Showing papers on "Thermal diffusivity published in 2004"

Diffuse-charge dynamics in electrochemical systems.

Abstract: The response of a model microelectrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate blocking electrodes, which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The "weakly nonlinear" limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter epsilon= lambdaD/L, where lambdaD is the screening length and L the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of lambdaDL/D (not lambdaD2/D), where D is the ionic diffusivity, but nonlinearity violates this common picture and introduces multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, L2/D. In the "strongly nonlinear" regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multicomponent electrolytes, and Faradaic processes.

Quantitative phase-field model of alloy solidification.

Abstract: We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect to previous phase-field models is achieved by the addition of a phenomenological "antitrapping" solute current in the mass conservation relation [Phys. Rev. Lett. 87, 115701 (2001)]]. This antitrapping current counterbalances the physical, albeit artificially large, solute trapping effect generated when a mesoscopic interface thickness is used to simulate the interface evolution on experimental length and time scales. Furthermore, it provides additional freedom in the model to suppress other spurious effects that scale with this thickness when the diffusivity is unequal in solid and liquid [SIAM J. Appl. Math. 59, 2086 (1999)]], which include surface diffusion and a curvature correction to the Stefan condition. This freedom can also be exploited to make the kinetic undercooling of the interface arbitrarily small even for mesoscopic values of both the interface thickness and the phase-field relaxation time, as for the solidification of pure melts [Phys. Rev. E 53, R3017 (1996)]]. The performance of the model is demonstrated by calculating accurately within a phase-field approach the Mullins-Sekerka stability spectrum of a planar interface and nonlinear cellular shapes for realistic alloy parameters and growth conditions.

Thermal conductivity, thermal diffusivity, and specific heat capacity of particle filled polypropylene

Abstract: By the addition of metal and oxide particles to plastics, thermal transport properties, heat capacity, and density of polymers can be varied systematically. Composites samples of polypropylene (PP) with various fillers in different fractions (up to 50 vol%) were prepared with an injection moulding process to study the evolution of the properties as a function of filler content. Standard filler materials like magnetite, barite, talc, copper, strontium ferrite and glass fibres were used. Thermal diffusivities, specific heat capacities and densities of the prepared composite samples were measured, and thermal conductivities were derived. Thermal conductivity of the polypropylene is increased from 0.27 up to 2.5 W/(m K) with 30 vol% talc in the polypropylene matrix. Thermal conductivities of the filled polypropylene samples are compared with the modelled values according to Hashin and Shtrikman. The interconnectivity of the particles in the polypropylene matrix is derived from a comparison between modelled and measured thermal conductivity values. For higher talc and glass fibre content in PP plastics, a complete interconnectivity is achieved, while copper particles in PP show a very poor interconnectivity. Specific heat capacities and thermal diffusivities of magnetite and barite filled polypropylene were measured in the temperature range from 300 to 395 K.

Analysis of convective instability and heat transfer characteristics of nanofluids

Abstract: The convective instability driven by buoyancy and heat transfer characteristics of nanofluids are investigated analytically. This paper proposes a factor which describes the effect of nanoparticle addition on the convective instability and heat transfer characteristics of a base fluid. The Bruggeman model based on the mean field approach for expressing the thermal conductivity enhancement is chosen as a lower bound of the thermal conductivity relationship. The results show that as the density and heat capacity of nanoparticles increase and the thermal conductivity and the shape factor of nanoparticles decrease, the convective motion in a nanofluid sets in easily. The heat transfer coefficient of a nanofluid is enhanced by all parameters with respect to the volume fraction of nanoparticles.

Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion.

Abstract: A phase-field model is developed for simulating quantitatively microstructural pattern formation in solidification of dilute binary alloys with coupled heat and solute diffusion. The model reduces to the sharp-interface equations in a computationally tractable thin-interface limit where (i). the width of the diffuse interface is about one order of magnitude smaller than the radius of curvature of the interface but much larger than the real microscopic width of a solid-liquid interface, and (ii). kinetic effects are negligible. A recently derived antitrapping current [Phys. Rev. Lett. 87, 115701 (2001)]] is used in the solute conservation equation to recover precisely local equilibrium at the interface and to eliminate interface stretching and surface diffusion effects that arise when the solutal diffusivities are unequal in the solid and liquid. Model results are first compared to analytical solutions for one-dimensional steady-state solidification. Two-dimensional thermosolutal dendritic growth simulations with vanishing solutal diffusivity in the solid show that both the microstructural evolution and the solute profile in the solid are accurately modeled by the present approach. Results are then presented that illustrate the utility of the model for simulating dendritic solidification for the large ratios of the liquid thermal to solutal diffusivities (Lewis numbers) typical of alloys.

