Showing papers on "Combined forced and 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.

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.

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.

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.

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.

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.

Axisymmetric convection in a rotating sphere. Part 1. Stress-free surface

Abstract: This paper examines large-scale nonlinear thermal convection in a rotating selfgravitating sphere of Boussinesq fluid containing a uniform distribution of heat sources. Conservative finite-difference forms of the equations of axisymmetric laminar motion are marched forward in time. The surface is assumed to be stress free and at constant temperature. Numerical solutions are obtained for Taylor numbers in the range 0 ≤ Λ ≤ 104 and Rayleigh numbers with \[ R_c \leqslant R\lesssim 10R_c. \] For high Prandtl number (P > 5) the solutions are steady and most of them resemble the solutions of the linear stability equations, though other steady solutions are also found. For P [lsim ] 1, the steady solutions have horizontal wavenumber l = 1 and nearly uniform angular momentum per unit mass, rather than nearly uniform angular velocity. This rotation law seems to be independent of many details of the model and may hold in the convective core of a rotating star.

A comprehensive correlating equation for forced convection from flat plates

Abstract: A correlating equation was developed which provides a continuous representation for all Pr and Re. Different constants are suggested for the local and mean Nusselt numbers and for uniform wall temperature and heating. These constants are based on the best available theoretical and experimental results.

Free convection and the burning of a horizontal fuel surface

Abstract: The free-convective flow induced when a semi-infinite horizontal fuel surface burns in a quiescent oxidizing atmosphere is considered. For high values of the Grashof number the dominant feature of the flow is a boundary layer close to the surface within which there is a flame or intense reaction zone. An outer flow or fire-wind is induced by entrainment into this boundary layer. A simple experiment supports this overall picture of the flow.

Laminar Natural Convection Boundary Layers on Near-Horizontal Plates

Abstract: The first order boundary-layer analysis for the laminar natural convection flow over a semi-infinite horizontal or near-horizontal heated plate has been extended to include variable properties effects. Detailed calculations are presented for air and water flows. It is shown further how these calculations can be extended to predict heat transfer rates on plates of rectangular planforms. Because of the lack of sufficiently detailed experimental data, a thorough comparison between the latter and the present calculations has not been possible. However, such comparisons as have been possible are encouraging and a significant improvement on previous theoretical predictions has been achieved. Although higher order corrections have not been discussed in detail, possible matching problems have been investigated briefly. Furthermore, it has been shown that stress work effects in the energy equation and the influence of pressure on density and temperature in the state relation are not only solely higher order effects but are of little significance at such orders.

Radiatively driven thermal convection bounded by an inversion—a laboratory simulation of stratus clouds

Abstract: The radiative loss from stratus clouds is simulated by the radiative heating of the lower part of a turbid warm layer of water overlying cold clear water. The color change of thymol blue indicator effects the turbidity change between layers and simulates changes in liquid water content between a cloud and the dry air above it. Heat absorption in the lowest level of the turbid layer produces unstable convection through this layer but with important differences from the more familiar cases of convective erosion by bottom surface heating or by convection between rigid surfaces. The experiments suggest that the velocity at which convectively driven entrainment lowers the inversion is scaled by Deardorff's (1970) convection velocity w* (proportional to the ⅓ power of the product of absorbed buoyancy flux times convection depth) and depends only weakly on inversion strength. The position of the turbidity interface in relation to the temperature inversion exerts a strong influence on entrainment, evidently through the effect of heat absorbed in this predominantly stably stratified region. A study is made of the possibility that the thickness of the absorbing region is determined by the vertical scale of convective penetration of the interface, and the results are applied to determine the rise rate of an inversion which caps typical stratus clouds. A realistic rate of about 1.5 cm/s is found.

Interaction between heat and mass transfer in simultaneous natural convection about an isothermal vertical flat plate

Abstract: In order to investigate how simultaneous heat and mass transfer by free convection interact, some numerical theoretical results are presented and discussed. The total flow rate appears to be an essential element in obtaining some insight into this interaction.

Transient Natural Convection of Water in a Horizontal Pipe With Constant Cooling Rate Through 4°C

Abstract: A theoretical analysis is carried out to study the influence of an anomalous density-temperature relationship of water on the transient natural convection in horizontal cylinders with wall temperature decreasing at a uniform rate. Numercial solutions are obtained for three cases involving different cooling rates, pipe diameters, and initial uniform water temperatures for temperature conditions between 0 and 7°C. The transient flow and temperature fields, and local and overall heat transfer rates are presented to study the inversion of flow patterns caused by the maximum density at 4°C. The numerical results are compared with the experimental measurements and predictions of a quasi-steady boundary-layer model reported by Gilpin [2], and generally a good agreement is observed. Some implications on the subsequent freezing process are pointed out.