SEARCH · Search NASA

Results for “melt flow”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

All sources NASA NTRS DOE OSTI

NASA NTRS1985

Thermocapillary Flows and Their Stability: Effects of Surface Layers and Contamination

The objective is to study quantitatively thermocapillary flows in two-dimensional and axisymmetric geometries in order to learn the impact of such flows on float-zone refining configurations. The work begins with the analytical study of steady flows in slots and zones to obtain predictions of surface curvature, flow and heat transport. It then examines the instability of such flows. Three new instability mechanisms have been identified and the results show that thermocapillary flows of high Prandtl number fluid become convectively unstable while those of low Prandtl number fluid become hydrodynamically unstable. The work includes numerical simulations of steady, high Marangoni number flows in unit aspect ratio boxes and asymptotic solutions in large boxes. Furthermore, the effect of surface contamination on the steady thermocapillary flows was examined. This fundamental study focused on fluid dynamical systems used to understand events in the flow of melts in float-zone geometries both on Earth and in microgravity environments.

Davis, S. H.↗

NASA NTRS1987

Discrete element weld model, phase 2

A numerical method was developed for analyzing the tungsten inert gas (TIG) welding process. The phenomena being modeled include melting under the arc and the flow in the melt under the action of buoyancy, surface tension, and electromagnetic forces. The latter entails the calculation of the electric potential and the computation of electric current and magnetic field therefrom. Melting may occur at a single temperature or over a temperature range, and the electrical and thermal conductivities can be a function of temperature. Results of sample calculations are presented and discussed at length. A major research contribution has been the development of numerical methodology for the calculation of phase change problems in a fixed grid framework. The model has been implemented on CHAM's general purpose computer code PHOENICS. The inputs to the computer model include: geometric parameters, material properties, and weld process parameters.

Prakash, C.↗

NASA NTRS2001

Metastability of Liquid Water on Mars

This talk reviews reasonable spatial and temporal scales for melting and flowing of water on Mars, and relates them to plausible martian conditions. Additional information is contained in the original extended abstract.

Hecht, M. H.↗

NASA NTRS2004

Traveling Magnetic Field Applications for Vertical Bridgman Growth: Modeling and Experiment

Traveling magnetic fields offer a direct control of the metallic melt meridional flow in long cylinders. It induces the Lorentz body force that can counteract with the buoyancy force induced by radial temperature non-uniformity. It can significantly offset a natural convection in the system, or it can even set up the flow in opposite direction, thus affecting the interface shape, the growth rate and macrosegregation. Results of our numerical modeling of the Vertical Bridgman crystal growth of InSb will be discussed. The experimental part of this investigation will address the effect of the applied traveling magnetic fields on the interface shape of InSb crystals. Specifics of the growth apparatus design for this research will be provided in details.

Mazuruk, Konstantin↗

NASA NTRS2006

Ar-Ar Dating of Martian Meteorite, Dhofar 378: An Early Shock Event?

Martian meteorite, Dhofar 378 (Dho378) is a basaltic shergottite from Oman, weighing 15 g, and possessing a black fusion crust. Chemical similarities between Dho378 and the Los Angeles 001 shergottite suggests that they might have derived from the same Mars locale. The plagioclase in other shergottites has been converted to maskelenite by shock, but Dho378 apparently experienced even more intense shock heating, estimated at 55-75 GPa. Dho378 feldspar (approximately 43 modal %) melted, partially flowed and vesiculated, and then partially recrystallized. Areas of feldspathic glass are appreciably enriched in K, whereas individual plagioclases show a range in the Or/An ratio of approximately 0.18-0.017. Radiometric dating of martian shergottites indicate variable formation times of ~160-475 Myr, whereas cosmic ray exposure (CRE) ages of shergottites indicate most were ejected from Mars within the past few Myr. Most determined Ar-39-Ar-40 ages of shergottites appear older than other radiometric ages because of the presence of large amounts of martian atmosphere or interior Ar-40. Among all types of meteorites and returned lunar rocks, the impact event that initiated the CRE age very rarely reset the Ar-Ar age. This is because a minimum time and temperature is required to facilitate Ar diffusion loss. It is generally assumed that the shock-texture characteristics in martian meteorites were produced by the impact events that ejected the rocks from Mars, although the time of these shock events (as opposed to CRE ages) are not directly dated. Here we report Ar-39-Ar-40 dating of Dho378 plagioclase. We suggest that the determined age dates the intense shock heating event this meteorite experienced, but that it was not the impact that initiated the CRE age.

