Showing papers on "Nusselt number published in 1983"

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.

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.

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.

Numerical solutions for laminar flow and heat transfer in a periodically converging-diverging tube, with experimental confirmation

Abstract: A solution methodology has been employed that enables the fully developed regime in a duct of periodically varying cross section to be determined without dealing with the entrance region. ...

Forced Convection Heat Transfer From on Elliptic Cylinder of Axis Ratio 1 : 2

Abstract: An experimental investigation has been made to clarify the heat transfer characteristics of an elliptic cylinder of axis ratio 1 : 2. The testing fluid was air and the Reynolds number ranged from about 5000 to 90000. The angle of attack α was varied from 0°to 90°. The local heat transfer behavior is clarified and it is quite different from that of a circular cylinder. In the region of α>40°, the heat transfer rate from the upstream surface, on which a laminar boundary layer develops, becomes lower than that from the downstream surface in the separated flow region. The mean heat transfer coefficient Num depends upon the angle of attack along with the Reynolds number. It is found that Num is the highest for α=75° to 90° and is the lowest for α=30° over the whole Reynolds number range studied. The mean heat transfer rate from the elliptic cylinder investigated in the present work is higher than that from the circular cylinder at all the angles of attack over the Reynolds number range studied.

Steady three-dimensional convection at high Prandtl numbers

Abstract: Three-dimensional solutions are computed describing convection in a layer of a Boussinesq fluid of infinite Prandtl number. Rigid boundaries of constant temperature are assumed. As many as four physically different solutions are found for a given rectangular horizontal periodicity interval. These are two solutions describing bimodal convection, and two ‘square-pattern’ solutions which correspond to two orthogonally superimposed convection rolls of nearly equal amplitude. The Galerkin method used in obtaining the steady solutions can also be employed for the investigation of their stability. The stability of the bimodal solutions agrees with the experimental determination of the stability region by Whithead & Chan (1976). The square-pattern solution is unstable in the investigated parameter range, even though it exhibits the highest Nusselt number.

Analysis of viscous dissipation effect on thermal entrance heat transfer in laminar pipe flows with convective boundary conditions

Abstract: Consideration is given to the influence of viscous dissipation on the thermal entrance region laminar pipe flow heat transfer with convective boundary condition. The Eigenfunction series expansion technique is employed to solve the governing energy equation. The results for axial distributions of dimensionless bulk and wall temperatures, local Nusselt number as well as modified local Nusselt number are presented graphically forNu 0 =0.1, 2, and 100. The complicated variations of conventional local Nusselt number is due to the inappropriate definition of conventional heat transfer coefficient in this problem. A modified local heat transfer coefficient, based on the difference of bulk fluid temperature and wall temperature, is introduced. Its value can clearly indicate the extent and the direction of heat exchange between the fluid in the pipe and the ambient. The effects of outside Nusselt number are also investigated. Significant viscous dissipation effects have been observed for large Br.

On the intermittency and crystallization mechanisms of sub-seafloor magma chambers

Abstract: Summary. The conventional view of a magma chamber being an essentially permanent feature of a fast-spreading ridge is not compatible with the physics of either oceanic crustal structure or internal magma convection. Cumulates form a large volumetric fraction of many ophiolites and are deposited at the bottom of magma chambers, so they are not available as an insulating layer between magma and seawater. Extrusives and dykes are cracked and highly permeable to hydrothermal convection, so they also do not offer much thermal resistance to the cooling of magma. Only the layer of ‘plated’ or ‘isotropic’ gabbro, often observed between cumulates and dykes, is limited to conductive heat transport; a 0.5 km thickness implies a chamber lifetime of no more than l0kyr km-’ of magma. The intermittency of the chamber on such a short time-scale requires that the plates move apart to make room much more rapidly than they could at the steady spreading rate. Fluctuating magma pressure can achieve such intermittent movement by stress-change diffusion through an elastic lithosphere overlying a viscous asthenophere. However, the space needed implies stress diffusion almost all around the Earth, and this, in turn, requires that the intermittent spreading be substantially synchronized all along a major segment of ridge. The pressure-dependent slopes of equilibrium temperatures between crystal phases and liquid silicate magmas exceed the adiabatic gradients of the magmas themselves by about 1°C kb-’. If this temperature difference is considered the convective drive, a 3 km high chamber reaches a Rayleigh number of 3 x and a Nusselt number of about 8000. The plated layer should grow until the heat loss rate decreases to that supplied by cumulatedepositing convection, implying a plated layer about 0.5 km thick, in agreement with observations. The boundary-layer/turbulent core structure of convection at high Rayleigh and Reynolds numbers is consistent with the formation of banded cumulates when a new type of fluid circulation is taken into account. If a suspended crystal phase is present in the bulk fluid, a ‘slow-convection’ mode is possible, where flow velocities are restricted by the equilibration rate between crystals and fluid, and the temperature profile is determined by the thermodynamics of crystal-fluid equilibria.

