Prandtl Number Liquid Research Articles

Experimental and Numerical Studies of Heat Transfer From a Liquid Bath due to an Impinging Gas Jet

There have been extensive heat transfer studies of impinging gas jets on solid surfaces, but few on impinging gas jets on a liquid bath. In this paper, air-jet-induced transport in a heated liquid bath is considered. Two different liquids having widely different Prandtl numbers (silicone oil and a molten metal alloy, Amalloy-203®) were used as bath liquids. Both numerical calculations and experimental measurements were carried out to characterize the jet-induced flow and heat transfer in the liquid bath. The numerical model developed considers the interaction of the jet flow and the liquid bath circulation. The mixing and thermal behavior of the heated bath were determined as functions of the air-jet characteristics (inlet temperature, Reynolds number) and the bath liquid properties (liquid Prandtl number and a “bath Grashof number”).

Experiments on the oscillatory convection of low Prandtl number liquid in Czochralski crystal growth under an axial magnetic field

Experimental results are presented on the oscillatory convection of mercury in a Czochralski configuration under an imposed axial magnetic field. A thermal wave propagating in an azimuthal direction under the axial magnetic field of moderate strengths is generated which proves the existence of azimuthal swirl flow in the oscillatory natural convection. In the presence of rotating flow by a Crystal-model disk rotation, axial magnetic field can also generate a long-period thermal wave and can amplify the temperature fluctuation depending on the magnitude of the relevant flow similarity parameters. A flow regime diagram is presented for the amplification and damping of the temperature fluctuation under an axial magnetic field in order to provide a data base for finding optimum growing conditions in a Czochralski process using axial magnetic field.

Analysis of laminar mixed-convection condensation on isothermal plates using the full boundary-layer equations: mixtures of a vapor and a lighter gas

Laminar film condensation from mixtures of a vapor and a lighter noncondensable gas flowing downward along inclined isothermal plates is investigated numerically using the full boundary-layer equations for the liquid film and the mixture. The adverse net body force due to high concentration of the lighter gas near the liquid–mixture interface gives rise to the possibility of boundary-layer separation. A numerical solution was developed based on a finite-control-volume method and it was marched along the plate up to the separation location. Results were obtained for three vapor–gas mixtures covering a wide range of liquid Prandtl numbers, high gas concentration and high liquid subcooling. Comparisons with previous models (which included various simplifying assumptions) showed that agreement is possible only for conditions of low gas concentration and liquid subcooling. Results of the separation distance exhibited interesting trends, which are discussed and explained. It is also demonstrated that lighter gases can have a more inhibiting effect on heat transfer than heavier gases.

A two-phase boundary-layer model for laminar mixed-convection condensation with a noncondensable gas on inclined plates

A finite-volume-based numerical model for mixed-convection laminar film condensation from a flowing mixture of a vapor and a heavier noncondensable gas on inclined isothermal flat plates is presented. The full boundary layer equations for the liquid film and the vapor-gas mixtures (including liquid inertia and energy convection terms) are solved implicitly with appropriate liquid-mixture interface conditions. Results were obtained for three mixtures, covering wide ranges of liquid Prandtl number and free-stream gas concentration in the forced-convection, mixed-convection and free-convection flow regimes. The effects of liquid inertia were found to be significant only for low-Prandtl-number fluids and lower gas concentrations. The effects of liquid energy convection were found to be significant only for high-Prandtl-number fluids and to be most significant for mixed-convection condensation.

Local convective heat transfer from a vertical flat surface to oblique submerged impinging jets of large Prandtl number liquid

An experimental study has been carried out to investigate the effect of the jet inclination on convective heat transfer from vertical heaters to circular submerged liquid jets. Local heat transfer measurements were made with obliquely impinging circular jets of transformer oil issued from both pipe-type and orifice-type nozzles in the range of jet Reynolds number from 162 to 958, corresponding to the jet velocity from 1.73 to 19.1 m/s. Variations both of the location and the magnitude of maximum heat transfer rates were determined and correlated in the range of jet inclination angles from 90° to 45°. Profiles of local heat transfer coefficients were obtained both along the x- and y- axes. A correlation was presented to predict the radial distribution of local Nusselt number in the x-axis. Comparison was made of the present results with those from available literature related to oblique circular liquid and air jets.

Effect of Liquid Subcooling on Film Boiling Heat Transfer from Finite-Size Horizontal Surfaces Facing Downward.