Park, J.↗

NASA NTRS2007

Metallic Concepts for Repair of Reinforced Carbon-Carbon Space Shuttle Leading Edges

The Columbia accident has focused attention on the critical need for on-orbit repair concepts for wing leading edges in the event that potentially catastrophic damage is incurred during Space Shuttle Orbiter flight. The leading edge of the space shuttle wings consists of a series of eleven panels on each side of the orbiter. These panels are fabricated from reinforced carbon-carbon (RCC) which is a light weight composite with attractive strength at very high temperatures. The damage that was responsible for the loss of the Colombia space shuttle was deemed due to formation of a large hole in one these RCC leading edge panels produced by the impact of a large piece of foam. However, even small cracks in the RCC are considered as potentially catastrophic because of the high temperature re-entry environment. After the Columbia accident, NASA has explored various means to perform on-orbit repairs in the event that damage is sustained in future shuttle flights. Although large areas of damage, such as that which doomed Columbia, are not anticipated to re-occur due to various improvements to the shuttle, especially the foam attachment, NASA has also explored various options for both small and large area repair. This paper reports one large area repair concept referred to as the "metallic over-wrap." Environmental conditions during re-entry of the orbiter impose extreme requirements on the RCC leading edges as well as on any repair concepts. These requirements include temperatures up to 3000 F (1650 C) for up to 15 minutes in the presence of an extremely oxidizing plasma environment. Figure 1 shows the temperature profile across one panel (#9) which is subject to the highest temperatures during re-entry. Although the RCC possesses adequate mechanical strength at these temperatures, it lacks oxidation resistance. Oxidation protection is afforded by converting the outer layers of the RCC to SiC by chemical vapor deposition (CVD). At high temperatures in an oxidizing environment, the SiC layer forms a protective SiO2 scale. However, CVD processing to form the SiC layer can result in the formation of small cracks in the outer surface. Hence, as a final fabrication step, a sodium silicate glass, known as "Type A," is applied as a sealant to fill any surface porosity and/or cracks in the coating and the outer portions of the RCC[1]. At relatively low temperatures, the Type A glass melts and flows into the cracks providing oxidation protection at the higher temperatures. In addition, the Type A coating, provides a "dark" coating with a high emissivity. This high emissivity allows the RCC to transfer heat by radiating outward to space as well as dispersing heat within the leading edge cavity. Lastly, the Type A possesses low catalycity which reduces surface temperatures by limiting oxygen recombination on the surface during re-entry.

Ritzert, Frank↗

NASA NTRS2013

Ceramic Adhesive and Methods for On-Orbit Repair of Re-Entry Vehicles

This adhesive is capable of repairing damaged leading edge components of reentry vehicles while in space, and is novel with regard to its ability to be applied in the vacuum of space, and in a microgravity environment. Once applied, the adhesive provides thermal and oxidation protection to the substrate (in this case, reinforced carbon/carbon composites, RCCs) during re-entry of a space vehicle. Although there may be many formulations for repair adhesives, at the time of this reporting, this is the first known adhesive capable of an on-orbit repair. The adhesive is an engineered ceramic material composed of a pre-ceramic polymer and refractory powders in the form of a paste or putty that can be applied to a scratched, cracked, or fractured composite surface, covering and protecting the damaged area. The adhesive is then "cured" with a heat cycle, thereby cross-linking the polymer into a hardened material and bonding it to the substrate. During the heat of reentry, the material is converted to a ceramic coating that provides thermal and oxidative stability to the repaired area, thus allowing the vehicle to pass safely from space into the upper atmosphere. Ceramic powders such as SiC, ZrB2 and Y2O3 are combined with allylhydridopolycarbosilane (AHPCS) resin, and are mixed to form a paste adhesive. The material is then applied to the damaged area by brush, spatula, trowel, or other means to fill cracks, gaps, and holes, or used to bond patches onto the damaged area. The material is then cured, in a vacuum, preferably at 250F (approximately equal to 121C) for two hours. The re-entry heating of the vehicle at temperatures in excess of 3,000F (approximately equal to 1,650C) then converts this material into a ceramic coating. This invention has demonstrated advantages in resistance to high temperatures, as was demonstrated in more than 100 arc-jet tests in representative environments at NASA. Extensive testing verified oxidation protection for the repaired substrate (RCC), and confirmed that the microstructure of the resulting repair leads to durability and resistance to melting or flow. Its processability and working life in a vacuum was demonstrated by NASA astronauts in glovebox processing studies, as well as on-orbit in the open space shuttle bay. All of these advantages increase the working life of NASA vehicles, as well as improve safety for any crew on a manned vehicle. The adhesive, trademarked NOAX(TM). or Non-Oxide Adhesive Experimental, flew on all space shuttle missions from Return To Flight (STS-114) until the final flight (STS- 135) as a crack repair material for the leading edges and nose cap of the vehicle. NOAX(TM) was patented under U.S. Patents 7,628,878 and 7,888,277.