Network equilibration and first-principles liquid water

Abstract: Motivated by the very low diffusivity recently found in ab initio simulations of liquid water, we have studied its dependence with temperature, system size, and duration of the simulations. We use ab initio molecular dynamics (AIMD), following the Born-Oppenheimer forces obtained from density-functional theory (DFT). The linear-scaling capability of our method allows the consideration of larger system sizes (up to 128 molecules in this study), even if the main emphasis of this work is in the time scale. We obtain diffusivities that are substantially lower than the experimental values, in agreement with recent findings using similar methods. A fairly good agreement with D(T) experiments is obtained if the simulation temperature is scaled down by approximately 20%. It is still an open question whether the deviation is due to the limited accuracy of present density functionals or to quantum fluctuations, but neither technical approximations (basis set, localization for linear scaling) nor the system size (down to 32 molecules) deteriorate the DFT description in an appreciable way. We find that the need for long equilibration times is consequence of the slow process of rearranging the H-bond network (at least 20 ps at AIMDs room temperature). The diffusivity is observed to be very directly linked to network imperfection. This link does not appear an artifact of the simulations, but a genuine property of liquid water.

Structural, elastic, thermophysical and dielectric properties of zinc aluminate (ZnAl2O4)

Abstract: Dense zinc aluminate (gahnite) ceramics have been prepared at different sinter temperatures ranging from 1200 to 1600 °C from zinc aluminate powder prepared via the solid-state synthesis. A maximum achieved relative density of 93% was achieved. Several bulk properties like Young's modulus, heat capacity, thermal diffusivity and conductivity have been determined and estimations of the bulk properties at 100% density are made. Furthermore, in spinel-type materials like zinc aluminate the process of cation inversion occurs, which is in general not taken into account in computer simulations for the prediction of bulk properties. In order to determine whether the amount of cation inversion can be influenced by the preparation method resulting in different bulk properties, zinc aluminate powders were synthesised using solid-state synthesis, co-precipitation and a sol-gel method at different temperatures. The resulting powders were zinc deficient due to the volatile nature of zinc at the calcining temperatures. The cation inversion of these powders was investigated using solid-state MAS 27A1 NMR indicating that the cation inversion is very small for pure zinc aluminate irrespective of the preparation method.

Self-diffusion in dense granular shear flows.

Abstract: Diffusivity is a key quantity in describing velocity fluctuations in granular materials. These fluctuations are the basis of many thermodynamic and hydrodynamic models which aim to provide a statistical description of granular systems. We present experimental results on diffusivity in dense, granular shear flows in a two-dimensional Couette geometry. We find that self-diffusivities D are proportional to the local shear rate gamma; with diffusivities along the direction of the mean flow approximately twice as large as those in the perpendicular direction. The magnitude of the diffusivity is D approximately gamma;a(2), where a is the particle radius. However, the gradient in shear rate, coupling to the mean flow, and strong drag at the moving boundary lead to particle displacements that can appear subdiffusive or superdiffusive. In particular, diffusion appears to be superdiffusive along the mean flow direction due to Taylor dispersion effects and subdiffusive along the perpendicular direction due to the gradient in shear rate. The anisotropic force network leads to an additional anisotropy in the diffusivity that is a property of dense systems and has no obvious analog in rapid flows. Specifically, the diffusivity is suppressed along the direction of the strong force network. A simple random walk simulation reproduces the key features of the data, such as the apparent superdiffusive and subdiffusive behavior arising from the mean velocity field, confirming the underlying diffusive motion. The additional anisotropy is not observed in the simulation since the strong force network is not included. Examples of correlated motion, such as transient vortices, and Levy flights are also observed. Although correlated motion creates velocity fields which are qualitatively different from collisional Brownian motion and can introduce nondiffusive effects, on average the system appears simply diffusive.

Thermal Conductivity of Yttria–Zirconia Single Crystals, Determined with Spatially Resolved Infrared Thermography

Abstract: The thermal diffusivity of yttria–zirconia (Y2O3–ZrO2) single crystals, with YO1.5 concentrations in the range of 0–60 mol%, has been determined using a new method that is based on spatially resolved (20 μm) infrared mapping of a modulated thermal field. The decreasing trend of the thermal conductivity (K), as a function of the YO1.5 content (up to 20 mol%), can be described using a model based on a Debye approach that has been modified by introducing a cut-off length for the phonon mean free path. At higher concentrations, K increases, as a result of a possible ordering of the point defects.

