Heat Transport Coefficients Research Articles

Simulation of Heat and Moisture Transfer in the Greenhouse Substrate due to a Heating System by Buried Pipes

The paper presents a mathematical model of the greenhouse substratum heating process, which occurs when tubes are positioned in the substratum. The model includes the processes of transpiration, evaporation and infiltration. The mass of water consumed by roots of cultivated vegetables was calculated as a transpiration model, treated as a source function and presented as a diffusion equation, which describes water flow in the substrate. The undoubted advantage of this approach is the ability to use diffusion and heat transfer theory to solve the problems posed. The processes in the substratum being studied were analysed by applying heat and mass transport coefficients calculated from the correlation equations widely used in chemical engineering. The tests demonstrated a high correlation between the predicted values (numerical calculations) and the measured values: coefficients of correlation r of 0.94 (for temperature) and 0.91 (for moisture content).

A continuum one-dimensional SOC model for thermal transport in tokamaks

Based on the now well-known and experimentally observed critical gradient length (LTe) in tokamaks, we present a continuum one-dimensional model for explaining self organized heat transport in tokamaks. The key parameters of this model include a hysteresis parameter, which ensures that the switching of the heat transport coefficient χ upwards and downwards takes place at two different values of R/LTe. Extensive numerical simulations of this model reproduce many features of present day tokamaks, such as sub-marginal temperature profiles, intermittent transport events, 1/f scaling of the frequency spectra, propagating fronts, etc. This model utilizes a minimal set of phenomenological parameters, which may be determined from experiments and/or simulations. Analytical and physical understanding of the observed features has also been attempted.

BXO mode-converted electron Bernstein emission diagnostic (invited)

Electron temperature profiles at densities above the electron cyclotron emission (ECE) cutoff are measured at the W7-AS stellarator by a novel diagnostic based on black body emission and Bernstein-extraordinary-ordinary mode conversion of electron Bernstein waves (EBWs). The radiation is collected along a special oblique line of sight by an antenna with gaussian optics. This was optimized for maximal conversion efficiency and minimal Doppler broadening by means of EBW ray tracing calculations in full stellarator geometry. The elliptical O-mode polarization detected along the oblique line of sight is changed into a linear polarization by a broadband quarter wave shifter, namely an elliptical waveguide. The signal is spectrum analyzed by an heterodyne radiometer and temperature profiles are derived from spectra by means of ray tracing. The diagnostic was applied to measurements of edge-localized modes to illustrate its advantages in terms of spatial and temporal resolution. Moreover, for the first time, the heat wave propagation method for the determination of local heat transport coefficients was extended beyond the ECE cutoff density by combining EBW emission measurements at the first harmonic (f=66–78 GHz) with modulated EBW heating at the second harmonic (140 GHz).

Heat transport and membrane distillation coefficients in direct contact membrane distillation

This work aims to provide detailed understanding of heat transport in direct contact membrane distillation (DCMD). The influence of mass transfer on heat transfer rates and on the heat transfer coefficient was identified, and the relative significance of each heat transfer mechanism was evaluated. The role of spacers in heat transfer improvement was analyzed. Alternative methods to evaluate the membrane thermal conductivity were also proposed. The heat transfer analysis of the experimental results showed that the effects of mass transfer on the heat transfer rates and on the film heat transfer coefficients were negligible. The heat transfer due to the vapor flow ( q v) in the membrane was equal to or greater than the heat conduction ( q c) for the membranes studied and increased with the feed temperature. When the feed temperature was lower than 323 K, the heat loss due to heat conduction across the membrane was the major contribution of the total heat transfer in the membrane. In addition, the temperature distributions in the membranes were closely linear. The membrane distillation (MD) coefficients for each membrane were constant over the flow rates and temperatures studied. The flow pattern in the spacer-filled channel was probably transition flow rather than turbulent flow. The alternative models for calculating the membrane thermal conductivity showed better agreement than the commonly used model.