Riedell, James A.↗

NASA NTRS2004

Metal-Silicate Segregation in Deforming Dunitic Rocks: Applications to Core Formation in Europa and Ganymede

Core formation is an important event in the evolution of a planetary body, affecting both the geochemical and geophysical properties of the body. Metal-silicate segregation could have proceeded either by settling of liquid metal through a magma ocean or by percolation of liquid metal through a solid silicate mantle. Percolation of metallic melt had previously been excluded as a viable segregation mechanism because metallic melts do not form an interconnected network under hydrostatic conditions, except at high melt fraction (>5 vol%), due to the high dihedral angle between metals and silicates (>60 ). Without an interconnected network, porous flow of metallic melt is impossible, leaving the magma ocean scenario as the only mechanism to form the core. Moment-of-inertia measurements of Europa and Ganymede from the Galileo probe indicate that they are differentiated. This evidence suggests that a method for segregating metals and silicates at temperatures low enough to retain volatile compounds must exist. We have investigated the effect of deformation on the distribution of metallic melts in silicates. We have deformed samples of olivine + 5-9 vol% Fe-S to strains of 2.5 in simple shear and find that the metallic melt segregates into melt-rich planes oriented at 20 to the shear plane. These metallic melt-rich bands are similar in structure to the silicate melt-rich bands reported by Holtzman, indicating that deformation can interconnect isolated metallic melt pockets and allow porous flow of non-wetting melts. Such a core formation process could have occurred in the jovian satellites.

Hustoft, J. W.↗

NASA NTRS1974

Float zone processing in a weightless environment

Results are given for investigations into: (1) the physical limits which set the maximum practical diameters of Si crystals that can be processed by the float-zone method in a near weightless environment, and (2) the economic impact of large, space-produced Si crystals on the electronics industry. The stability of the melt is evaluated. Heat transfer and fluid flow within the melt as dependent on the crystal size and the degree and type of rotation imparted to the melt are studied. Methods of utilizing the weightless environment for the production of large, stress-free Si crystals of uniform composition are proposed. The economic effect of large size Si crystals, their potential applications, likely utilization and cost advantages in LSI, integrated circuits, and power devices are also evaluated. Foreseeable advantages of larger diameter wafers of good characteristics and the possibilities seen for greater perfection resulting from stress-free growth are discussed.

Fowle, A. A.↗

NASA NTRS1990

Effect of a crystal-melt interface on Taylor-vortex flow

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case that the stationary outer cylinder is a crystal-melt interface rather than a rigid surface. A radial temperature difference is maintained across the liquid gap, and equations for heat transport in the crystal and melt phases are included to extend the ordinary formulation of this problem. The stability of this two-phase system depends on the Prandtl number. For small Prandtl number the linear stability of the two-phase system is given by the classical results for a rigid-walled system. For increasing values of the Prandtl number, convective heat transport becomes significant and the system becomes increasingly less stable. Previous results in a narrow-gap approximation are extended to the case of a finite gap, and both axisymmetric and nonaxisymmetric disturbance modes are considered. The two-phase system becomes less stable as the finite gap tends to the narrow-gap limit. The two-phase system is more stable to nonaxisymmetric modes with azimuthal wavenumber n = 1; the stability of these n = 1 modes is sensitive to the latent heat of fusion.