The effect of liquid subcooling on the convective film boiling heat transfer from a finite-size horizontal downward-facing surface was investigated both theoretically and experimentally. The approximate solution with some simplified assumptions was obtained by solving the two-phase boundary layer equations including the energy equation for the liquid boundary layer. The average Nusselt number, Nuco, derived from the solution may be expressed in a simple form with the parameters of Grashof number, density ratio, (density-viscosity) ratio, liquid Prandtl number, dimensionless degree of wall superheating and dimensionless degree of liquid subcooling. The theoretical results were compared in terms of a ratio of the average Nusselt number for the case of subcooled liquid to that for the case of the saturated liquid, Nuco/Nuco, sat, with the experimental data obtained by Nishio et al. under the steady-state condition and those obtained by the present authors using a quenching methed. For the case of subcooled liquids, a correlation equation of heat transfer was proposed to effectively correlate the experimental data obtained under both quenching and steady-state conditions within ±15 percent.

Experiments on the oscillatory convection of low Prandtl number liquid in Czochralski configuration for crystal growth with cusp magnetic field

This paper presents results of experiments on the oscillatory convection of mercury in a Czochralski configuration with cusp magnetic field. Temperature fluctuation measurements are carried out to determine the critical Rayleigh number for the onset of time dependent natural convection. The effects of a cusp magnetic field on the supercritical natural convection coupled with rotation of crystal disk are investigated. In the presence of a rotating flow it is found that a cusp magnetic field can induce a new long wave instability and can amplify the temperature fluctuation depending on the magnitude of the relevant flow similarity parameters and the melt aspect ratios. A flow regime diagram for the amplification and damping of the temperature fluctuations is presented to provide an experimental data base for finding optimum growth conditions in the cusp magnetic field Czochralski process.

Maximum Heat Transfer to Metallic-Liquid Flows from a Cluster of Vertical, Parallel-Plate Channels Heated Symmetrically

The problem of optimizing a cluster of isothermal or isoflux parallel-plate channels where the coolant is a metallic liquid is addressed. The pressure difference is fixed, and laminar forced convection is caused by the simultaneous development of velocity and temperature from free-stream conditions of the liquid. The Fanning friction factor is invariant with the fluid. However, local and streamwise-mean Nusselt number distributions for each heating condition are carefully computed exploiting the physical analogy between transient conduction in a flat plate and steady temperature development inside a parallel-plate channel under the premise of slug flow. The qualitative influence of diminute Prandtl number liquids (Pr = 0.01 and 0.005) is reported in terms of the optimal heat transfer and the optimal plate-to-plate spacing for the two heating conditions employed.

Numerical study of recovery effect and impingement heat transfer with submerged circular jets of large Prandtl number liquid

A numerical study was conducted to characterize the thermal behavior of laminar circular liquid jets. The main goal of this work was to clarify the significant recovery effect of large Prandtl number liquid jets reported by the present authors. Radial distribution of local recovery factor was studied in numerical detail. The effects of many factors were investigated including Reynolds number, Prandtl number, nozzle-to-plate spacing, jet velocity, nozzle diameter and velocity profile at nozzle exit. Very large recovery factors over 20 were obtained with high Prandtl number fluid jets at medium velocity. The results exhibited good agreement with the experimental data by the present authors, verifying the great significance of recovery effect with large Prandtl number liquid jets.

Local characteristics of impingement heat transfer with oblique round free-surface jets of large Prandtl number liquid

Abstract An experimental study was performed to investigate the local convective heat transfer from a vertical heated surface to an obliquely impinging circular free-surface jet of transformer oil. The effect of jet inclination was examined in the range of Reynolds number between 235 and 1745 with jet angle from 90 to 45 deg. Maximum heat transfer coefficient was found to decrease with the increasing of jet inclination, while its location shifted to the upstream side. Correlations were developed to predict the variations of the magnitude and the location of the peak heat transfer. Profiles of local Nusselt number were measured both in x and y-axes. The profiles along x-axis displayed an increasing asymmetry with increasing jet inclination. An empirical correlation was presented for predicting the x-axis profiles. With y-axis profiles, a symmetry appeared inside the stagnation zone, but a gravity-induced asymmetry was observed outside that zone.