Measurement of poloidal flow, radial electric field and E × B shearing rates at ASDEX Upgrade

The theoretical model of transport reduction by E × B shear decorrelation is tested experimentally for ASDEX Upgrade discharges. The radial force balance is used to determine the radial electric field from charge exchange recombination spectroscopy measurements. As the effective rate coefficient for photon emission of the charge exchange process depends on the collision energy, the alignment of the lines of sight with respect to the neutral beam gives rise to apparent velocities and temperatures. In addition, the gyro-motion of the observed species along with the finite lifetime of the observed excited state leads to lineshifts in spectra measured in the poloidal direction. Both effects require corrections, which will be discussed. The corrections are tested using the measurements of a discharge with a locked mode. From the profiles of an H mode discharge with improved confinement and a discharge with an internal transport barrier (ITB) the ion heat transport coefficients, E × B shearing rates and the maximum linear growth rates of the instabilities are calculated. Comparison of these results supports the assumption that turbulent transport due to the ion temperature gradient instability is suppressed inside the transport barrier in the ITB discharge. However, due to the dominant influence of the toroidal rotation velocity on the central E × B shear, they do not prove the shear decorrelation model, because Er naturally rises during the phases with improved confinement if unbalanced neutral beam heating is applied.

The radial structure of a plasma column sustained by a surface wave

The self-consistent radial profiles are obtained for a steady-state, surface-wave-sustained, unmagnetized argon plasma in a cylindrical dielectric tube surrounded by a conductor. The density profiles obtained using the correct constant mean-free-path ion–neutral collision differ considerably from those obtained using the common (but here quite incorrect) approximation of constant mean free time, but are little affected by changes in the profile of wave energy deposition. Various profiles for some typical cases are also compared for three different electron heat transport assumptions. These electron heat transport coefficients are as follows: (i) The correct value, (ii) 102× the correct value, to obtain the essentially isothermal case, and (iii) 10−2× the correct value, to approximate negligible heat transport (the adiabatic case). From the comparison of the temperature profiles, it became clear that the best electron heat transport simplification is to take the electrons to be isothermal [i.e., assumption (ii)], in which case only the total absorption per unit length is important, and not the details of the surface wave behavior.

Correlations for effective heat transport coefficients in beds packed with cylindrical particles

A wall heat conduction model (Λ(r)-model by Winderberg et al. (2000) for packed beds of spheres) has been extended to beds of cylindrically shaped particles with almost equal diameter and length (d≃l). Very satisfactory accuracy could be attained in the description of measured temperature profiles for a total of 85 experiments from literature. These cover a range of tube to (equivalent) particle diameter ratios from D/d p =4.1 to D/d p =34.9 and Reynolds numbers from Re 0 =7.4-1786 for particles of relatively low thermal conductivity like catalyst pellets. In all cases the fluid flowing through the bed has been air. Model parameters have been shown to be independent from the thermal boundary condition at the tube wall. The latter is implemented directly in the model, without introduction of an artificial wall heat transfer coefficient. Mass transport and chemical reaction have not been investigated.

The Effect of Working Fluid Inventory on the Performance of Revolving Helically Grooved Heat Pipes

The results of a recently completed experimental and analytical study showed that the capillary limit of a helically-grooved heat pipe (HGHP) was increased significantly when the transverse body force field was increased. This was due to the geometry of the helical groove wick structure. The objective of the present research was to experimentally determine the performance of revolving helically-grooved heat pipes when the working fluid inventory was varied. This report describes the measurement of the geometry of the heat pipe wick structure and the construction and testing of a heat pipe filling station. In addition, an extensive analysis of the uncertainty involved in the filling procedure and working fluid inventory has been outlined. Experimental measurements include the maximum heat transport, thermal resistance and evaporative heat transfer coefficient of the revolving helically grooved heat pipe for radial accelerations of |a⃗r|=0.0, 2.0, 4.0, 6.0, 8.0, and 10.0-g and working fluid fills of G=0.5, 1.0, and 1.5. An existing capillary limit model was updated and comparisons were made to the present experimental data.

Transport Phenomena in Turbulent Falling Films

This study was concerned with transport phenomena in turbulent falling films, with negligible interfacial shear. Emphasis was on the development of general expressions for eddy diffusivities, which could then be utilized to predict transport coefficients for various momentum and heat- and mass transfer processes. Experiments were pursued to obtain new data for heat transfer during film evaporation, a phenomenon that involves significant boundary layer resistance at both the wall and the free interface. These new data extended the existing database by an order of magnitude in the Prandtl number. When predictions of the new model are assessed against both new and existing experimental information, good agreement was found for film thickness, sensible heat transfer at the wall, mass transfer at the free surface, and film evaporation.

On the stabilization of neoclassical tearing modes by phased electron cyclotron waves

The stabilization of neoclassical tearing modes by phased electron cyclotron current drive (ECCD) and electron cyclotron resonance heating (ECRH) is studied numerically. The dependence of the saturated magnetic island width on the magnitude, width and location of the driven current and the corresponding resistivity perturbation are investigated. Since the saturated island size cannot become much smaller than the width of the driven current layer, this width is one of the most important parameters. Assuming usual heat transport coefficients, the stabilization by ECRH is found to be more effective than that by ECCD for a large island in a middle-size tokamak, while the stabilization by ECCD should be more effective for a tokamak reactor.

