Review on thermal energy storage with phase change: materials, heat transfer analysis and applications

The major methods of mathematical modelling of solidification and melting problems are reviewed in this paper. Different analytical methods, nowadays still used as standard references to validate numerical models, are presented. Various mathematical formulations to numerically solve solidification and melting problems are categorized. Relative merits and disadvantages of each formulation are analysed. Recent advances in modelling solidification and melting problems associated with convective motion of liquid phase are discussed. Based on this comprehensive survey, basic guidelines are outlined to choose a correct mathematical formulation for solving solidification and melting problems.

https://iopscience.iop.org/article/10.1088/0965-0393/4/4/004/pdf

Mathematical modelling of solidification and melting: a review

Latent thermal energy storage is one of the favorable kinds of thermal energy storage methods considered for renewable energy source utilization, as in solar photothermal systems. Heat is ...

Characterization of Alkanes and Paraffin Waxes for Application as Phase Change Energy Storage Medium

Numerical study of PCM solidification in a triplex tube heat exchanger with internal and external fins

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

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A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems

Melting from an electrically heated horizontal cylinder embedded in a paraffin (n-octadecane, fusion temperature 301·3 °K) has been studied experimentally. The shape of the solid-liquid interface has been determined photographically, and the local heat transfer coefficients have been measured using a shadowgraph technique. The experiments provide conclusive evidence of the important role played by natural convection in melting a solid due to an embedded cylindrical heat source. The four distinct pieces of quantitative evidence which contribute to this conclusion are the melt shape, surface temperature, local and average heat transfer coefficients and their variation with time.The experimental findings prove the importance of natural convection in phase change problems involving melting and indicate that continued practice of neglecting the effects in the analysis of such problems does not appear reasonable. Natural convection should be considered in analysis and design of systems involving phase change.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112079002172

An experimental investigation of natural convection in the melted region around a heated horizontal cylinder

Heat Transfer and Interface Motion During Melting and Solidification around a Finned Heat Source/Sink

Melting from an array of three staggered, electrically heated cylinders imbedded in a paraffin (n-octadecane) has been studied. The shape of the melting front has been determined photographically, and the local heat transfer coefficients were measured using a shadowgraph technique. The experiments provide conclusive evidence of the important role played by natural convection on the timewise variation of the melt shape, the surface temperature and the instantaneous local as well as circumferentially averaged heat transfer coefficients around the imbedded heat sources. After a common solid-liquid interface is formed around the cylinders, natural convection circulation around each cylinder interacts strongly with the other two cylinders. The arrangement of heat sources affects significantly the melt shape but the circumferentially averaged instantaneous heat transfer coefficients differ only by about 10 percent for the two arrangements studied. The experimental findings indicate that natural convection effects are important and should be considered in analysis and design of systems involving phase change.

A. G. Bathelt

Papers

An experimental investigation of natural convection in the melted region around a heated horizontal cylinder

Heat Transfer and Interface Motion During Melting and Solidification around a Finned Heat Source/Sink

Latent Heat-of-Fusion Energy Storage: Experiments on Heat Transfer from Cylinders During Melting

Heat transfer from cylinders during melting of a thermal energy storage material