Melting and solidification of a metal system in a rectangular cavity
TL;DR: In this article, the role of natural convection on solid-liquid interface motion during melting and solidification of Lipowitz metal in a rectangular cavity was studied, and measurements of both temperature distributions and temperature fluctuations were used as a qualitative indication of the natural convective flow regimes and structures of melt during phase transformation.
About: This article is published in International Journal of Heat and Mass Transfer.The article was published on 1984-01-01. It has received 112 citations till now. The article focuses on the topics: Natural convection.
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TL;DR: In this article, the melting of pure gallium in a rectangular cavity has been numerically investigated using the enthalpy-porosity approach for modeling combined convection-diffusion phase change.
Abstract: The melting of pure gallium in a rectangular cavity has been numerically investigated using the enthalpy-porosity approach for modeling combined convection-diffusion phase change. The major advantage of this technique is that it allows a fixed-grid solution of the coupled momentum and energy equations to be undertaken without resorting to variable transformations. In this work, a two-dimensional dynamic model is used and the influence of laminar natural-convection flow on the melting process is considered. Excellent agreement exists between the numerical predictions and experimental results available in the literature. The enthalpy-porosity approach has been found to converge rapidly, and is capable of producing accurate results for both the position and morphology of the melt front at different times with relatively modest computational requirements. These results may be taken to be a sound validation of this technique for modeling isothermal phase changes in metallurgical systems.
1,377 citations
TL;DR: In this paper, an enthalpy formulation for convection/diffusion phase change is developed, where latent heat effects are isolated in a source term, and three alternative schemes for achieving this are presented.
Abstract: An enthalpy formulation for convection/diffusion phase change is developed. The essential feature of this formulation is that latent heat effects are isolated in a source term. This formulation is applicable to a general convection/diffusion phase change, i.e. it is valid in the cases of evolution of latent heat either at an isothermal temperature or over a temperature range. Before implementation of the enthalpy formulation, a technique is required to ensure that velocities predicted to be in a solid region actually take the value zero. Three alternative schemes for achieving this are presented.
The enthalpy formulation and velocity correction schemes are independent of the numerical technique. As an example of how the method can be implemented a control volume numerical discretization is chosen. This implementation is applied to two test problems: a solidification phase change in a cavity under conduction and the same phase change under conduction and natural convection. The natural convection problem is used to compare the performances of the various velocity correction schemes. The results of the problems are in good agreement with available analytical solutions and previous numerical solutions.
539 citations
01 Oct 1992-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this article, a general implicit source-based enthalpy method is presented for the analysis of solidification systems, which is both robust and efficient, and is illustrated by application to a number of problems taken from recent metallurgical literature.
Abstract: In the present work, a general implicit source-based enthalpy method is presented for the analysis of solidification systems. The proposed approach is both robust and efficient. The performance of the method is illustrated by application to a number of problems taken from recent metallurgical literature.
241 citations
TL;DR: In this article, the authors investigated the dynamic thermal behavior of phase change material (PCM) melting in a rectangular enclosure at various inclination angles and found that the inclination has a significant effect on the formation of natural convection currents and consequently on the heat transfer rate and melting time of the PCM.
236 citations
TL;DR: Tarzia et al. as discussed by the authors presented a bibliografía on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems, which contains 5869 titles referring to 588 scientific journals, 122 books, 88 symposia, 30 collections, 59 thesis and 247 technical reports.
