 5·0 the surface of the wall opposite a vertical heated wall has achieved over 99% of the hot-wall temperature when radiation is included but has yet to change from the initial temperature for pure convection in the enclosure. At the same time the air at the centre of the enclosure achieves 33% and 13% of the hot-wall temperature with and without radiation, respectively. For a hot upper wall the convection velocities are not only opposite in direction but an order of magnitude larger when radiation transfer between the walls is included.

Axisymmetric convection in a cylinder

Abstract: In three-dimensional BBnard convection regions of rising and sinking fluid are dissimilar. This geometrical effect is studied for axisymmetric convection in a Boussinesq fluid contained in a cylindrical cell with free boundaries. Near the critical Rayleigh number R, the solution is obtained from a perturbation expansion, valid only if both the Reynolds number and the PBclet number are small. For values of the Nusselt number N 1 there is a viscous regime with N M 2(R/Rc)i; when R/R, 2 pb, N increases more rapidly, approximately as R0.4. At high Rayleigh numbers a large isothermal region develops, in which the ratio of vorticity to distance from the axis is nearly constant.

An experimental study of turbulent convection in air

Abstract: An experiment was performed in a 3·5 by 3·5 m variable-height, closed convection box, with conditions ranging from a Rayleigh number of 4 × 104 up to 7 × 109, using air as the working fluid. Heat-flux measurements made at Rayleigh numbers up to 7 × 109 yielded a Nusselt number Nu = 0·13Ra0·30. Velocities and temperatures were measured up to Ra = 1·7 × 107, and Fourier spectra calculated to find the predominant horizontal scales of the motion midway between the boundaries. The predominant scale at Ra ∼ 105 was approximately four times the distance between plates, changing to six as Ra increased to 106. With side walls introduced so that the transverse aspect ratio was equal to five, Fourier spectra indicated considerable smaller scale motions, approximately equal to the layer depth. These motions decreased in size as Ra was increased. The results are discussed in relation to previous experimental and theoretical work.

Natural Convection in a Porous Medium: Effects of Confinement, Variable Permeability, and Thermal Boundary Conditions

Abstract: Two-dimensional numerical calculations are reported for natural convection of a fluid in a porous, horizontal layer heated from below. Effects of the following parameters are examined: rigid (impermeable) and constant-pressure (permeable) upper boundaries; isothermal and uniform heat flux at the lower boundary; and permeabilities which are constant, or which vary with depth to simulate compaction of a porous medium or property variations of real fluids within the medium. Steady-state results are presented for the heat flux distribution on the upper surface, as well as for flow and temperature fields in the interior.

Convection due to internal heat sources

Abstract: This paper is concerned with convection generated by uniformly distributed internal heat sources. By a numerical method it is found that the planform is down-hexagons for infinite Prandtl numbers and Rayleigh numbers up to at least 15 times the critical value. The motion is also studied for finite Prandtl numbers and small supercritical Rayleigh numbers by using an amplitude expansion. It turns out that a small subcritical regime exists. Moreover, it also emerges that for Prandtl numbers less than 0.25 the stable planform is up-hexagons. In §3 a necessary condition in order to obtain a hexagonal planform is derived when the coefficients in the differential equations are a function of the vertical co-ordinate z.

Growth Dynamics of the Convectively Mixed Layer

Abstract: A model for the growth of a convectively mixed layer is derived by layer integrating the basic equations and parameterizing unknown terms in the mixed layer turbulence kinetic energy equation by means of free convection similarity theory. When shear generation of turbulence energy is neglected in the turbulent inversion layer capping the mixed layer, the model essentially reduces to that of Tennekes. This shear generation is found to be important only in cases of significant baroclinicity and shallow mixed layer depth or small free flow stratification.

Stresses produced in gasses by temperature and concentration inhomogeneities. New types of free convection

Abstract: The main results of theoretical investigation of slow (Re ~ l) non-isothermal (temperature drop in the gas ? = ? T/T ~ 1) are reported. These flows are described by equations that differ from the classical Navier-Stokes equations for a compressible liquid in that the momentum equation contains besides the viscous-stress tensor, also a temperature-stress tensor of the same order of magnitude. The question of the influence of temperature stresses on the motion of the gas are analyzed, as are the forces acting on bodies placed in the gas. This question was first raised long ago by J. Maxwell, who used implicitly linearization in ? and reached the conclusion that the temperature stresses cause neither motion of the gas nor forces. However, when ? is not small, a new type of convection of the gas appears in the absence of external forces (e.g., of gravitation), namely, the temperature stresses cause the gas to move near uniformly heated (cooled) bodies; some examples of this convection are presented. In addition, for the case of small ?, an electrostatic analogy is established, describing the force interaction between these bodies as a result of the temperature stresses. The problem of the flow around a uniformly heated sphere at Re? 1 (the Stokes problem) is solved: the temperature stresses exert an ever increasing influence on the resistance of the sphere with increasing sphere temperature. Analogous phenomena, produced in gas mixtures by concentration (diffusion) stresses, are indicated.