A numerical method for the Rubinstein binary-alloy problem in the presence of an under-cooled liquid

Voller, V. R.

doi:10.1016/j.ijheatmasstransfer.2007.04.020

Cited by 12 publications

(12 citation statements)

References 24 publications

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“…of the thermal and solutal fields is done correctly in the numerical treatment, the similarity in the system will implicitly impose these values; see discussion in Voller [9].…”

Section: Similarity Solutionmentioning

confidence: 99%

“…This solution is a special case of the fixed grid enthalpy method developed by Voller [9,11] . The small novelty here is that the method is developed in the context of a general coordinate system (planar, cylindrical or spherical); the previous solution only considered the planar case.…”

Section: A Numerical Solutionmentioning

confidence: 99%

“…The approach can be readily modified to deal with more general problems in one [9] and two [11] dimensions. In the later case, however, imposed crystal anisotropy and surface tension needs to be included to recover a stable crystal growth.…”

Section: In a Similar Vain To Previous Observations By Alexiadesmentioning

confidence: 99%

“…A more careful reading of the literature, however, in particular Chapter XI in the second edition of Carslaw and Jaeger [5], reveals a physically rich selection of analytical solutions with direct relevance to the more general solidification systems of current interest, e.g., the heat conduction controlled solidification of an undercooled melt. Beyond the solutions in Carslaw and Jaeger, other works [6][7][8][9][10]16] develop analytical solutions of general models of solidification, including those that couple both heat and mass (solute) transfer. Together these analytical solutions provide ample opportunity for meaningful verification of the recent crop of sophisticated solidification process models aimed at understanding coupled heat and mass transfer and crystal growth phenomena.…”

Section: Introductionmentioning

confidence: 99%

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Analytical models of solidification phenomena

Voller

2009

Trans Indian Inst Met

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Even as numerical models tackle increasingly complex solidification process and phenomena, analytical test problem can still be constructed to provide meaningful verification for the numerical modeling codes. In this paper, under the assumptions of zero surface energy, no crystal anisotropy, and infinite mobility, an analytical solution for the solidification of a solid seed in an undercooled binary melt is derived. This solution couples two previous literature solutions, one for the solidification of a seed in an undercooled pure melt, the other for the solidification of a binary alloy. The resulting solution provides insight into key crystal growth behavior and provides an excellent test solution for verification of more general multidimensional numerical solidification codes.

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“…of the thermal and solutal fields is done correctly in the numerical treatment, the similarity in the system will implicitly impose these values; see discussion in Voller [9].…”

Section: Similarity Solutionmentioning

confidence: 99%

Section: A Numerical Solutionmentioning

confidence: 99%

Section: In a Similar Vain To Previous Observations By Alexiadesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytical models of solidification phenomena

Voller

2009

Trans Indian Inst Met

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“…The macrosegregation phenomenon and the problem of binary alloy solidification are considered in [8][9][10][11][12][13][14][15][16][17][18]. In some of these articles, for describing the concentration there were used models in which the immediate equalization of the alloy chemical composition in the liquid phase and in the solid phase is assumed (the lever arm rule) [14,[19][20][21][22][23]; in some other articles, the Scheil model was applied [14,[19][20][21][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Numerical Procedure for Heat Transfer Coefficient Identification in Solidification of Binary Alloys and Its Experimental Verification

Hetmaniok

2015

Numerical Heat Transfer, Part B: Fundamentals

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In this article the inverse problem consisting of determination of the heat transfer coefficient in the process of binary alloy solidification is considered. Additional information on the inverse problem is delivered by measurements of temperature at selected points of the cast. In the model discussed, the distribution of temperature is described by means of the heat conduction equation with the substitute thermal capacity, with the liquidus and solidus temperatures varying in dependence on the concentration of the alloy component. For describing the concentration, the Scheil model is used. For solving the direct problem, the finite-difference method supplemented by the generalized alternating phase truncation method is applied. For minimization of the properly constructed functional, the artificial bee colony algorithm is employed. Additionally, the article contains the results of a numerical experiment as well as the results of an experimental verification illustrating the usefulness of the proposed procedure.

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Explicit solutions related to the Rubinstein binary‐alloy solidification problem with a heat flux or a convective condition at the fixed face

Lucas

Cirelli

Tarzia

2023

Math Methods in App Sciences

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Similarity solutions for the two‐phase Rubinstein binary‐alloy solidification problem in a semi‐infinite material are developed. These new explicit solutions are obtained by considering two cases: A heat flux or a convective boundary conditions at the fixed face, and the necessary and sufficient conditions on data are also given in order to have an instantaneous solidification process. We also show that all solutions for the binary‐alloy solidification problem are equivalent under some restrictions for data. Moreover, this implies that the coefficient that characterizes the solidification front for the Rubinstein solution must verify an inequality as a function of all thermal and boundary conditions.

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A numerical method for the Rubinstein binary-alloy problem in the presence of an under-cooled liquid

Cited by 12 publications

References 24 publications

Analytical models of solidification phenomena

Analytical models of solidification phenomena

Numerical Procedure for Heat Transfer Coefficient Identification in Solidification of Binary Alloys and Its Experimental Verification

Explicit solutions related to the Rubinstein binary‐alloy solidification problem with a heat flux or a convective condition at the fixed face

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