Boundary Melting Research Articles

Heat Flow in Earth's Core From Invariant Electrical Resistivity of Fe‐Si on the Melting Boundary to 9 GPa: Do Light Elements Matter?

AbstractThe electrical resistivity and thermal conductivity of liquid Fe alloys are the least constrained parameters in Earth's outer core (OC). These parameters are important as they modulate energy budget available for the geodynamo and affect the spatiotemporal evolution of the core. We report results of electrical resistivity measurements on solid and liquid Fe‐4.5 wt%Si from 3–9 GPa using a large volume multianvil press. The internally modified 18/11 octahedron cell was used to maintain the geometry of the liquid sample and to delay the onset of contamination. Electrical resistivity of solid Fe‐4.5Si decreases steadily with pressure and is very sensitive to increasing temperature‐driven onset of phase transitions. Along the melting boundary and within error, electrical resistivity remains constant and assumes the same value of 120 μΩcm as observed in pure liquid Fe. The results are interpreted in the context of icosahedral short‐range order (ISRO) structures that exhibit higher concentration with increasing pressure. Along the melting line, the increasing concentration of ISROs reduces charge carrier mean free path and prevents decrease of electrical resistivity with increasing pressure as seen in liquid metals, Cu, Ag, and Au, which do not have ISROs. In light of recent developments in understanding of the structure and dynamics of liquid transition metals and alloys, we postulate that our findings are applicable to other Fe alloys in the OC with small light element (C, S, and O) content. We calculated an adiabatic heat flow of 9.4–12 TW at the OC‐CMB interface, which admits thermal convection.

Mechanisms of TiAl alloys isomorphic inoculation from cryo-milled Ti-Al-Nb powders

Isomorphic inoculation has recently been introduced by the authors as a successful method to grain refine cast titanium aluminides [1]. Analyses of the cast grain size together with introduced particle size distributions revealed anomalously high grain refinement efficiency which was attributed to the particles breaking up during the holding stage prior to solidification [2]. In the present work, the microstructure of the inoculant powders is investigated in both the cryo-milled state as well as after simulated thermal cycles to reproduce their heating and holding in the melt. Results show that milling time does not impact the grain size in the particles, only their size distributions. Heat treatments between 1500 and 1600°C for short periods of time allowed the activation energy for grain growth and evaluation of the grain size evolution in the particles during the isomorphic inoculation process to be determined. Assuming that grain boundary melting is the predominant break up mechanism, a model to estimate dissolution of the powders is presented which includes diffusion and fluid flow. Despite its relative simplicity, the predicted number of particles remaining after heating and holding, which lead to grains in the as-cast structure, are in good agreement with the measured grain size. Finally, the paper summarizes the main features and mechanism making isomorphic inoculation a promising route for grain refining as-cast alloys.

Magmatic inflation in 2008–2010 at Mt. Fuji, Japan, inferred from sparsity-promoting L1 inversion of GNSS data

Mt. Fuji, the tallest volcano in Japan, has not erupted since the Plinian eruption in 1707, but its volcanic activity has not finished. Here, using GNSS (Global Navigation Satellite System) time-series data, we investigate an inflation event of Mt. Fuji in 2008–2010. Referring to recent studies of igneous processes, we focus on “vertically-extensive” magma systems and estimate depth distribution of geodetic inflation sources. A sparsity-promoting L1 regularization algorithm for inversion analysis allows us to improve performance of data fitting. Our result shows that the inflation sources were mainly distributed in a depth range from 20 km to 15 km, and the total volume change was on the order of 0.01 cubic kilometers (approximately a sphere of radius 100 m). The 15 km depth may correspond to the upper boundary of partial melt of basaltic magma. Our sparsity-promoting method is useful to constrain magma movement from limited observation data.

Structural transformations including melting and recrystallization during shock compression and release of germanium up to 45 GPa

Solid-solid and solid-liquid transformations were examined in Ge(100), using in situ x-ray diffraction measurements during uniaxial strain compression and release. For final stresses above 15.7 GPa, the Ge transformed to a highly textured tetragonal $\ensuremath{\beta}$-Sn phase. At 31.5 GPa and above, Ge transformed to the molten phase. Full stress release (uniaxial strain) from the $\ensuremath{\beta}$-Sn phase, from the melt boundary, and from the completely molten phase, resulted in reversion to an untextured cubic diamond (cd) phase. These findings demonstrate that the cd to $\ensuremath{\beta}$-Sn phase change is reversible, and that recrystallization from the liquid phase occurs on nanosecond timescales during release.