An Experimental Study of Free Corrective Heat Transfer in a Parallelogrammic Enclosure

Abstract: Experimental measurements are presented for free convective heat transfer across a parallelogrammic enclosure with the various tilt angles of parallel upper and lower walls insulated. The experiments covered a range of Rayleigh numbers between 3.4 × 104 and 8.6 × 107 , and Prandtl numbers between 0.70 and 480. Those also covered the tilt angles of the parallel insulated walls with respect to the horizontal, φ, of 0, ±25, ±45, ±60, and ±70 deg under an aspect ratio of H/W = 1.44. The fluids used were air, transformer oil, and water. It was found that the heat transfer coefficients for φ = −70 deg were decreased to be about 1/18 times those for φ = 0 deg. Experimental results are given as plots of the Nusselt number versus the Rayleigh number. A correlation equation is given for the Nusselt number, Nu, as a function of φ, Pr, and Ra.

Laminar Natural Convection in an Inclined Rectangular Box With the Lower Surface Half-Heated and Half-Insulated

Abstract: The pattern of circulation and the rate of heat transfer were determined experimentally and also by three-dimensional, finite-difference calculations for an inclined 2 × 1 × 1 rectangular enclosure with a 1 × 1 segment of the lower 2 × 1 surface at a uniform temperature, the other 1 × 1 segment and four side walls insulated, and the upper surface at a lower uniform temperature. As contrasted with an enclosure heated and cooled on the horizontal surfaces, a fluid motion occurs and the rate of heat transfer exceeds that for pure conduction for all temperature differences and orientations. The effects of elevation of the heated and insulated segments were investigated, as well as of inclination about the longer dimension. Despite differences in the Prandtl and Rayleigh numbers, the observed and predicted patterns of circulation are in good agreement, and the measured and predicted rates of heat are in qualitative agreement.

Local Heat Transfer Coefficients for Condensation in Stratified Countercurrent Steam-Water Flows

Abstract: A study of steam condensation in countercurrent stratified flow of steam and subcooled water has been carried out in a rectangular channel inclined 33 deg to the horizontal. The variables in this experiment were the inlet water and steam flow rates, and the inlet water temperature. Condensation heat transfer coefficients were determined as functions of local steam and water flow rates, and the degree of subcooling. Correlations are given for the local Nusselt number for the smooth and for the rough interface regimes, and also for the dimensionless wave amplitude. A turbulence-centered model is also developed. It is shown that better agreement with the data can be obtained if the characteristic scales in the turbulent Nusselt number and Reynolds numbers are related to measured interfacial parameters rather than the bulk flow parameters. The important effect of interfacial shear, missing in previous eddy-transport models, is thus implicitly included.

Heat Transfer Characteristics for Jet Array Impingement With Initial Crossflow

Abstract: Two-dimensional arrays of circular air jets impinging on a heat transfer surface parallel to the jet orifice plate are considered. The jet flow, after impingement, is constrained to exit in a single direction along the channel formed by the jet orifice plate and the heat transfer surface. In addition to the crossflow which originates from the jets following impingement, an initial crossflow is present which approaches the array through an upstream extension of the channel. The temperature of the initial crossflow air may differ from the jet air temperature. The configurations considered are intended to model the impingement cooled midchord region of gas turbine airfoils in cases where an initial crossflow is also present. Nusselt numbers and dimensionless adiabatic wall temperatures resolved to one streamwise jet hole spacing were experimentally determined for ratios of the initial crossflow rate to the total jet flow rate ranging from zero to unity. These are presented and discussed relative to the flow and geometric parameters.

Viscous thermocapillary convection at high Marangoni number

Abstract: A liquid, contained in a quarter plane, undergoes steady motion due to thermocapillary forcing on its upper boundary, a free surface separating the liquid from a passive gas. The rigid vertical sidewall has a strip whose temperature is elevated compared with the liquid at infinity. A boudnary-layer analysis is performed that is valid for large Marangoni numbers M and Prandtl numbers P. It is found that the Nusselt number N for the horizontal heat transport satisfies N proportional to min (M to the 1 2/7/power, M to the 1 1/5/power, M to the 1 1/10/power) Generalizations are discussed.

Natural Convection Heat Transfer of Water Within a Horizontal Cylindrical Annulus With Density Inversion Effects

Abstract: The effect of density inversion on steady natural convection heat transfer of cold water, between two horizontal concentric cylinders of gap width, L, is studied numerically. Water near its freezing point is characterized by a density maximum at 4°C. Numerical solutions are obtained for cylinders with nonlinear Rayleigh numbers RA ranging from 2 × 103 to 7.6 × 104 , a radius ratio 1.75 ≤ ra ≤ 2.6 and an inversion parameter γ, relating the temperature for maximum density with the cavity wall temperatures, between −2 and 2. The results obtained are presented graphically in the form of streamline and isotherm contour plots. The heat transfer characteristics, velocity profiles, and local and overall Nusselt numbers are studied. The results of the present study were found qualitatively valid when compared with an experimental investigation carried out in the past.

Heat Transfer Coefficient in Ducts With Constant Wall Temperature

Abstract: An analytical method for the numerical calculation of the heat transfer coefficient in arbitrarily shaped ducts with constant wall temperature at the boundary is presented The flow is considered to be laminar and fully developed, both thermally and hydrodynamically The method presented herein makes use of Galerkin-type functions for computation of the Nusselt number This method is applied to circular pipes and ducts with rectangular, isosceles triangular, and right triangular cross sections A three-term or even a two-term solution yields accurate solutions for circular ducts The situation is similar for right triangular ducts with two equal sides However, for narrower ducts, a larger number of terms must be used