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

Publisher Summary The basic characteristics of heat transfer between dispersed and continuous media are of both scientific and practical interest. The advantages of direct-contact heat transfer over the conventional processes using metallic transfer surfaces have lately stimulated research on its utilization for water desalination projects. Despite intensive efforts toward better understanding of transfer phenomena between drops and continuous media, accurate prediction of the transfer coefficients for a given system can as yet only be hoped for. Nevertheless, accumulated experience may provide an indication of the transfer mechanism to be encountered and the relevant coefficients may be estimated accordingly. This chapter discusses heat transfer to drops moving in a constant-temperature field and continuously varying temperature field. Heat is transferred to drops and bubbles with simultaneous phase change. While discussing about constant-temperature field, three models are taken into account: rigid drop, completely mixed drop, and drop with internal circulation. Work on direct-contact heat exchangers was stimulated earlier by the quest for economic water-desalination units. Multiphase exchange, where latent heat is transferred among the immiscible fluids, has been effectively used in direct-contact freezing units in which a dispersed volatile fluid evaporates in the saline water with simultaneous freezing of part of the water.

Direct Contact Heat Transfer Between Immiscible Liquids

Heat transfer prediction for a direct contact ice thermal energy storage

Vaporization process of single drops of pentane or furan in an aqueous glycerol has been studied photographically in the region where the geometrically simple configuration and rectilinear motion of vaporizing two-phase bubbles are realized. The instantaneous velocity of rise of two-phase bubbles agreed approximately with Stokes' theory in the range Re < 1. The liquid-liquid interfacial area takes almost a constant value slightly higher than the initial surface area of the liquid drop in the range below 10% of the vaporization ratio, and then reduces gradually. The vaporization does not bring an effective increase of heat transfer area.

Vaporization of single liquid drops in an immiscible liquid Part I: Forms and motions of vaporizing drops

Turbulent direct-contact heat transfer between two immiscible fluids

Transfer characteristics are presented for a perforated plate-spray column in which a volatile dispersed phase evaporates while rising in the continuous, counterflowing, immiscible phase. Optimal column heights, volumetric transfer coefficients, holdup, and foam heights are reported as functions of flow rate and temperature approach for a pentane-water system, A comparison with related studies is presented.

Direct contact heat transfer with change of phase: Spray‐column studies of a three‐phase heat exchanger

The initial drop size of volatile fluids evaporating within immiscible, nonvolatile liquids was experimentally related to the overall heat transfer coefficient in single and multiparticle systems. Coalescence and turbulence diminish the effects of the initial size, which are thus limited to the lower part of the exchanger where single-drop characteristics are maintained. Condensation data of single bubbles are in good agreement with the single-drop relationship.

Yehuda Gat

Papers

Direct contact heat transfer with change of phase: Spray‐column studies of a three‐phase heat exchanger

Direct contact heat transfer with change of phase: Effect of the initial drop size in three-phase heat exchangers