Experimental study of thermocapillary convection on a liquid bridge consisting of fluid with low Prandtl number in a floating half-zone

A device of mercury liquid bridge of floating half-zone is designed to experimentally explore thermocapillary convection and its instability of a low Prandtl number liquid. Noncontacted diagnostic techniques were developed to monitor surface flow and surface deformation. The surface flow and the influence of a growing surface film (or skin) on the flow were observed. It is shown that the film is a key factor in changing the behavior associated with the thermocapillary convection. The experiment indicates that the critical Marangoni number should be much higher than that expected by the numerical simulation. The condition and process of surface film growth are discussed. The surface oscillation of the mercury bridge wrapped with ''dirt-film'' was observed, and the characteristics and the frequency associated with this oscillation are given.

Experiment on the thermocapillary convection of a mercury liquid bridge in a floating half zone

A liquid bridge of a floating half zone consisting of liquid mercury sealed in a glass tube with nitrogen atmosphere was used for the experiment of thermocapillary convection with a low Prandtl number liquid. A non-contacted diagnostic method was developed to monitor the surface flow and the surface oscillation. A growing surface film (or skin) is a crucial source to suppress thermocapillary convection, and is discussed in this paper. For the case of a mercury liquid bridge, the critical Marangoni number was obtained as 900, and the oscillatory frequency was around 5 Hz.

Thermocapillary flow in drops under low gravity analysed by the use of liquid crystals

Thermocapillary flow within large sized drops of diameters up to 15 mm was studied experimentally during KC-135 parabolic flights. For the simultaneous observation of the flow and the temperature fields inside the drops, visualisation by means of liquid crystal tracers was applied. Due to the curved surfaces of the drops, a special evaluation method has to be taken into account. The experimental set up and the test procedure as well as a qualitative description of the observed flow behaviour in high Prandtl number liquids are described.

Melting of Metals Driven by Natural Convection in the Melt: Influence of Prandtl and Rayleigh Numbers

The analysis of the melting process of a pure material from an isothermal vertical wall has motivated a significant number of experimental and numerical studies in the last ten years. When the only external field is gravity and if no capillary or solutal effects have to be taken into account, the melting process is controlled by thermally induced natural convection in the liquid phase. Most of the available experimental and numerical results have been obtained for the melting of phase-change materials (PCMs) with a high Prandtl number liquid phase. Detailed experimental results concerning melting of PCMs with a low Prandtl number (metals) have appeared only recently and comparisons with numerical solutions show qualitative agreement, but the influence of the governing parameters on the kinetics of the melting process has not been clearly analyzed. The purpose of this paper is to provide results on the heat transfer characteristics of the system over a wide range of Rayleigh and Prandtl numbers in the low Prandtl domain.

Low Prandtl number convection in a rectangular cavity with longitudinal thermal gradient and transverse [formula omitted

MATERIALS processing in space, such as crystal growth, may be sometimes disturbed by residual accelerations, or g-jitters, which act on the space carrier: atmospheric drag, gravity gradient effect, vibrations, crew activities, etc. Because of the presence of thermal gradients (and thus of density gradients) in the liquid phase of the experiment these residual accclerations may give rise to convective motions ; in turn, these convective flows may act on the solute field and lead to heterogeneities of dopant in the grown crystal. Thus it is important to be able to predict the possible influence of gjitters on solidification experiments, and to forecast whether or not they may lead to a lower quality of space-grown crystals. With this aim, this note will be devoted to g-jitter convection in an ideal crystal growth configuration. A second paper (to be published) will be devoted to the influence of ,qjitter convection on the distribution of solute (or dopant) in the liquid phase. Here we shall assume that the liquid alloy is dilute enough to enable a separate computation of velocity and solute fields (no solutal convection). The crystal growth experiment is modelled by a hidimensional, rectangular cavity (Fig. I), with end walls held at temperatures T,,-AT/2 and T,+AT/2, and totally filled with a Newtonian, low Prandtl number liquid at mean temperature To ; side walls are adiabatic and all surfaces are rigid no-slip boundaries. We shall study convective flows induced by gjitters transverse to the thermal gradient ; we chose this orientation of the g-jitters because it is the most ‘critical’, i.e. there is no threshold for the onset of convection as there would be in a ‘Rayleigh-BCnard’ configuration. The pioneering work

Surface temperature oscillations of a floating zone resulting from oscillatory thermocapillary convection

Abstract The surface temperature of stationary molten zones in Mo and Nb rods was measured as a function of the heating power. At well defined stability limits, single-mode temperature oscillations were detected. The frequency agreed well with that determined from periodic impurity striations characteristic for crucibleless electron zone melting of Mo at a critical zone length. The results are regarded as an experimental verification of a transition of stationary Marangoni convection to an oscillatory state for low Prandtl number liquids.