An Experimental Investigation of Thermal Effects in a Cavitating Inducer

Abstract: The thermal effects which affect the development of leading edge cavitation in an inducer were investigated experimentally using refrigerant R114. For different operating conditions, the evolution of the cavity length with the cavitation parameter was determined from visualizations. The tests were conducted up to two-phase breeding. The comparison of tests in R114 and in cold water allowed us to estimate the amplitude of the thermodynamic effect. The results show that the B-factor depends primarily upon the degree of development of cavitation but not significantly upon other parameters such as the inducer rotation speed or the fluid temperature, at least in the present domain of investigation. These trends are qualitatively in agreement with the classical entrainment theory. In addition, pressure fluctuations spectra were determined in order to detect the onset of cavitation instabilities and particularly of alternate blade cavitation and rotating cavitation. If the onset of alternate blade cavitation appeared to be connected to a critical cavity length, the results are not so clear concerning the onset of rotating cavitation. NOMENCLATURE a thermal diffusivity or eddy diffusivity B B-factor of Stepanoff (eq.2) p C pressure coefficient l p c liquid heat capacity D characteristic diameter of the inducer e cavity thickness l cavity length h convection heat transfer coefficient L latent heat of vaporization l

Thermal transport properties of magnetic refrigerants La(FexSi1−x)13 and their hydrides, and Gd5Si2Ge2 and MnAs

Abstract: La(FexSi1−x)13 and their hydrides exhibit large magnetocaloric effects due to the itinerant-electron metamagnetic transitions in a wide temperature range covering room temperature. Thermal conductivity and diffusivity of La(Fe0.88Si0.12)13 and La(Fe0.88Si0.12)13H1.0 have been investigated, together with those of other candidates for magnetic refrigerants working in the vicinity of room temperature such as Gd, Gd5Si2Ge2 and MnAs. The thermal conductivity in the vicinity of room temperature for La(Fe0.88Si0.12)13H1.0 is larger than that for Gd5Si2Ge2 and MnAs, and almost identical to that for Gd. Furthermore, the thermal diffusivity in the vicinity of room temperature for La(Fe0.88Si0.12)13H1.0 is as large as that for Gd and Gd5Si2Ge2, and larger than that for MnAs. Consequently, La(FexSi1−x)13 and their hydrides are promising as the magnetic refrigerants from the standpoint of thermal transport properties.

Equations for the Calculation of the Thermo-physical Properties of Stainless Steel

Abstract: Equations have been derived to calculate values of the thermophysical properties of all stainless steels for temperatures between 300 and 1800 K (austenitic 3 series, ferritic-4 series and precipitation-hardened 6-series alloys). Values of the following properties are given in both figures and tables: density (ρ), thermal expansion coefficient (α), heat capacity (Cp), enthalpy (HT−H298), thermal conductivity (λ) and thermal diffusivity (a), electrical resistivity (R), viscosity (η) and surface tension (γ).

Heat and mass transfer in MHD flow by natural convection from a permeable, inclined surface with variable wall temperature and concentration

Abstract: An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a permeable, inclined surface with variable wall temperature and concentration, taking into consideration the effects of ohmic heating and viscous dissipation. Power-law temperature and concentration variations are assumed at the inclined surface. The resulting governing equations are transformed using suitable transformations and then solved numerically by an implicit finite-difference method. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Eckert number, the buoyancy ratio between species and thermal diffusion, Prandtl number, Schmidt number, wall temperature and concentration exponent, the inclination angle from the vertical direction, and the injection parameter. A parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for the velocity, temperature, and concentration distributions as well as the local friction coefficient, local Nusselt number, and the local Sherwood number.

Thermal conductivity of zigzag single-walled carbon nanotubes: Role of the umklapp process

Abstract: Considering the three-phonon process, we calculate the thermal conductivity of zigzag tubes. It is found that thermal conductivity of an isolated (6, 0) single-walled carbon nanotube increases with the increase of temperature at low temperature, and would show a peak behavior at about 85 K before falling off at high temperature. Moreover, thermal conductivity is high for single-walled carbon nanotubes with small diameters as compared to the tubes with large diameters. The thermal conductivity at 300 K is approximately inversely proportional to the tube's diameter.

Diffusivity of ions in agarose gels and intervertebral disc: Effect of porosity

Abstract: The effect of tissue porosity on ion (sodium, potassium, and chloride) diffusivity in agarose gels and porcine intervertebral disc tissues was investigated using an electrical conductivity method. An empirical, constitutive model for diffusivity (D) of solutes in porous fibrous media was proposed: D/D o=exp [−α(r s/κ1/2)β] where r s is the Stokes radius of a solute, κ is the Darcy permeability of the porous medium, D o is the diffusivity in free solution, α and β are two positive parameters whose values depend on material structure. It is found that α=1.25±0.138, β=0.681±0.059 (95% confidence interval, R 2=0.92, n=72) for agarose gels and α=1.29±0.171 and β=0.372±0.088 (95% confidence interval, R 2=0.88, n=86) for porcine annulus fibrosus. The functional relationship between solute diffusivity and tissue deformation was derived. Comparisons of our model prediction with experimental data on diffusion coefficients of macromolecules (proteins, dextrans, polymer beads) in agarose gels in the literature were made. Our results were also compared to the data on ion diffusivity in charged gels and in cartilaginous tissues reported in the literature. There was a good agreement between our model prediction and the data in the literature. The present study provides additional information on solute diffusivity in uncharged gels and charged tissues, and is important for understanding nutritional transport in avascular cartilaginous tissues under different mechanical loading conditions.