Abstract: We present a bibliography on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems. It contains 5869 titles referring to 588 scientific Journals, 122 books, 88 symposia (having at least 3 contributions on the subject), 30 collections, 59 thesis and 247 technical reports. It tries to give a comprehensive account of the western existing mathematicalphysical-engineering literature on this research field. RESUMEN Se presenta una bibliografía sobre problemas de frontera móvil y libre para la ecuación del calor-difusión, en particular sobre el problema de Stefan y problemas relacionados. Contiene 5869 títulos distribuidos en 588 revistas científicas, 122 libros, 88 simposios (teniendo al menos 3 contribuciones en el tema), 30 colecciones, 59 tesis y 247 informes técnicos o prepublicaciones. Se da un informe amplio de la bibliografía matemática, física y de las ingenierías existente en occidente sobre este tema de investigación. Primary Mathematics Subject Classification Number (*): 35R35, 80A22 Secondary Mathematics Subject Classification Number (*): 35B40, 35C05, 35C15, 35Kxx, 35R30, 46N20, 49J20, 65Mxx, 65Nxx, 76R50, 76S05, 76T05, 93C20. (*) Following the 1991 Mathematics Subject Classification compiled by Mathematical Reviews and Zentralblatt fur Mathematik. Primary key words: Enthalpy formulation or method, Filtration, Free boundary problems, Freezing, Melting, Moving boundary problems, Mushy region, Phase-change problem, Solidification, Stefan problem. Secondary key words: Continuous mechanics, Diffusion process, Functional analysis, Heat conduction, Mathematical methods, Numerical methods, Partial differential equations, Variational inequalities, Weak solutions. Palabras claves primarias: Método o formulación en entalpía, Filtración, Problemas de frontera libre, Congelación, Derretimiento, Problemas de frontera móvil, Región pastosa, Problema de cambio de fase, Solidificación, Problema de Stefan. Palabras claves secundarias: Mecánica del continuo, Procesos difusivos, Análisis funcional, Conducción del calor, Métodos matemáticos, Métodos numéricos, Ecuaciones diferenciales a derivadas parciales, Inecuaciones variacionales, Soluciones débiles. El manuscrito fue recibido y aceptado en octubre de 1999. D.A. Tarzia, A bibliography on FBP. The Stefan problem, MAT Serie A, # 2 (2000). 3
224 citations
References
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TL;DR: In this article, an analysis of multidimensional melting is performed which takes account of natural convection induced by temperature differences in the liquid melt, and the results differ decisively from those corresponding to a conventional pure-conduction model of the melting problem.
Abstract: An analysis of multidimensional melting is performed which takes account of natural convection induced by temperature differences in the liquid melt. Consideration is given to the melt region created by a heated vertical tube embedded in a solid which is at its fusion temperature. Solutions were obtained by an implicit finite-difference scheme tailored to take account of the movement of the liquid-solid interface as melting progresses. The results differed decisively from those corresponding to a conventional pure-conduction model of the melting problem. The calculated heat transfer rate at the tube wall decreased at early times and attained a minimum, then increased and achieved a maximum, and subsequently decreased. This is in contrast to the pure conduction solution whereby the heat transfer rate decreases monotonically with time. The thickness of the melt region was found to vary along the length of the tube, with the greatest thickness near the top. This contrasts with the uniform thickness predicted by the conduction solution. These findings indicate that natural convection effects, although unaccounted for in most phase change analyses, are of importance and have to be considered.
245 citations
01 Sep 1971
TL;DR: In this paper, the authors provide theory and data needed by the thermal design engineer to bridge the gap between research achievements and actual flight systems, within the limits of the current state of the art of phase change materials (PCM) technology.
Abstract: This handbook is intended to provide theory and data needed by the thermal design engineer to bridge the gap between research achievements and actual flight systems, within the limits of the current state of the art of phase change materials (PCM) technology. The relationship between PCM and more conventional thermal control techniques is described and numerous space and terrestrial applications of PCM are discussed. Material properties of the most promising PCMs are provided; the purposes and use of metallic filler materials in PCM composites are presented; and material compatibility considerations relevant to PCM design are included. The engineering considerations of PCM design are described, especially those pertaining to the thermodynamic and heat transfer phenomena peculiar to PCM design. Methods of obtaining data not currently available are presented. The special problems encountered in the space environment are described. Computational tools useful to the designer are discussed. In summary, each aspect of the PCM problem important to the design engineer is covered to the extent allowed by the scope of this effort and the state of the art.
154 citations
TL;DR: In this paper, the phase-change boundary motion of n-octadecane has been studied experimentally and analytically in a rectangular test cell suitable for photographic observations.
105 citations
TL;DR: In this paper, experiments were performed for freezing under conditions where the liquid phase is either above or at the fusion temperature (i.e., superheated or nonsuperheated liquid).
Abstract: Experiments were performed for freezing under conditions where the liquid phase is either above or at the fusion temperature (i.e., superheated or nonsuperheated liquid). The liquid was housed in a cylindrical containment vessel whose surface was maintained at a uniform, time-invariant temperature during a data run, and the freezing occurred on a cooled vertical tube positioned along the axis of the vessel. The phase change medium was n-eicosane, a paraffin which freezes at about 36/sup 0/C (97/sup 0/F). In the presence of liquid superheating, the freezing process is drastically slowed and ultimately terminated by the natural convection in the liquid. The terminal size of the frozen layer an the time at which freezing terminates can be controlled by setting the temperature parameters which govern the intensity of the natural convection. The stronger the natural convection, the thinner the frozen layer an the shorter the freezing time. In the absence of liquid superheating, a cylindrical frozen layer grows continuously as predicted by theory, but the growth rate is higher than the predictions because of the presence of whisker-like dendrites on the freezing surface.
68 citations