Nonintrusively Measured Temperature Distributions as Evidence for Free Convection in Immunoassay Incubation

Immunoassay incubation is classically performed at elevated temperatures to speed up reaction processes. This acceleration has long been assumed to be due to an increased association constant between reactants. Using an interferometric method to visualize temperature differences inside a small reaction cuvet, we demonstrate that the temperature profiles inside the liquid cannot be caused by conduction but only by thermal convection. Numerical simulations further support this experimental evidence. This paper conclusively demonstrates that thermally induced mass transport occurs in immunoassay incubation. Current data show that earlier estimates of heat transport coefficients in such incubations have been probably overestimated by a factor 3.

Superheating of YBa2Cu3O7−x thin-film microbridges

It is found that the hysteresis that develops with decreasing temperature in the current-voltage characteristics of thin-film YBa2Cu3O7−x microbridges is due to superheating of the bridges by the transport current. The heat transport coefficient is determined to be α=5500–7500 V/(cm2·K) and the thermal resistance of the YBa2Cu3O7−x /MgO film-substrate interface is R if=(1.3–1.8)×10−4 (cm2·K)/W.

Assessment of the DIVIMP ‘onion-skin’ model in the JET Mark I divertor

The DIVIMP-NIMBUS [1] ‘Onion-Skin’ model has been used to predict upstream plasma parameters using as input measurements by Langmuir probes in the divertor target tiles. Measurements of density and temperature (both T i and T e ) across the SOL close to the stagnation point at the top of the torus have been made using a reciprocating probe carrying both Langmuir and retarding field analyzer (RFA) heads. In addition, a lithium beam diagnostic has been used to measure radial distributions of density upstream. Ohmic, L-mode and H-mode discharges have been studied, and good agreement with code predictions in the three cases has been found. The heat transport coefficient, χ ⊥( r), has been evaluated across the SOL, and is found to increase with increasing distance from the separatix.

Heat, Water, and Solution Transfer in Unsaturated Porous Media: I -- Theory Development and Transport Coefficient Evaluation

A detailed theory describing the simultaneous transfer of heat, water, and solute in unsaturated porous mediais developed. The theory includes three fully-coupledpartial differential equations. Heat, water, andsolute move in the presence of temperature, T; matricpressure head, Ψ m ; solution osmotic pressure head Ψ o ; and solute concentration C gradients. Thetheory can be applied to describe the mass and energyin radioactive waste repositories, food processing,underground energy storage sites, buried electriccables positions, waste disposal sites, and inagricultural soil. Several transport coefficients forheat, water, and solute are included in the theory. The coefficients are evaluated for a silty clay loamsoil to clarify their dependence on water content (θ),T, and C. The thermal vapor diffusivity D Tv first increased as θ increased to0.22 m3/m3 then decreased with furtherincreases in θ. D Tv was 3 orders of magnitudegreater than either isothermal vapor D mv orosmotic vapor D ov , diffusivities at θ of0.20~m3/m3, T of 50°C, and C of 0.001mol/kg. All of the liquid and vapor water transport coefficients increased with increasing T. D Tv decreased with increasing C to a greater extent thanD mv and D ov . The effective thermalconductivity decreased slightly with increasing C. Thesolute diffusion coefficient D d was 6 to 7orders of magnitude greater than the thermal soluteand salt sieving diffusion coefficients at θ of0.20~m3/m3, T of 50°C, and C of 0.001 mol/kg.

Heat transport properties of ferroelectrics and related materials

Abstract A review of experimental data on heat transport properties of crystals with ferroelectric and ferrodistortive phase transitions is presented. Special attention is paid to the temperature dependence of the thermal conductivity coefficient in order-disorder and displacive type phase transitions. An interpretation and a qualitative approach to the description of the heat transport coefficients anomalies are discussed.

