On the use of Green's functions for solving melting or solidification problems

Chuang, Yu-Lin; Szekely, J.

doi:10.1016/0017-9310(71)90178-5

Cited by 54 publications

(7 citation statements)

References 4 publications

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“…For multidimensional problems, mesh adjustment is necessary but much easier to perform than in standard domain methods. The solution of Stefan condition based on boundary integral methods started in the early 1970s with papers by Chuang and Szekely . Other applications include those of Wrobel, Heinlein et al, Hsieh et al, and Ahmed and Meshrif …”

Section: Heat Transfer Analysismentioning

confidence: 99%

Review on heat transfer analysis in thermal energy storage using latent heat storage systems and phase change materials

2018

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Summary Thermal energy storage (TES) is a technology that stocks thermal energy by heating or cooling a storage medium so that the stored energy can be used later for heating and cooling applications and for power generation. TES has recently attracted increasing interest to thermal applications such as space and water heating, waste heat utilisation, cooling, and air conditioning. Phase change materials (PCMs) used for the storage of thermal energy as latent heat are special types of advanced materials that substantially contribute to the efficient use and conservation of waste heat and solar energy. This paper provides a comprehensive review on the development of latent heat storage (LHS) systems focused on heat transfer and enhancement techniques employed in PCMs to effectively charge and discharge latent heat energy, and the formulation of the phase change problem. The main categories of PCMs are classified and briefly described, and heat transfer enhancement technologies, namely dispersion of low‐density materials, use of porous materials, metal matrices and encapsulation, incorporation of extended surfaces and fins, utilisation of heat pipes, cascaded storage, and direct heat transfer techniques, are also discussed in detail. Additionally, a two‐dimensional heat transfer simulation model of an LHS system is developed using the control volume technique to solve the phase change problem. Furthermore, a three‐dimensional numerical simulation model of an LHS is built to investigate the quasi‐steady state and transient heat transfer in PCMs. Finally, several future research directions are provided.

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Section: Heat Transfer Analysismentioning

confidence: 99%

Review on heat transfer analysis in thermal energy storage using latent heat storage systems and phase change materials

2018

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“…In both publications, they solved the heat transfer Equation for spherical coordinates and with the application of the Greeńs function method. The theory using Greeńs functions for solving melting or solidification problems was described in detail by Chuang and Szekely and Chuang et al For the validation of their numerical simulation, they carried out experiments with spherical samples 0.015 m in diameter in a 20 kg induction furnace under argon atmosphere. Through a fitting process with the numerical model, using constant material data, a heat transfer coefficient of 32 000 Wm −2 K −1 was determined for metal spheres.…”

Section: Heat Transfermentioning

confidence: 99%

“…The use of Greeńs functions for solving moving boundary problems like melting or solidification processes was mathematically described by Chuang and Szekely ref. . In some simple examples, using constant physical and transport parameters, the melting of a steel slab in carbon‐saturated hot metal was realized.…”

Section: Modeling Of the Scrap Melting And Dissolution Processmentioning

confidence: 99%

A Review of Steel Scrap Melting in Molten Iron‐Carbon Melts

Penz¹,

Schenk

2019

steel research int.

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In the current economic climate, the recycling of steel scrap is become one of the most interesting tasks for the optimization of integrated steel plants. Steelmaking aspects such as jet/bath interaction, slag formation or foaming, lime dissolution as well as slag/metal reactions have received more attention in recent years than the melting and dissolution phenomena of steel scrap in molten steel baths. Since the dynamic modeling of steelmaking processesespecially the Linz Donawitz oxygen steelmaking process (LD) -is becoming more important, interest in the melting and dissolution behaviour is increasing. Several researchers have investigated the complex transactions of coupled heat and mass transfer in the past. Small-scale experiments are carried out under conditions where only mass transfer or heat transfer were considered. A few authors have reported on pilot-scale investigations or commercial converters. The coupled heat and mass transfer has also been analyzed by several authors in mathematical models and numerical simulations. The present paper reviews the research on steel scrap melting and dissolution done in the last 50 years. A summary of all reported heat and mass transfer coefficients will be given and the differences between natural and forced convection will be explained. In addition, an overview of recently published numerical simulation describing the problem will give an outlook for future work.

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“…The first of Crank's approaches consists of a preliminary transformation which fixes the boundary and an implicit finite-difference approximation in the so-obtained domain; the second approach consists of Lagrange interpolation and finite difference approximations to space derivatives at unequally spaced points. Among the so-called boundary integral methods, we recall the work of Chuang and Szekely [4]. Their semianalytical method is, however, only formal.…”

Section: Introductionmentioning

confidence: 99%

“…Although quite simple, the one-phase Stefan problems occurring in slabs still provide realistic models for describing phenomena of practical interest such as, for instance, melting and solidification processes in metallurgy, especially when ablation is present (cf. [4], [27]), and foodstuff freezing technology. Moreover, these models may represent an intermediate step in solving more complicate problems, such as two-dimensional problems, e.g.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution for the one-phase Stefan problem by Piecewise constant approximation of the interface

Sartoretto

Spigler

1990

Computing

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Numerische Liisung des Ein-Phasen Stefan Problems dureh stiiekweise konstante Approximation derInterphase. Das klassische ein dimensionale Ein-Phasen Stefan Problem wird numerisch fiber wachsende Rechtecke Rj gelrst, die yon der Stefan Bedingung geregelt werden. Dieses Verfahren beruht auf einer Methode, die von E. Di Benedetto und R. Spigler 1983 entwickelt wurde. Die praktische Implementierung beruht auf einer Darstellung mittels thermischer Potentiale der Lrsung uJ(x, t) der Whrmegleichung in Rj. Der Wert u~ (xj,j3t), der das (j + 1)-ste Rechteck bestimmt, wird analytisch durch die explizite L6sung einer Integralgleichung berechnet. Die Lrsung in Rj +1 wird durch numerische Berechnung eines anderen Integralausdruckes bestimm t. Der Algorithmus wird an zwei Problemen getestet, deren L6sung explizit bekannt ist. Die Konvergenz, die Stabilit~it und die Konvergenzgeschwindgkeit ffir •x---, O, At--, 0 werden ebenfalls getestet und graphisch dargestellt.

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On the use of Green's functions for solving melting or solidification problems

Cited by 54 publications

References 4 publications

Review on heat transfer analysis in thermal energy storage using latent heat storage systems and phase change materials

Review on heat transfer analysis in thermal energy storage using latent heat storage systems and phase change materials

A Review of Steel Scrap Melting in Molten Iron‐Carbon Melts

Numerical solution for the one-phase Stefan problem by Piecewise constant approximation of the interface

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