Mcfadden, G. B.↗

NASA NTRS2006

Chromite-Plagioclase Assemblages as a New Shock Indicator; Implications for the Shock and Thermal Histories of Ordinary Chondrites

Chromite in ordinary chondrites (OC) can be used as a shock indicator. A survey of 76 equilibrated H, L and LL chondrites shows that unshocked chromite grains occur in equant, subhedral and rounded morphologies surrounded by silicate or intergrown with metallic Fe-Ni and/or troilite. Some unmelted chromite grains are fractured or crushed during whole-rock brecciation. Others are transected by opaque veins; the veins form when impacts cause localized heating of metal-troilite intergrowths above the Fe-FeS eutectic (988 C), mobilization of metal-troilite melts, and penetration of the melt into fractures in chromite grains. Chromite-plagioclase assemblages occur in nearly every shock-stage S3-S6 OC; the assemblages range in size from 20-300 microns and consist of 0.2-20-micron-size euhedral, subhedral, anhedral and rounded chromite grains surrounded by plagioclase or glass of plagioclase composition. Plagioclase has a low impedance to shock compression. Heat from shock-melted plagioclase caused adjacent chromite grains to melt; chromite grains crystallized from this melt. Those chromite grains in the assemblages that are completely surrounded by plagioclase are generally richer in Al2O3, than unmelted, matrix chromite grains in the same meteorite. Chromite veinlets (typically 0.5-2 microns thick and 10-300 microns long) occur typically in the vicinity of chromite-plagioclase assemblages. The veinlets formed from chromite-plagioclase melts that were injected into fractures in neighboring silicate grains; chromite crystallized in the fractures and the residual plagioclase-rich melt continued to flow, eventually pooling to form plagioclase-rich melt pockets. Chromite-rich chondrules (consisting mainly of olivine, plagioclase-normative mesostasis, and 5-15 vol.% chromite) occur in many shocked OC and OC regolith breccias but they are absent from primitive type-3 OC. They may have formed by impact melting chromite, plagioclase and adjacent mafic silicates during higher-energy shock events. The melt was jetted from the impact site and formed droplets due to surface tension. Crystallization of these droplets may have commenced in flight, prior to landing on the parent-body surface. Chromite-plagioclase assemblages and chromite veinlets occur in 25 out of 25 shock-stage S1 OC of petrologic type 5 and 6 that I examined. Although these rocks contain unstrained olivine with sharp optical extinction, most possess other shock indicators such as extensive silicate darkening, numerous occurrences of metallic Cu, polycrystalline troilite, and opaque veins. It seems likely that these rocks were shocked to levels at least as high as shock-stage S3 and then annealed by heat generated during the shock event. During annealing, the olivine crystal lattices healed but other shock indicators survived. Published Ar-Ar age data for some SI OC indicate that many shock and annealing events occurred very early in the history of the parent asteroids. The common occurrence of shocked and annealed OC is consistent with collisions being a major mechanism responsible for metamorphosing OC.

Rubin, Alan E.↗

NASA NTRS1986

The effect of fluid flow due to the crystal-melt density change on the growth of a parabolic isothermal dendrite

The Ivantsov (1947) analysis of an isolated isothermal dendrite (with zero surface tension) growing into a supercooled liquid is extended to include the effects of the fluid flow due to volume contraction or expansion upon solidification. For an axisymmetric paraboloidal dendrite, an analytic solution to the Navier-Stokes equations is obtained. The magnitude of the flow is proportional to the relative density change epsilon, and the flow becomes negligible far from the surface of the dendrite. The temperature field consistent with this flow can also be found explicitly. The well-known expression that relates the dimensionless supercooling to the Peclet number in the absence of fluid flow is modified for nonzero epsilon, but the effect is of order epsilon and hence is seen to be minor for most values of epsilon and dimensionless supercooling that occur in practice.

