Showing papers on "Natural convection published in 1983"

Natural convection of air in a square cavity: A bench mark numerical solution

Abstract: Details are given of the computational method used to obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls. Second-order, central difference approximations were used. Mesh refnement and extrapolation led to solutions for 103⩽Ra⩽10 6 which are believed to be accurate to better than 1 per cent at the highest Rayleigh number and down to one-tenth of that at the lowest value.

Natural convection in a square cavity: A comparison exercise

Abstract: A number of contributed solutions to the problem of laminar natural convection in a square cavity have been compared with what is regarded as a solution of high accuracy. The purposes of this exercise have been to confirm the accuracy of the bench mark solution and to provide a basis for the assessment of the various methods and computer codes used to obtain the contributed solutions.

The “Heatline” Visualization of Convective Heat Transfer

Abstract: Proposition d'une nouvelle methode de visualisation du transfert de chaleur dans un ecoulement de fluide. Application a la convection naturelle dans une enceinte carree chauffee lateralement

Multicellular natural convection in a vertical slot

Abstract: In this article we present numerical solutions to multicellular natural convection in a vertical enclosure The calculated streamlines faithfully represent what has been seen in the laboratory by smoke traces in air and particle traces in oils The calculated isotherms for air correspond to reported interferometric patterns Solutions exhibiting travelling waves for water were calculated near conditions where they should occur according to linear stability theory Heat-transfer results for air are given and their dependence on the aspect ratio of the enclosure exhibited

Numerical methods in heat transfer

Abstract: Topics discussed in this book include modelling the effects of fire, ablation, heat flow in porous rock, thermal stress and dissolving coal. Alternative energy sources such as geothermal reservoirs and solar radiation are also discussed. Includes bibliographies at the end of the papers, a cited author index, and a subject index. Contents, abridged: Exact finite element solutions for linear steady state thermal problems. Steep gradient modelling in diffusion problems. Numerical solution of coupled conduction-convection problems using lumped-parameter methods. The prediction of turbulent heat transfer by the finite element methods. The influence of creep and transformation plasticity in the analysis of stresses due to heat treatment. Heat and moisture movement in wood composite materials during the pressing operation-a simplified model. Index.

Heat transfer and horizontally averaged temperature of convection with large viscosity variations

Abstract: It is pointed out that the understanding of convection in large-Prandtl-number Boussinesq fluids with uniform properties and contained in simple geometries is virtually complete. Present efforts are typically directed towards relaxing some of the original assumptions by going to lower Prandtl number, more complicated geometries, variable material properties, or introducing new dynamical processes such as the Lorentz forces. A description is given of experiments which are concerned with the effect on convection of relaxing the assumption of a uniform viscosity. The reported experiments were designed to measure both the horizontally averaged temperature as a function of depth and the heat transfer of convection over a range of viscosity variations up to 100,000.

An experimental and theoretical investigation of the onset of convection in rotating spherical shells

Abstract: Convection in a rapidly rotating spherical layer with constant-temperature boundary conditions is studied in a laboratory experiment. The asymptotic theory of Busse (1970) is extended to permit a comparison with the observations of the onset of convection and its properties. It is found that the prediction of the power-law dependences of the critical buoyancy number and the critical wavenumber on the rotation rate are borne out, although discrepancies in the actual values of these quantities do exist. Calculations on the basis of equations proposed by Roberts (1968) show that a thermal wind that is present in the basic state of the model has a stabilizing influence on the onset of convection. Stewartson layers not taken into account in the asymptotic analysis for vanishing Ekman number E appear to be responsible for the remaining disagreement between theoretical predictions and observations at finite values of E.

Radiation-Natural Convection Interactions in Two-Dimensional Complex Enclosures

Abstract: A numerical finite-difference study has been carried out for the two-dimensional radiation-natural convection interaction phenomena in square enclosures with equal vertical finite-thickness partitions located at the centers of the ceiling and floor. Both participating gases (CO2 and NH3 ) and nonparticipating gas (air) are considered. In the radiation calculations, the nongray exponential wide-band models for CO2 and NH3 are used, together with a radial flux method utilizing a more realistic polar description for the radiation exchange in the enclosure. Results on the effects of both surface and gas radiation on the velocity and temperature fields and the overall heat transfer rates as functions of the partition heights at two levels of the Grashof number are presented and discussed in terms of the physical phenomena.

Natural convection cooling system for electronic components

Abstract: Natural convection cooling of power carrying electronic components mounted within an enclosure is achieved by mounting the power components at the base of the enclosure at the opening of an inner chimney which separates the enclosure interior into forward and rearward compartments. The inner chimney serves to duct the heated air rising from the components at the base of the enclosure forward compartment to the top of the enclosure. A heat exchanger is mounted on the inside face of the enclosure door to provide a cooled surface so that warm air at the top of the enclosure forward compartment is drawn downwardly along the heat exchanger surface to the base of the enclosure thereby creating natural air turbulence within the enclosure. Natural convection cooling is further improved by adding a plurality of heat sinks to the chassis base so that the heat sink fins extend into the rearward compartment which forms an outer chimney by virtue of air ducts being provided in the front and top walls of the enclosure in communication of the rearward compartment. The outer chimney creates an increased draft of cool air along the fins thereby reducing the average temperature of the air rising through the fins. In this way, convection cooling is achieved without the need for separate mechanical air handling equipment.

