Showing papers on "Nusselt number published in 1989"

Scaling of hard thermal turbulence in Rayleigh-Bénard convection

Abstract: An experimental study of Rayleigh-Benard convection in helium gas at roughly 5 K is performed in a cell with aspect ratio 1. Data are analysed in a ‘hard turbulence’ region (4 × 107 < Ra < 6 × 1012) in which the Prandtl number remains between 0.65 and 1.5. The main observation is a simple scaling behaviour over this entire range of Ra. However the results are not the same as in previous theories. For example, a classical result gives the dimensionless heat flux, Nu, proportional to . A new scaling theory is described. This new approach suggests scaling indices very close to the observed ones. The new approach is based upon the assumption that the boundary layer remains in existence even though its Rayleigh number is considerably greater than unity and is, in fact, diverging. A stability analysis of the boundary layer is performed which indicates that the boundary layer may be stabilized by the interaction of buoyancy driven effects and a fluctuating wind.

A benchmark comparison for mantle convection codes

Abstract: Summary We have carried out a comparison study for a set of benchmark problems which are relevant for convection in the Earth's mantle The cases comprise steady isoviscous convection, variable viscosity convection and time-dependent convection with internal heating We compare Nusselt numbers, velocity, temperature, heat-flow, topography and geoid data Among the applied codes are finite-difference, finite-element and spectral methods In a synthesis we give best estimates of the ‘true’ solutions and ranges of uncertainty We recommend these data for the validation of convection codes in the future

Forced Convection in a Channel Filled With a Porous Medium: An Exact Solution

Abstract: In this paper fully developed forced convection in a porous channel bounded by parallel plates is considered based on the general flow model. Exact solutions are obtained and presented for both the velocity and the temperature fields. From these results the Nusselt number can be expressed in terms of the Darcy number and the inertia parameter. Finally, comparisons are made with the limiting case of no inertia and/or boundary effects. These results provide an in-depth insight into the underlying relationships between all of the pertinent variables. Furthermore, they can be used as strong candidates for bench marking of many numerical schemes.

A Detailed Examination of Gas and Liquid Phase Transient Processes in Convective Droplet Evaporation

Abstract: A finite volume numerical technique has been used to model the evaporation of an n-heptane droplet with an initial Reynolds number of 100 in air at 800 K, 1 atm. The effects of variable thermophysical properties, liquid phase motion and heating, and transient variations in droplet size and velocity are included in the analysis. With appropriate corrections for the effects of variable properties and liquid phase heating, quasi-steady correlations are shown to predict accurately the transient histories of the drag coefficient and Nusselt and Sherwood numbers. For the case investigated here, the transient effects of importance were the variation in droplet velocity, the decline in the liquid phase velocities, and the rise in the droplet surface and volume average temperatures. In spite of the transient rise in the droplet temperature, the nature of the liquid phase heating, as characterized by the liquid Nusselt number, was found to remain constant during most of the droplet lifetime.

Natural Convection Along a Vertical Wavy Surface With Uniform Heat Flux

Abstract: Laminar free convection along a semi-infinite vertical wavy surface has been studied by Yao (1983) for the case of uniform surface temperature. This is a model problem for the investigation of heat transfer from roughened surfaces in order to understand heat transfer enhancement. In many applications of practical importance, however, the surface temperature is nonuniform. In this note, the case of uniform surface heat flux rate, which is often approximated in practical applications and is easier to measure in a laboratory, has been investigated. Numerical results have been obtained for a sinusoidal wavy surface. The results show that the Nusselt number varies periodically along the wavy surface. The wavelength of the Nusselt number variation is half of that of the wavy surface, while the amplitude gradually decreases downstream where the boundary layer grows thick. It is hoped that experimental results will become available in the near future to verify the results of this investigation.

High Rayleigh Number Laminar Natural Convection in an Asymmetrically Heated Vertical Channel

Abstract: Experiments have been performed to determine local heat transfer data for the natural convective flow of air between vertical parallel plates heated asymmetrically. A uniform heat flux was imposed along one heated wall, with the opposing wall of the channel being thermally insulated. Local temperature data along both walls were collected for a wide range of heating rates and channel wall spacings corresponding to the high modified Rayleigh number natural convection regime. Laminar flow prevailed in all experiments. Correlations are presented for the local Nusselt number as a function of local Grashof number along the channel. The dependence of both average Nusselt number and the maximum heated wall temperature on the modified Rayleigh number is also explored. Results are compared to previous analytical and experimental work with good agreement.