Mcfadden, G. B.↗

NASA NTRS2001

Morphological Stability of Faceted Interfaces

The major focus of this investigation is to study the fundamentals of layer spreading mechanisms during growth of doped Ge (a facet forming material), and to determine the conditions for morphological instability of vicinal solid-liquid interfaces. The investigation will also lead to the determination of the effect of dopants on the layer growth kinetics, step free energy, and dopant capture by the advancing ledges. The theoretical treatment of growth of faceted interfaces indicates that the kinetics of a step on a growing vicinal interface considerably depends on its angle of inclination, the melt concentration, and characteristics of flow currents in the melt. The morphological stability of the interface also depends on these parameters, as well as on the density and spreading velocity of the steps. However, the treatment of the instability of the interface by the layer growth mechanism is rather difficult because it requires exact knowledge of the thermal and solutal fields, hydrodynamics of the melt, and supercooling at the interface. The results of recent space experiments of the principal investigator involving directional solidification of faceted Bi-Sn alloys have shown that the morphological stability of various crystallographic orientations is significantly affected by the anistropy in interfacial properties of the faceted alloy in general, and the interface kinetics in particular. These findings have also raised many important and fundamental questions, particularly with respect to the behavior of interfacial steps, which need to be addressed via additional groundbased and microgravity experiments. For the present investigation we will use a novel crystal growth technique which provides axial heat flux close to the solid-liquid boundary. The Axial Heat Processing (AHP) technique allows for precise control and determination of the heat and mass transfer close to the crystallization front, and the establishment of a planar interface over the entire cross-section of the growing crystal.

Abbaschian, Reza↗

NASA NTRS1993

Crystal growth of compound semiconductors in a low-gravity environment (InGaAs crystals) (M-22)

Compound semiconductor crystals, such as gallium arsenide and indium phosphide crystals, have many interesting properties that silicon crystals lack, and they are expected to be used as materials for optic and/or electro-optic integrated devices. Generally speaking, alloy semiconductors, which consist of more than three elements, demonstrate new functions. For example, values of important parameters, such as lattice constant and emission wavelength, can be chosen independently. However, as it is easy for macroscopic and/or microscopic fluctuations of composition to occur in alloy semiconductor crystals, it is difficult to obtain crystals having homogeneous properties. Macroscopic change of composition in a crystal is caused by the segregation phenomenon. This phenomenon is due to a continuous change in the concentration of constituent elements at the solid-liquid interfacing during solidification. On Earth, attempts were made to obtain a crystal with homogeneous composition by maintaining a constant melt composition near the solid-liquid interface, through suppression of the convection flow of the melt by applying a magnetic field. However, the attempt was not completely successful. Convective flow does not occur in microgravity because the gravity in space is from four to six orders of magnitude less than that on Earth. In such a case, mass transfer in the melt is dominated by the diffusion phenomenon. So, if crystal growth is carried out at a rate that is higher than the rate of mass transfer due to this phenomenon, it is expected that crystals having a homogeneous composition will be obtained. In addition, it is also possible that microscopic composition fluctuations (striation) may disappear because microscopic fluctuations diminish in the absence of convection. We are going to grow a bulk-indium gallium arsenide (InGaAs) crystal using the gradient heating furnace (GHF) in the first material processing test (FMPT). The structure of the sample is shown where InGaAs polycrystals in a crucible are doubly sealed in two quartz tubes for safety. The GHF consists of two zones, namely, high temperature and low temperature zones, which results in a large temperature gradient at the interface. Crystal growth is performed by moving the furnace (i.e. the temperature profile) from the left to right at a definite rate. Thus, we will grow crystals both on Earth and in space under the same conditions. As previously described, it is possible to obtain good quality crystals which are homogeneous in composition both macroscopically and microscopically due to the lack of convection in space. We are planning to study the effects of convection on crystal growth from a melt by comparing and characterizing the properties of crystals grown on Earth with those grown in space.