The problem of melting ice in a porous medium saturated with ice and gas

The problem of ice formation in a dry, cold, porous medium saturated with ice and gas (air) when pumping warm water is considered in a flat one-dimensional self-similar formulation. The task was considered in volume area. During the injection of warm water from the beginning deep into the reservoir, it spread in a volume region that will divide the reservoir into 3 zones. The first zone was filled with water, the second zone was filled with ice and water, and the third zone was filled with ice and gas. To describe the process of heat and mass transfer, the following hypotheses were used: the temperature of the saturated substance (water, ice or gas) is equal to the temperature of the porous medium; ice and skeleton still; water, ice and skeleton of the reservoir are incompressible; skeletal porosity is constant. On the basis of constructed self-similar solutions, a numerical analysis was performed illustrating the effect of the initial parameters of a dry porous medium saturated with ice and gas, as well as the temperature of the injected water on the temperature and pressure distribution in the porous medium. It has been established that an increase in the temperature of the injected water does not lead to a significant increase in the area of ice decomposition. It is also established that if the pressure of the injected water is increased, this will not lead to a large increase in the area of ice decomposition. However, based on the results obtained, it can be seen that the speed of movement of the melting boundary increases, in particular, as the pressure increases by <i>p<sub>e</sub></i>=0.05 MPa, the intermediate region increases by one and a half times. It was found that it is economically more profitable to pump water with a lower temperature, because water with a higher temperature slightly increases the freezing area of the porous soil.

Boundary layer flow and melting heat transfer of Prandtl fluid over a stretching surface by considering Joule heating effect

PurposeThe purpose of this paper is to study the impact of Joule heating on boundary layer flow and melting heat transfer of Prandtl fluid over a stretching sheet in the presence of fluid particles suspension. The transformed boundary layer equations are solved numerically by RKF-45 method. The influence of the non-dimensional parameters on velocity and temperature growths in the boundary layer region is analyzed in detail and the results are shown graphically. The results indicate that the larger estimation ofαandβreduces for both velocity and temperature profile. Further, the rate of heat transfer decreases by increasing melting parameter.Design/methodology/approachThe converted set of boundary layer equations is solved numerically by RKF-45 method. Obtained numerical results for flow and heat transfer characteristics are deliberated for various physical parameters. Furthermore, the skin friction coefficient and Nusselt number are also presented.FindingsIt is found that the heat transfer rates are advanced in the occurrence of non-linear radiation camper to linear radiation. Also, it is noticed that velocity profile increases by increasing Prandtl parameter but establishes opposite results for temperature profile.Originality/valueThe authors intend to analyze the boundary layer flow and melting heat transfer of a Prandtl fluid over a stretching surface in the presence of fluid particles suspension. The governing systems of partial differential equations have been transformed to a set of coupled ordinary differential equations by applying appropriate similarity transformations. The reduced equations are solved numerically. The pertinent parameters are discussed through graphs and plotted graphs. The present results are compared with the existing limiting solutions, showing good agreement with each other.

Effect of non-uniform heat source/sink on MHD boundary layer flow and melting heat transfer of Williamson nanofluid in porous medium

PurposeThe purpose of this paper is to examine the influence of magnetic field on Williamson nanofluid embedded in a porous medium in the presence of non-uniform heat source/sink, chemical reaction and thermal radiation effects.Design/methodology/approachThe governing physical problem is presented using the traditional Navier–Stokes theory. Consequential system of equations is transformed into a set of non-linear ordinary differential equations by means of scaling group of transformation, which are solved using the Runge–Kutta–Fehlberg method.FindingsThe working fluid is examined for several sundry parameters graphically and in a tabular form. It is noticed that with an increase in Eckert number, there is an increase in velocity and temperature along with a decrease in shear stress and heat transfer rate.Originality/valueA good agreement of the present results has been observed by comparing with the existing literature results.