Transient Liquid Crystal Measurement of Local Heat Transfer on a Rotating Disk With Jet Impingement

Abstract: An experimental technique has been developed for measurement of local convection heat transfer characteristics on rotating surfaces, utilizing thin liquid crystal surface coatings in a thermal transient test procedure. The encapsulated liquid crystal coatings used are sprayed directly on the test surface and their response is observed and processed during the transient with automated computer vision and data acquisition system

Turbulent Heat Transfer and Friction in Pin Fin Channels With Lateral Flow Ejection

Abstract: Experiments were conducted to study the effects of lateral flow ejection on the overall heat transfer and pressure drops for turbulent flow through pin fin channels. The two test sections of the investigation were rectangular channels with staggered arrays of six and eight streamwise rows of pins, respectively. The pin length-to-diameter ratio was one and both the streamwise and spanwise pin spacings were 2.5 times the pin diameter. Heat transfer and friction data were obtained for various ejection exit geometries, for ejection ratios between 0 and 1, and for Reynolds numbers between 6,000 and 60,000. The results of the study show that, for any given ejection ratio, the overall Nusselt number increases with increasing Reynolds number. However, the overall Nusselt number is reduced by as much as 25% as the ejection ratio is increased from 0 to 1 over the range of Reynolds number studied. The Nu-Re-{epsilon} relationship, which is insensitive to varying the ejection exit geometry, can be correlated by the equation (Nu/Nu{sub 0}) = (Nu{sub 1}/Nu{sub 0}){sup {epsilon}}, where Nu{sub 0} = c{sub 0}Re{sup m} and Nu{sub 1} = c{sub 1}Re{sup n} are the overall Nusselt numbers in the 0 and 100% lateral flow ejection cases, respectively. Themore » results also show that the overall friction factor is independent of the flow Reynolds number over the range of Reynolds number studied. However, the friction factor is strongly dependent on the ejection ratio as well as the geometries of the straight flow exit and lateral ejection flow exit.« less

k-ε Predictions of Heat Transfer in Turbulent Recirculating Flows Using an Improved Wall Treatment

Abstract: Different wall treatments, proposed in conjunction with the k-e turbulence model to predict heat or mass transfer rates, are critically reviewed. Published comparisons with experimental data for recirculating flows show that, in most cases, Nusselt or Sherwood numbers are not well predicted in the reattachment and redevelopment regions by methods based on conventional wall functions. The use of low-Reynolds-number models leads to even more unreliable results. A new treatment is proposed that formally retains classic wall functions and scaling based on the near-wall turbulent kinetic energy, but allows the nondimensional thickness of the viscous sublayer to vary as a function of the local turbulence intensity. The rationale for this approach, and its physical meaning, are discussed in the context of recent near-wall turbulence data. Using the k-e computer code FLOW3D, results are compared with those from a standard treatment, and with experimental data, for different geometries including single an...

Heat Transfer Characteristics in Two-Phase Closed Conventional and Concentric Annular Thermosyphons

Abstract: The heat transfer in the condenser sections of conventional and annular two-phase closed thermosyphon tubes has been studied experimentally and analytically. In addition, the results of a series of experiments on the flooding phenomena of the same thermosyphons are reported. Freon 113 and acetone were used as working fluids. An improved correlation was developed to predict the performance limits of conventional thermosyphons using the present and previously existing experimental data for flooding with different working fluids. The prediction of the theoretical Nusselt number for the situations associated with measured heat transfer coefficients in the condenser section indicated that the effect of interfacial shear on the film flow is small. The increase of the experimental reflux condensation heat transfer coefficients over theoretical predictions is attributed to waves at the vapor-liquid interface.

