Analysis of two-dimensional diffusion-controlled moving boundary problems

Duda, J. L.; Malone, Michael F.; Notter, Robert H.; Vrentas, J. S.

doi:10.1016/0017-9310(75)90182-9

Cited by 74 publications

(16 citation statements)

References 7 publications

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“…It is, however, convenient to use a coordinate transformation in order to immobilize the boundary as suggested by Duda et al (1975). It is, however, convenient to use a coordinate transformation in order to immobilize the boundary as suggested by Duda et al (1975).…”

Section: (3)mentioning

confidence: 99%

Gas absorption with instantaneous chemical reaction in a laminar falling film

1986

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Gas absorption in a laminar falling film with instantaneous chemical reaction with a reactant in solution has been theoretically analysed using a boundary immobilization technique. The profile of the reaction front, concentration distributions, the dimensionless quantity of gas absorbed and the enhancement factor have been computed for different values of the diffusivity ratio D and the concentration ratio p. Although the concentration distribution of the dissolved reactant is dependent on D and p, that for the dissolved gas is nearly independent of these parameters for small depth of penetration. The enhancement factor shows a convex profile for small D , an explanation for which has been provided.L'absorption du gaz dans un film tombant laminaire avec rkaction chimique instantanke impliquant un rkactif dans la solution, a fait I'objet d'une analyse thkorique utilisant une technique d'immobilisation aux limites. Le profil du front de reaction, les distributions des concentrations, la quantitt adimensionnelle de gaz absorbte et le facteur d'augmentation ont eti calculks pour diffkrentes valeurs du rapport des diffusivitks D et du rapport des concentrations p. Bien que la distribution de concentration du rkactif dissous dkpende de D et de p, celle du gaz dissous est presque indipendante de ces parametres pour des petites profondeurs de phktration. Le facteur d'augmentation indique un profil convexe pour des valeurs de D petites, ce pourquoi une explication est fournie.as absorption in a laminar falling film is of consid-

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Section: (3)mentioning

confidence: 99%

Gas absorption with instantaneous chemical reaction in a laminar falling film

1986

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“…Some references for analytical methods can be found in Goodman [4], Rasmussen [5]. Some examples for numerical approaches are found in Creyer [6], Furzeland [7,8], Aitchison [9,10], Landau [11], Gupta and Kumar [12], Ferris and Hill [13], Beaubauff and Chapman [14], Duda et al [15]. Öziş and Gülkaç [1,2] prepared a numerical method to solve the multi-dimensional phase change problems by an independent variable interchange which extension and as well as modification of Boadway's transformation.…”

Section: Introductionmentioning

confidence: 99%

İki-Boyutlu Konvektif Sınır Koşullu Erime Problemi İçin Nümerik Yaklaşım

Gülkaç¹

2017

SAÜ Fen Bilimleri Enstitüsü Dergisi

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ÖZBu çalışmada, daha önce çözdüğümüz, iki-boyutlu konvektif sınır koşullu erime probleminde, türevlerin bir kısmında açık yöntem kullanırken bir kısmında da kapalı yöntem kullanarak sonlu farklar oluşturulmuştur ve bu denklemlerin çözümü için bir iteratif yöntem geliştirilmiştir. Metod (x, y) koordinatlarında ikinci dereceden doğruluğa sahiptir. Bu metodla elde edilen sonuçlar, önceki araştırmacılar tarafından verilen sonuçlarla tamamen uyumludur.Anahtar Kelimeler: Flux Limiters, LOD metodu, hareketli sınır problemleri, Strang splitting. Numerical Approach for the two-dimensional heat equation problem with convective boundary conditions ABSTRACTIn this work, we extended our earlier study on the solution of two-dimensional heat equation problem by considering a class of time-split finite difference methods. Operator splitting is used as a procedure for computing, some derivatives are computed explicitly and some of them computed implicitly during this procedure. The procedure is second order accurate in time and in (x, y) coordinates. The results of computing by present procedure are in totally compatible with the results obtained previously by other researches.

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“…Both the interface and the outer boundary can be treated in the transform. Various finite difference approaches are analysed 8 . In the fixed grid and the moving-phase boundary methods, the moving boundary is not explicitly considered in the finite difference solution.…”

Section: Introductionmentioning

confidence: 99%

Effect of Boundary Conditions on Freezing in Porous Media

Basu

2004

DSJ

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/"" ' This paper examines a model for coupled heat and mass transfer for freezing in a porous media with Dirichlet and convective boundary conditions. Variables include porosity, heat transfer coefficients, thermal and mass diffusivity, density, latent heat, and boundary temperatures. A simulation for the slab illustrates the appearance of undercooling. A stability criterion for the phase interface is linked with well-known metallurgical parameters like undercooling and freezing rate. A possible mechanism for freckling in ingots of niobium-rich superalloys is examined. It has been shown that heat and mass transfer balance at the interface can affect stability. The effect of boundary conditions on the velocity of freezing is computed for some cases, including the self-freezing process.

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Analysis of two-dimensional diffusion-controlled moving boundary problems

Cited by 74 publications

References 7 publications

Gas absorption with instantaneous chemical reaction in a laminar falling film

Gas absorption with instantaneous chemical reaction in a laminar falling film

İki-Boyutlu Konvektif Sınır Koşullu Erime Problemi İçin Nümerik Yaklaşım

Effect of Boundary Conditions on Freezing in Porous Media

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