Modeling heterogeneous melting in phase change memory devices

We present thermodynamic crystallization and melting models and calculate phase change velocities in Ge2Sb2Te5 based on kinetic and thermodynamic parameters with a focus on the impacts of grain boundary melting. The calculated phase change velocities are strong functions of grain size, with smaller grains beginning to melt at lower temperatures. Phase change velocities are continuous functions of temperature which determine crystallization and melting rates. Hence, set and reset times as well as power and peak current requirements for switching are strong functions of grain size. Grain boundary amorphization can lead to a sufficient increase in cell resistance for small-grain phase change materials even if the whole active region does not completely amorphize. Isolated grains left in the amorphous regions, the quenched-in nuclei, facilitate templated crystal growth and significantly reduce set times for phase change memory cells. We demonstrate the significance of heterogeneous melting through 2-D electrothermal simulations coupled with a dynamic material phase change model. Our results show reset and set times on the order of ∼1 ns for 30 nm wide confined nanocrystalline (7.5 nm–25 nm radius crystals) phase change memory cells.

Comment on the paper: “Thermal radiation and chemical reaction effects on boundary layer slip flow and melting heat transfer of nanofluid induced by a nonlinear stretching sheet, M.R. Krishnamurthy, B.J. Gireesha, B.C. Prasannakumara, and Rama Subba Reddy Gorla, Nonlinear Engineering 2016, 5(3), 147-159”

Abstract The present comment concerns some doubtful results included in the above paper.

Numerical and experimental researches of thermal energy storage processesduring phase transformations of phase change materials with nanoparticles

It is evident that nowadays materials with phase or chemical transformations are significantly considered to be in surpassing demand in the society being used for accumulating thermal energy. Furthermore, this usage leads to the process of increasing accumulated thermal energy per unit mass concentration to be achieved in a much beneficial and reliable manner. In comparison to these materials, well-known and widely–used solid and liquid ones are mainly associated with productivity and efficiencylosses. One of the methods, having desirable attributes for substantial enhancement in the energy productivity of phase change materials is proved to be the addition of solid nanoparticles with a large coefficient of thermal conductivity. This work focuses on numerical and experimental investigation the influence of nanoparticles of various materials and sizes on the processes of thermal energy storage in paraffin. In particular, the proceeding data of the thermophysical properties of paraffin with nanoparticles as being found by the optical spectroscopy method. Moreover, due to comprehensive results in experimental and numerical studies, the heat accumulating capacity of the phase change materials, as well as the dynamics and profile of the melting boundary around cylindrical heat sources were reported to be determined. Besides, the comparison of heatstorage capacity for phase change materials with and without nanoparticles is managed.

Rayleigh–Bénard convection with a melting boundary

We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane-layer geometry, this can be seen as classical Rayleigh–Bénard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier–Stokes equations in the Boussinesq approximation. The advantage of this approach is that it requires only moderate modifications of classical numerical methods. We focus on the case where the solid is initially nearly isothermal, so that the evolution of the topography is related to the inhomogeneous heat flux from thermal convection, and does not depend on the conduction problem in the solid. From a very thin stable layer of fluid, convection cells appear as the depth – and therefore the effective Rayleigh number – of the layer increases. The continuous melting of the solid leads to dynamical transitions between different convection cell sizes and topography amplitudes. The Nusselt number can be larger than its value for a planar upper boundary, due to the feedback of the topography on the flow, which can stabilize large-scale laminar convection cells.

Nanosecond Melting and Recrystallization in Shock-Compressed Silicon.

Insitu, time-resolved, x-ray diffraction and simultaneous continuum measurements were used to examine structural changes in Si shock compressed to 54GPa. Shock melting was unambiguously established above ∼31-33 GPa, through the vanishing of all sharp crystalline diffraction peaks and the emergence of a single broad diffraction ring. Reshock from the melt boundary results in rapid (nanosecond) recrystallization to the hexagonal-close-packed Si phase and further supports melting. Our results also provide new constraints on the high-temperature, high-pressure Si phase diagram.

SAFR/V1 (EVKLID/V2 Integral Code Module) Aided Simulation of Melt Movement Along the Surface of a Fuel Element in a Fast Reactor During a Serious Accident

The basic approaches used in the SAFR/V1 module of the integral code EVKLID/V2 to simulate the movement of the melt formed upon melting of fuel elements are presented. The system of mass, energy, and momentum conservation equations used to simulate the movement of melt is presented. Special attention is devoted to methods of numerical approximation of the equations as well as to the solution of problems involving smearing of the solution at the melt boundary. The realized methods of stimulating the motion of melt have been verified on the basis of tests with known analytical solutions.