Measurements of slip at the wall during flow of high-density polyethylene through a rectangular conduit

Abstract: A hot-film probe has been used to measure slip of high-density polyethylene flowing through a conduit with a rectangular cross section. A transition from no slip to a stick-slip condition has been observed and associated with irregular extrudate shape. Appreciable extrudate roughness was initiated at the same flow rate as that at which the relationship between Nusselt number and Peclet number for heat transfer from the probe departed from the behavior expected for a no-slip condition at the conduit wall.

Modal exchange mechanisms in Lapwood convection

Abstract: Techniques of bifurcation theory are used to study the porous-medium analogue of the classical Rayleigh-Benard problem: Lapwood convection in a two-dimensional saturated porous cavity heated from below. Two particular aspects of the problem are focused upon: (i) the existence of multiple steady solutions and (ii) the influence of aspect ratio.Convection begins only when the applied temperature difference (say) exceeds a critical value defined by linear stability theory. The resulting convective flow pattern depends both on the magnitude of the temperature difference and on the aspect ratio of the cavity. A weakly nonlinear analysis reveals the roles played by so-called secondary bifurcations in determining the formation of further, anomalous patterns at fixed aspect ratio. In addition to giving rise to alternative stable flows for identical operating conditions, the secondary bifurcations are required for the modal exchanges which take place as the aspect ratio varies, a process which causes an abrupt change in preferred flow pattern at certain critical values of the aspect ratio.As a complement to and an extension of the weakly nonlinear analysis, numerical methods are used to determine the bifurcation processes and to elucidate the modal exchange mechanisms in both weakly and strongly convective flows. The effect of container size is studied by continuation methods to predict the variation of the critical Rayleigh number of the bifurcation points for aspect ratios in the range 0.5 to 2.0. In this way a stability map is obtained which shows the alternative patterns expected for particular operating conditions. The Nusselt number is computed and it is found that the alternative stable modes transfer significantly different amounts of heat through the medium.The study has provided new information on the existence and characteristics of, and interactions between, alternative steady modes of two-dimensional Lapwood convection. The results have important ramifications for the modelling and design of physical systems in which convective flow in a saturated porous medium is stimulated by an imposed unstable temperature gradient.

Time-dependent large aspect-ratio thermal convection in the earth's mantle

Abstract: Numerical simulations of two-dimensional time-dependent thermal convection in a Boussinesq, isoviscous, infinite Prandtl number fluid with isothermal, stress-free boundaries have been performed in large aspect-ratio configurations, in which the fluid is heated from below as well as internally. The value of the basal heated Rayleigh number ranged from 16000 to 800 000 and the Rayleigh number based on internal heat generation was varied from zero to 4 500 000. Large aspect-ratio cells are found to exist, however, they are time-dependent even at small values of the Rayleigh number. In the absence of internal heating, the onset of time-dependence occurs as a regular oscillation in the flow characteristics (Nusselt number, kinetic energy), and is accompanied by the presence of boundary layer instabilities (BLI) which exist within a large aspect-ratio circulation. At high values of the Rayleigh number the BLI are powerful features which leave the confines of the boundary layer and strongly perturb the ...

Heat/mass transfer from surface films to shear flows at arbitrary Peclet numbers

Abstract: An efficient numerical method is described for studying the combined conductive and convective transport from a surface film on a planar boundary to a fluid in simple shear flow. Such problems arise most commonly in the use of hot film anemometers, electrochemical shear probes, or in simple models of chemical reactions. The method is illustrated by calculating the total flux (Nusselt number) and variation of the flux along the surface for isothermal circular disks at arbitrary values of the Peclet number (dimensionless shear rate) and is compared with asymptotic results valid at high and low Peclet numbers. The theoretical low Peclet number results of Phillips [Q. J. Mech. Appl. Math. (in press)] lie within 2% of the numerical results for Peclet numbers as high as P=2. At high Peclet numbers, a theoretical estimate for the neglected flux from the edge regions is used, together with the numerical simulations, to propose a correction to the standard one‐term asymptotic expression. This approximate relationship remains within 7% of the numerical calculations for Peclet numbers as small as P=5. In addition, results for the total heat transfer as a function of Peclet number are presented for isolated elliptical disks at two orthogonal orientations with respect to the flow and an asymptotic expression for high Peclet numbers is presented for arbitrary disk orientations.