Tatsumi, Masami↗

NASA NTRS1999

Double Diffusive Convection in Materials Processing

A great number of crystals grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity (g-jitter). As a specific example, past HgCdTe crystal growth space experiments by Lehoczky and co-workers indicate radial compositional asymmetry in the grown crystals. In the case of HgCdTe the rejected component into the melt upon solidification is HgTe which is denser than the melt. The space grown crystals indicate the presence of three dimensional flow with the heavier HgTe-rich material clearly aligned with the residual gravity (0.55-1.55 micro g) vector. This flow stems from double-diffusive convection, namely, thermal and solutal buoyancy driven flow in the melt. The study of double-diffusive convection is multi-faceted and rather vast. In our investigation, we seek to focus on one specific aspect of this discipline that is of direct relevance to materials processing especially crystal growth, namely, the side ways heating regime. This problem has been widely studied, both experimentally and numerically, in the context of solar ponds wherein the system is characterized by a linear salt (solutal) gradient with an imposed lateral temperature gradient. The induced flow instabilities arise from the wide disparity between the fluid thermal diffusivity and the solute diffusivity. The extension of the analysis to practical crystal growth applications has however not been rigorously made and understood. One subtle but important difference in crystal growth systems is the fact that die system solute gradient is non-linear (typically exponential). Besides, the crystal growth problem has the added complexities of solidification, both lateral and longitudinal thermal gradients and segregation phenomena in systems where binary and ternary compounds are being grown. This paper treats the side ways heating problem alone in a model fluid system. Results from detailed numerical calculations, mainly two dimensional are provided. The interactions between a non-linear solute gradient and an imposed transverse thermal gradient are investigated. The buoyancy effects are treated in the traditional Boussinesq approximation and also in a more complete density formulation to address recent concerns of the first approach especially in simulations of the system response in a reduced gravity environment. Detailed flow, temperature and solute field plots along with heat and mass transfer results are presented in the paper. Implications to practical crystal growth systems as discerned from the modeling results are also explored and reported.

Ramachandra, Narayanan↗

NASA NTRS1982

Natural convection in melt crystal growth - The influence of flow pattern on solute segregation

The results of two lines of research aimed at calculating the structure of the flows driven by buoyancy in small-scale crystal growth systems and at understanding the coupling between these flows, the shape of the solidification interface, and dopant segregation in the crystal are reviewed. First, finite-element methods are combined with computer-aided methods for detecting multiple steady solutions to analyze the structure of the buoyancy-driven axisymmetric flows in a vertical cylinder heated from below. This system exhibits onset of convection, multiple steady flows, and loss of the primary stable flow beyond a critical value of the Rayleigh number. Second, results are presented for calculations of convection, melt/solid interface shape, and dopant segregation within a vertical ampoule with thermal boundary conditions that represent a prototype of the vertical Bridgman growth system.

Brown, R. A.↗

NASA NTRS1995

The role of silver in the processing and properties of Bi-2212

The influence of the silver content and the oxygen partial pressure on the solidus temperature and the weight loss during melting of Bi2Sr2Ca1Cu2O(x) has been examined by means of DTA and TGA. By decreasing the oxygen partial pressure the solidus is lowered (e.g. del T = 59 C by decreasing pO2 from 1 atm to 0.001 atm) and the weight loss is increased. The addition of silver causes two effects: (1) the solidus is further decreased (e.g. 2 wt% Ag lower T (solidus) by up to 25 C, depending on the oxygen partial pressure); and (2) the weight loss during melting is reduced. Thick films (10-20 micron in thickness) with 0 and 5 wt% silver and bulk samples with) and 2.7 wt% silver were melt processed in flowing oxygen on a silver substrate in the DTA, allowing the observation of the melting process and a good temperature control. The critical current densities are vigorously dependent on the maximum processing temperature. The highest j(sub c) in thick films (8000 A/sq cm at 77 K, O T) was reached by melting 7 C above the solidus temperature. The silver addition shows no significant effect on the processing parameters or the superconducting properties. The highest j(sub c) for bulk samples (1 mm in thickness) was obtained by partial melting at 900 C or 880 C, depending on the silver content of the powder (0 or 2.7 wt%). The j(sub c) of the samples is slightly enhanced from 1800 A/sq cm (at 77 K, O T) to 2000 A/sq cm by the silver addition. To be able to reach at least 80% of the maximum critical current density, the temperature has to be controlled in a window of 5 C for thick films and 17 C for bulk samples.

Lang, TH.↗

NASA NTRS1984

Coupled convective instabilities at crystal-melt interfaces

The stability of the parallel flow between a vertical crystal-melt interface and a vertical wall held at a temperature above the melting point of the crystal is analyzed for Prandtl numbers, P, ranging from 0.01 to 100. Three modes of instability occur: (1) a buoyant mode, (2) a shear mode, and (3) a coupled crystal-melt mode. The buoyant and shear modes are similar to those that occur for flow between two vertical rigid walls held at different temperatures. For Prandtl numbers greater than approximately two, the coupled crystal-melt mode occurs at a lower Grashof number than the other two modes. Specific results are given for succinonitrile (P = 22.8) and lead (P = 0.0225). These calculations and similar calculations for a cylindrical geometry were motivated by and are in general agreement with recent experiments on succinonitrile.

Coriell, S. R.↗