Decreasing electrical resistivity of gold along the melting boundary up to 5 GPa

ABSTRACTThe electrical resistivity of gold was experimentally measured at high pressures from 2 to 5 GPa and temperatures ∼300 K above melting. The resistivity decreased as a function of pressure and increased as a function of temperature as expected. The temperature dependence of resistivity in the solid and liquid phases are comparable to 1 atm results. The observed melting temperatures at each pressure agree well with previous experimental and theoretical studies. The essential result of this study is that resistivity decreases along the pressure-dependent melting boundary, conflicting with a prediction of invariant behavior as reported in the literature. This result is discussed in terms of the interaction between s and d-bands as both pressure and temperature increase along the melting boundary. The thermal conductivity of gold was calculated from the measured electrical resistivity using the Wiedemann-Franz law. The temperature-induced effect on the thermal conductivity at high temperatures is as expected in both the solid and liquid phase while the pressure-effect shows some variability.

Thermodynamic properties ofMgSiO3at super-Earth mantle conditions

Recent discoveries of terrestrial exoplanets distant from our solar system motivate laboratory experiments that provide insight into their formation and thermal evolution. Using laser-driven shock wave experiments, we constrain high-temperature and high-pressure adiabats and the equation of state of ${\mathrm{MgSiO}}_{3}$, a dominant mantle constituent of terrestrial exoplanets. Critical to the development of a habitable exoplanet is the early thermal history, specifically the formation and freezing of the magma ocean and its role in enabling convection in the mantle and core. We measure the adiabatic sound speed and constrain the melt transition along the Hugoniot and find that the adiabats and melt boundary of silicate magmas are shallower than predicted. This suggests that small changes in the temperature of a super-Earth mantle would result in rapid melting and solidification of nearly the entire mantle.

Scrutinization of Joule Heating and Viscous Dissipation on MHD Flow and Melting Heat Transfer Over a Stretching Sheet

The present paper deals with an analysis of the combined effect of Joule heating and viscous dissipation on an MHD boundary layer flow and melting heat transfer of a micro polar fluid over a stretching surface. Governing equations of the problem are transformed into a set of coupled nonlinear ordinary differential equations by applying proper transformations and then they are solved numerically using the RKF-45 method. The method is verified by a comparison with the established results with limiting solution. The influence of the various interesting parameters on the flow and heat transfer is analyzed in detail through plotted graphs.

Trace element diffusion and kinetic fractionation in wet rhyolitic melt

Piston-cylinder experiments were run to determine the chemical diffusivities of 21 trace elements (Sc, V, Y, Zr, Nb, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb, Lu, Hf, Th and U) in hydrous rhyolitic melts at 1 GPa pressure and temperatures from 850 to 1250 °C. Diffusion couple glasses were doped with trace elements in low concentrations to characterize the diffusivities of all cations in a single experiment. Laser ablation ICP-MS was used to evaluate the trace element concentration gradients that developed in the silicate glasses. All calculated diffusion coefficients correspond to the temperature dependence D = D0exp(-Ea/RT). Rhyolite liquids contained either ∼4.1 wt% or ∼6.2 wt% dissolved H2O; separate Arrhenius relationships are produced for each melt composition. Trace element diffusivities in the melt with 6.2 wt% H2O are roughly two times higher than those in the less hydrous melt.Calculated trace element diffusion coefficients cover nearly two orders of magnitude at a given temperature. The high field strength elements are the slowest diffusers, followed by the transition metals and heavy rare earth elements. The light rare earth elements have the fastest diffusion rates in hydrous rhyolitic melt. The measured diffusion coefficients range down to values sufficiently low to preclude diffusive homogenization over geochemically realistic time scales in some cases. The substantial differences in the diffusivities of individual cations may result in fractionated trace element signatures in rhyolite melt pockets. A simple model is used to explore the potential for kinetic fractionation of REE during growth of an apatite crystal in a diffusive boundary layer locally saturated in P2O5. The faster-diffusing light REE are more efficiently transported away from the crystal interface than the slower-moving heavy REE. Diffusion effects will enrich the melt boundary layer in slow-moving HREE relative to the faster LREE. The kinetic fractionation of REE in the melt growth medium will result in a precipitated apatite crystal with a disequilibrium trace element composition.