The Basic Physics of Water Penetration into Hot Rock

Abstract: There are a number of rival ideas about how heat is transferred to the hot fluids of major geothermal areas. One of these is the theory of water penetration into hot rock, where thermal shrinkage of the rocks permits them to crack on a relatively small scale and then transport heat away from the hot boundary thus formed. The theory has the advantage of requiring a relatively small area of contact between water and hot rock to produce the high hermal outputs of large geothermal areas: of the order of 1 km2. This is because the thermal boundary layer is established by the advance of a cracking front into the rock itself, and is a function of front velocity rather than preexisting geological structure. A critical review of the physics of the process shows that the weakest areas of the theory are in the understanding of the mechanics of the cracking process and in the structure of the porous-medium convection that discharges the heat. The problems in both these areas stem from a basic lack of knowledge of the physics, and not from weaknesses in the theory itself. The one-dimensionality of the treatment is not a serious limitation because the predicted crack spacing, of the order of a meter, is much smaller than the kilometer scale of three-dimensionality in the geometry.

Comprehensive, theoretically based, correlating equations for free convection from isothermal spheres

Abstract: Correlating equations are developed for the local and mean Nusselt number for free convection from an isothermal sphere as a function of the Rayleigh and Prandtl numbers. These expressions are based primarily on theoretical solutions for limiting cases, and hence are presumed to be more reliable than purely empirical correlations. The predictions of the proposed expressions are, however, validated by comparisons with prior experimental data. The expressions for the mean Nusselt number are shown to be applicable for all Ra and Pr. The expressions for the local Nusselt number are limited in applicability to the laminar boundary layer regime. The same equations are applicable to mass transfer and to combined heat and mass transfer in terms of the Sherwood, Schmidt and appropriately modified Rayleigh numbers.

Laminar natural convection from a horizontal plate and the influence of plate-edge extensions

Abstract: Laminar natural convection from a horizontal plate is studied by a finite-difference analysis and by experiments for Rayleigh numbers from 10 to 104. The plate with uniform surface temperature or concentration on one side and insulated on the other is situated in an ‘infinite’ fluid medium. The buoyancy near the surface is directed either outward or inward normal to the active surface – equivalent to a heated plate facing upward or downward. The effect of insulated vertical and horizontal extensions to the plate are also examined.Finite-difference solutions are obtained for a heated strip in a two-dimensional domain for a Prandtl number of 0·7. Mass-transfer experiments are performed with square naphthalene plates in air. Both numerical and experimental results justify a 1/5-power law in the present range of Rayleigh number – i.e. Nusselt number or Sherwood number proportional to the Rayleigh number raised to the 1/5 power. The horizontal extensions cause a limited reduction in the transfer rate for the plate generating ‘outward buoyancy’, and a larger reduction with ‘inward buoyancy’. The vertical walls block the fluid flow directly, and thus greatly lower the transfer rate with either outward or inward buoyancy.

Period doubling and chaos in partial differential equations for thermosolutal convection

Abstract: Numerical experiments on two-dimensional thermosolutal convection reveal a transition from periodic oscillations to chaos through a sequence of period-doubling bifurcations. Within the chaotic region there are narrow periodic windows. This is the first example of period-doubling in solutions of partial differential equations. A truncated model indicates that this behavior is associated with heteroclinic explosions.

Similarity analysis and scaling criteria for LWRs under single-phase and two-phase natural circulation

Abstract: Scaling criteria for a natural circulation loop under single phase and two-phase flow conditions have been derived. For a single phase case the continuity, integral momentum, and energy equations in one-dimensional area average forms have been used. From this, the geometrical similarity groups, friction number, Richardson number, characteristic time constant ratio, Biot number, and heat source number are obtained. The Biot number involves the heat transfer coefficient which may cause some difficulties in simulating the turbulent flow regime. For a two-phase flow case, the similarity groups obtained from a perturbation analysis based on the one-dimensional drift-flux model have been used. The physical significance of the phase change number, subcooling number, drift-flux number, friction number are discussed and conditions imposed by these groups are evaluated. In the two-phase flow case, the critical heat flux is one of the most important transients which should be simulated in a scale model. The above results are applied to the LOFT facility in case of a natural circulation simulation. Some preliminary conclusions on the feasibility of the facility have been obtained.

Estimation of formation temperature from borehole measurements

Abstract: Summary. A new numerical method is described for modelling the thermal disturbance around a borehole and a comparison is made with the commonly used line source model. The numerical model generally gives an estimate of the equilibrium formation temperature which is up to about 20 per cent higher than the ‘Horner plot’ method. The relaxation of the borehole temperature is sensitive to the contrast between the thermal properties of the drilling fluid and of the surrounding rock as well as to the disturbance time. The importance of vertical temperature gradients and fluid motion (both free convection in the borehole and flow in the formation) is also examined. It is found that vertical temperature gradients are unlikely to be important provided temperatures are measured more than 10 borehole radii above the bottom. Convective heat transfer can be important under some drilling conditions.

Free Convection in a Vertical Annulus With Constant Heat Flux on the Inner Wall

Abstract: Heat transfer measurements are presented for free convection in a vertical annulus wherein the inner cylinder is at constant surface heat flux and the outer cylinder is at constant temperatuare. Overall heat transfer data re corrected for thermal radiation in the annulus. Rayleigh numbers span the conduction, transition and boundary layer regimes of flow, and average heat transfer coefficients are obtained with air and helium as the working fluids. The range of Rayleigh number is 10/sup 3/