Laminar free-convection from spherical segments

An experimental investigation of laminar free-convection heat transfer from heated, isothermal, spherical segments to a high Prandtl number liquid is reported. The effect of an extended insulator base on heat transfer is estimated. The experimentally obtained results are compared with theoretically predicted data.

Transient laminar-film condensation on a vertical plate

This work addresses the problem of transient, laminar-film condensation onto a vertical surface. It examines the behavior of the liquid film in response to changes in the temperature drop across the film or in the interfacial shear stress. Numerical solutions of the governing equations are compared with a simpler quasisteady analysis. The quasisteady analysis is adequate in many cases (e.g., atmospheric water). However, as the Jakob number or Jakob divided by Prandtl number approaches unity, the full equations and the quasisteady analysis yield significantly different predictions for heat transfer and mass flux during the transient. This reflects the increasing importance of accounting for the development of the temperature and velocity profiles. Nomenclature Cp = liquid specific heat D2 = finite-difference form of the Laplacian operator g = gravitational acceleration hfg = latent heat of vaporization Ja = Jakob number, Cp AT+ /hfg k = liquid thermal conductivity L = plate length Pr = liquid Prandtl number, v/a q = interfacial heat flux T = temperature t = time u = streamwise velocity v = cross-stream velocity x = streamwise coordinate y = cross-stream coordinate a = liquid thermal diffusivity T = liquid mass flux per unit width of plate d = film thickness d yy = film thickness at x + = L using Nusselt theory A = difference or increment fj. = liquid dynamic viscosity v = liquid kinematic viscosity p = liquid density i = interfacial shear stress

An experimental study of flash evaporation from liquid pools

The objective of this study is, based on experiments, to improve the understanding of flash evaporation from pools, and to develop empirical correlations of the total quantity of vapor released and the rate of vapor generation (both in non-dimensional form) as a function of the primary nondimensional parameters which govern the process: the Jakob number (Ja p), Prandtl number (Pr), a dimensionless hydrostatic head (Δp/H), and the salt concentration (C). The work was done in the range of parameters characteristic to desalination plants and to open-cycle ocean-thermal energy conversion. Experiments were performed with fresh water and with saline water (3.5% NaCl concentration), for initial temperatures from 25°C – 80°C, flash-down temperature differences from 0.5°C – 10°C, and pool depths of 6.5″ (165 mm), 12″ (305 mm) and 18″ (457 mm). The prediction of flashed mass as a function of the nondimensional parameters is accurate to within 7.5%. A new time scale τ = (σ/Δp) 2/α 1, (where σ = surface tension, α 1 = thermal diffusivity of the liquid, and Δp = pressure difference between the liquid and the vapor space) was employed. The expressions for the rate of flashed steam using this time scale show a scatter of ± 68%. The asymptotic value of the flashed mass increases with Jakob number, increases slightly with pool depth, and decreases with increasing liquid Prandtl number. The comparisons show very good agreement with the experimental values, but underpredict the data obtained from other experiments.

Thermal boundary layer on a continuous moving plate with freezing

The growth of a solidified layer or on the surface of a chilled continuous plate traveling steadily through a bath of warm liquid is investigated analytically. The behavior of the thermal boundary layer in the liquid flowfield that is induced by the motion of the plate is modeled along with the process of heat conduction in the solid phase to determine the location of the freezing front. Using the method of similarity, axial variations of the freeze-coat thickness and the coefficient of local convective heat transfer from the liquid to the solid phase are obtained as functions of various controlling parameters of the system. It is found that, while the shape of the freeze coat depends strongly on the local convective heat flux, the flow is, in turn, heavily influenced by the variation of the solid /liquid interface location. Because of this mutual interaction between the phase change process and the flow, the local convective heat-transfer coefficient at the freezing front is considerably larger than the corresponding value for the case of forced convection over a continuous moving plate without freezing. The effect of flow/freezing interaction is found to be quite pronounced, especially when the liquid Prandtl number is large and the freeze coat grows rapidly in the axial direction.