An urban-based climatology of winter precipitation in the northeast United States

Varying forms of precipitation during winter weather events cause disruptions to commercial operations and transportation networks, particularly in densely populated regions. Developing a better understanding of the characteristics surrounding these events may lead to better prediction and subsequent mitigation. This study constructs a 21-year cold season climatology of precipitation type over highly urbanized areas of the northeastern United States. By using quality-controlled station reports, a specific focus is placed on the influence of urbanization in precipitation processes. In events involving multiple precipitation types, the ambient atmospheric profile is very close to the freezing point in lower levels. The influence of the boundary layer urban heat island may play a role in increasing melting of hydrometeors. Statistically significant findings from linear regression modeling show that proximity to urban centers, as derived from mean road density, plays a role in the surface observation of mixed precipitation events. 21% of any mixed precipitation observation may be attributed to its distance from a high density urban area. Decreases in mean surface wind speed and direction during mixed precipitation events increase the likelihood of an intact boundary layer urban heat island and melting of hydrometeors when compared to stronger wind speeds during snowfall events.

Decreasing electrical resistivity of silver along the melting boundary up to 5 GPa

ABSTRACTThe electrical resistivity of Ag was experimentally measured at high pressures up to 5 GPa and at temperatures up to ∼300 K above melting. The resistivity decreased as a function of pressure and increased as a function of temperature as expected and is in very good agreement with 1 atm data. Observed melting temperatures at high pressures also agree well with previous experimental and theoretical studies. The main finding of this study is that resistivity of Ag decreases along the pressure- and temperature-dependent melting boundary, in conflict with prediction of resistivity invariance. This result is discussed in terms of the dominant contribution of the increasing energy separation between the Fermi level and 4d-band as a function of pressure. Calculated from the resistivity using the Wiedemann–Franz law, the electronic thermal conductivity increased as a function of pressure and decreased as a function of temperature as expected. The decrease in the high pressure thermal conductivity in the liquid phase as a function of temperature contrasts with the behavior of the 1 atm data.

Thermodynamically complete equation of state of MgO from true radiative shock temperature measurements on samples preheated to 1850 K

Plate impact experiments in the 100--250 GPa pressure range were done on a $\ensuremath{\langle}100\ensuremath{\rangle}$ single-crystal MgO preheated before compression to 1850 K. Hot Mo(driver)-MgO targets were impacted with Mo or Ta flyers launched by the Caltech two-stage light-gas gun up to 7.5 km/s. Radiative temperatures and shock velocities were measured with 3%--4% and 1%--2% uncertainty, respectively, by a six-channel pyrometer with 3-ns time resolution, over a 500--900-nm spectral range. MgO shock front reflectivity was determined in additional experiments at 220 and 248 GPa using $\ensuremath{\approx}50/50$ high-temperature sapphire beam splitters. Our measurements yield accurate experimental data on the mechanical, optical, and thermodynamic properties of B1 phase MgO from 102 GPa and 3900 K to 248 GPa and 9100 K, a region not sampled by previous studies. Reported Hugoniot data for MgO initially at ambient temperature, $T=298$ K, and the results of our current Hugoniot measurements on samples preheated to 1850 K were analyzed using the most general methods of least-squares fitting to constrain the Gr\uneisen model. This equation of state (EOS) was then used to construct maximum likelihood linear Hugoniots of MgO with initial temperatures from 298 to 2400 K. A parametrization of all EOS values and best-fit coefficients was done over the entire range of relevant particle velocities. Total uncertainties of all the EOS parameters and correlation coefficients for these uncertainties are also given. The predictive capabilities of our updated Mie-Gr\uneisen EOS were confirmed by (1) the good agreement between our Gr\uneisen data and five semiempirical $\ensuremath{\gamma}(V)$ models derived from porous shock data only or from combined static and shock data sets, (2) the very good agreement between our 1-bar Gr\uneisen values and $\ensuremath{\gamma}(T)$ at ambient pressure recalculated from reported experimental data on the adiabatic bulk modulus ${K}_{s}(T)$, and (3) the good agreement of the brightness temperatures, corrected for shock reflectivity, with the corresponding values calculated using the current EOS or predicted by other groups via first-principles molecular dynamics simulations. Our experiments showed no evidence of MgO melting up to 250 GPa and 9100 K. The highest shock temperatures exceed the extrapolated melting curve of Zerr and Boehler by $g3300$ K and the upper limit for the melting boundary predictions of Aguado and Madden by $g2600$ K and those of Strachan et al. by $g2100$ K. We show that the potential for superheating in our shock experiments is negligible and therefore out data put a lower limit on the melting curve of B1 phase MgO in $P\text{\ensuremath{-}}T$ space close to the set of consistent independent predictions by Sun et al., Liu et al., and de Koker and Stixrude.