Planar or radial freezing with solid-solid transitions and convective heating atthe solid-liquid interface
01 Jan 1984-Numerical Heat Transfer Part A-applications (Taylor & Francis Group)-Vol. 7, Iss: 1, pp 17-38
TL;DR: In this paper, numerical solutions for planar or radial freezing on a cooled wall or cylinder maintained at a uniform temperature lower than the fusion temperature were obtained by using an implicit/explicit method developed in the preceding paper.
Abstract: Numerical solutions have been carried out for planar or radial freezing on a cooled wall or cylinder maintained at a uniform temperature lower than the fusion temperature. The solutions were obtained by using an implicit/explicit method developed in the preceding paper in this issue. Results are presented for the frozen layer thick-ness, the instantaneous heat flux at the cooled surface, and the time-integrated heat transfer at the surface, all as a function of time from the beginning of the freezing period. These quantities are normalized in various ways to illuminate their short-time and long-time behaviors and to enable comparisons between planar and radial freezing. Convection at the solid-liquid interface had virtually no effect on the freezing process at short times, but at longer times the convection significantly slowed the freezing and ultimately terminated it. Solid-solid transitions tended to slow the freezing and also to increase the heat transfer at the cooled surface.
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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
TL;DR: In this article, a two-dimensional model for the phase change, conduction based heat transfer problem around a tube immersed in the pcm is presented, where the energy equation is written in the enthalpy form, and the heat and flow problems are coupled by an energy balance on the fluid element flowing inside the tube.
94 citations
TL;DR: In this paper, an experimental and numerical study on ice banks of the parallel plate type with the objective of identifying the relative importance of the geometrical and operational parameters and their influence on the performance of the ice bank is presented.
25 citations
TL;DR: Synthese bibliographique et Bibliographie des publications mondiales sur le transfert de chaleur en 1984 as mentioned in this paper, et al., 1984
12 citations
01 Jan 2023
TL;DR: In this paper , the authors presented the results of a numerical investigation on the thermal performance of a latent heat storage unit of cylindrical annular geometry and alternate fins including the effects of the geometrical and operational parameters.
Abstract: This paper presents the results of a numerical investigation on the thermal performance of a latent heat storage unit of cylindrical annular geometry and alternate fins including the effects of the geometrical and operational parameters. In the storage unit considered, the water as the phase change material is allocated in the shell while the working fluids flow in the inner tube and the outer shell. The mathematical model is based upon two dimensional formulation of the pure conduction based phase change around an externally and internally finned cylinders. The numerical solution is realized using the finite control volume method and the ADI scheme. The coupling of the phase change problem with the two working fluids, is obtained by energy balance on the respective fluid and phase changing elements, and consequently the fluid bulk temperature is determined in terms of the time and space. The numerical predictions are compared with available results due to other authors in an attempt to validate the present model. The solidified/melt mass fraction, the energy stored and the temperature profiles are analyzed in terms of the variation in the geometry, number of fins, the annular spacing, the Biot and Stefan numbers, and Reynolds numbers of the working fluids.
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TL;DR: In this paper, the authors describe the instantaneous frozen layer thickness and temperature profile in solidified layer obtained by iteration technique using iteration technique and iterative technique, and show that the thickness of the frozen layer can be estimated by iteration.
69 citations
TL;DR: In this article, a computationally efficient and highly accurate solution scheme for phase change problems is described which combines an implicit treatment of the temperature field equations with an explicit treatment of interface energy balance (s).
Abstract: A computationally efficient and highly accurate solution scheme for phase-change problems is described which combines an implicit treatment of the temperature field equations with an explicit treatment of the interface energy balance (s). This scheme avoids the iterative interaction between the field and interface solutions which characterizes a fully implicit treatment. No time-step limitations were encountered in the wide range of numerical solutions that were carried out with the methodology. The accuracy characteristics were established by comparisons with alternative solutions of a number of specific problems involving plane or radial freezing, one or two solid phases, and, in some cases, convective heating at the solid-liquid interface. Depending on the problem, the alternative solutions were analytical, semianalytical, or numerical. The accuracy level of the solid layer thicknesses given by the solution scheme were found to be in the 0.1% range.
30 citations
18 citations
01 Jan 1974
5 citations