Two-dimensional solidification with natural convection in the melt and convective and radiative boundary conditions
01 Jan 1981-Numerical Heat Transfer Part A-applications (Taylor & Francis Group)-Vol. 4, Iss: 4, pp 469-484
TL;DR: In this paper, the effect of natural convection on the heat transfer at the interface and on the movement and shape of the interface is found to be significant compared to the results obtained by neglecting NAT in the melt.
Abstract: Two-dimensional solidification in a rectangular enclosure has been analyzed, taking into account the effects of natural convection and considering the convective and radiative boundary conditions at the surface of the mold and at the top of the enclosure. The bottom is taken as insulated. The dimensionless equations governing the unsteady velocity profiles in the melt and the unsteady temperature profiles in the melt, the solid, and the mold are solved by finite-difference methods, using the alternating direction implicit technique for the vorticity and the stream function. The effect of natural convection on the heat transfer at the interface and on the movement and shape of the interface is found to be significant compared to the results obtained by neglecting natural convection in the melt.
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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 comparison of two frequently used computational techniques for solving phase-change problems is presented, where the governing equations for the conservation of mass, momentum, and energy are solved using a control-volume-based discretization scheme.
Abstract: A comparison of two frequently used computational techniques for solving phase-change problems is presented. The governing equations for the conservation of mass, momentum, and energy are solved using a control-volume-based discretization scheme. In Ike first approach, the physical space is mapped onto a simpler domain and the moving boundary is immobilized using Landau transformation. The computations are carried out on a uniform orthogonal grid in the transformed space using the stream function-vorticity formulation. The need to retain all the terms in the governing equations arising from the transformation, for an accurate simulation, is investigated. Simplifications in the governing equations have been used in the literature and are discussed. Both implicit and explicit methods are used to track the phase front. In the second approach, the computations are carried out on a uniform fixed grid in the physical space with primitive variables. The enthalpy-porosity formulation, with appropriate so...
130 citations
TL;DR: In this article, the authors present an analysis of the melting process in a rectangular enclosure, driven by the coupling of heat conduction in the solid phase and natural convection in the melt of the phase change material (PCM).
80 citations
TL;DR: In this article, the physical and thermodynamic bases of frost heave modeling are discussed, and a selection of specific mathematical models is discussed, in light of the points raised in the general discussion.
72 citations
TL;DR: In this article, a three-dimensional transient mathematical model is used to study the interaction of double-diffusive natural convection and non-equilibrium solidification of a binary mixture in a cubic enclosure cooled from a side.
69 citations
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3,125 citations
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
TL;DR: In this article, a general, implicit, numerical, marching procedure is presented for the solution of parabolic partial differential equations, with special reference to those of the boundary layer, where the main novelty lies in the choice of a grid which adjusts its width so as to conform to the thickness of the layer in which significant property gradients are present.
132 citations
01 Aug 1970
TL;DR: In this article, a formulation is given and computed solutions are presented for transient solidification accompanied by natural convection in a vertical slot, where the simplifying assumptions made limit the validity of the solutions to systems where GrPr < 500, i.e., to narrow slots or to low values of the superheat.
Abstract: A formulation is given and computed solutions are presented for transient solidification accompanied by natural convection in a vertical slot. It was found that appreciable fluid velocities may be produced by natural convection, the values of which could be comparable to the terminal rising velocities of typical nonmetallic inclusions. The simplifying assumptions made limit the validity of the solutions to systems where GrPr < 500,i.e., to narrow slots or to low values of the superheat; nonetheless, the results should be indicative of the effects of convection at much higher values of GrPr.
72 citations