Significance of the radial porosity profile for the description of heat transport in wall-cooled packed beds

The influence of a radial porosity and velocity profile on the predicted temperature and concentration profiles in wall-cooled packed beds is studied, with and without an exothermic first-order chemical reaction, on the basis of literature correlations for the effective transport coefficients. Furthermore, values for the effective heat transport coefficients are obtained from “cold-flow” experiments by means of model fitting, with and without taking the radial velocity profile into account. The radial porosity and velocity profiles are approximately by step-function, which is referred to as the “two-region model”. It is shown that the effective radial heat conductivity can be taken constant over the radius, despite the wall effect. Nevertheless, the influence of a radial superficial velocity profile can be significant through the convective term in the heat balance, especially for low tube-to-particle diameter ratios. The predicted NTU can increase the order of 20% for high values of the Reynolds number and up to 100% for low values. This is confirmed by the results obtained from the model fitting. In case of a first-order exothermic reaction, significantly higher values for the hot-spot temperatures are predicted, if a radial porosity and velocity profile is incorporated in the heat and mass balances. This is found to be mainly caused by the non-uniform distribution of active catalyst over the radius, due to the porosity profile.

Dynamic behaviour of power compensated differential scanning calorimeters: Part 2. The signal flow

The dynamic behaviour of the measured signal of a power compensated DSC is studied in terms of linear response taking into account the measuring system, the sample, the reference, the control circuits, the heat transport coefficients and the heat losses. As a result it is shown that the apparatus (or Green's) function of the DSC (including sample and heat transfer) is different from that necessary to desmear the sample heat flow. The quality of the extracted Green's function is discussed for different measuring conditions.

MODELLING OF RADIAL HEAT TRANSPORT IN WALL-COOLED PACKED BEDS CONFIDENCE INTERVALS OF ESTIMATED PARAMETERS AND CHOICE OF BOUNDARY CONDITIONS

Abstract The heat transport in a wall-cooled packed tube in which a hot gas is cooled down is often described with a pseudo-homogeneous one-dimensional or two-dimensional model. Assuming a radially flat inlet temperature profile at the bed entrance can lead to erroneous results, if the actual profile at the entrance is curved. It can cause an apparent length dependence of the effective heat transport coefficients, the so called “length effect”. The reason being that the amount of heat entering the packed bed is overestimated, which is compensated for by higher values for the heat transport coefficients. Using a parabolic inlet temperature profile, as measured in the packed bed at a certain minimal bed length, eliminates the length dependence of the heat transport coefficients. An experimental investigation showed that for the gas flow rates applied. Pep s= 52 to 785, a wall heat transfer coefficient αw has to be used for modelling the heat transport with a two-dimensional model. Confidence intervals are g...

Data analysis on TFTR using the SNAP transport code

This paper describes the between shots data analysis on TFTR using the one-dimensional equilibrium kinetic analysis code SNAP. SNAP accepts as input data: the measured plasma size and current, toroidal field, surface voltage, plasma composition (total Zeff and Zeff contribution from metallic impurities), edge neutral density, auxiliary heating power data (neutral beam power, energy, injection geometry and/or rf power and frequency), and measured profiles of Te(R), ne(R), Ti(R), Vφ(R), and Prad(R). SNAP iteratively calculates: (1) the mapping of profile data to a minor radius grid, (2) the magnetic topology including Shafranov shifted circular flux surfaces, (3) neutral beam attenuation and deposition profiles, (4) unthermalized beam ion density and beam power density delivered to thermal plasma species from a numerical solution to the Fokker–Planck equation, (5) the neutral density profile, (6) local heat and particle transport coefficients consistent with the measured profiles and calculated source terms, (7) ICRF power profiles from a reduced order full wave analysis and isotropic Stix quasilinear model, and (8) total neutron emissivity and plasma stored energy. Several ion heat transport models (including neoclassical χi and χi∝χe) are available to calculate an expected Ti(r) profile in the absence of measurements.

High energy ion beam mixing in dense collision cascades

Atomic mixing of tracer atoms in dense collision cascades in metals is calculated. The model used in the calculations describes the atomic transport from the initial collisional phase to the late thermalized stage. The collisional mixing is calculated by Monte Carlo simulation and a thermal spike model is used to describe the late phase of the cascade. The cooling of a thermal spike is described by coupled heat conduction equations for conduction electrons and lattice. Atomic transport takes place above the glass transition temperature of a metallic matrix and the transport is treated as diffusion in liquids. The heat exchange between conduction electrons and lattice allows rapid quenching of thermal spikes in metals with high d-electron density. Mass and heat transport coefficients are calculated on the basis of elementary solid state models, accordingly; the model for ion beam mixing contains no adjustable parameters Calculations for metal markers in Ni, Cu, Ag, Pd, Au and Pt are in agreement with experimental results, when the cohesive energy of marker atoms is sufficiently similar to that of matrix atoms. The model predicts a pronounced temperature dependence for the high-energy ion-beam mixing in Cu, Ag and Au.