The solution of a two-dimensional freezing problem including convection effects in the liquid region

Kroeger, P.G.; Ostrach, Simon

doi:10.1016/0017-9310(74)90120-3

Cited by 75 publications

(15 citation statements)

References 11 publications

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“…To determine the temperature distribution in the solid and liquid domains Eqs". (17) to (19) Equations (2) (17) and (18) are more difficult to solve.…”

Section: Description Of the Problemmentioning

confidence: 99%

“…However, in recent years, the study of fluid flow in the melt and the study of the effects of fluid flow on the solid-liquid interface morphology has acquired major importance [1,[4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Fluid flow due to natural convection occurs in a majority of solidification processes where parts of the melt are at a temperature higher than the phase transition temperature.…”

Section: Introductionmentioning

confidence: 99%

“…Kroeger and Ostrach [17], solved the freezing problem in the presence of natural convection for a two dimensional continuous slab casting problem. They used iterative finite difference and conformal transformation of the domain.…”

mentioning

confidence: 99%

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A finite element method for the study of solidification processes in the presence of natural convection

Yoo

Rubinsky

1986

Numerical Meth Engineering

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A new numerical technique has been developed for the analysis of two‐dimensional transient solidification processes in the presence of time‐dependent natural convection in the melt. The method can cope with irregular, transient morphologies of the solid—liquid interface using a new Galerkin formulation for the energy balance on the solid—liquid interface. The finite element solution to the Galerkin formulation yields the displacement of individual nodes on the solid—liquid interface. The displacement of the nodes is expressed by uncoupled components in the x and y directions. The fluid flow problem was solved using a ‘penalty’ formulation. Numerical experiments were performed for Rayleigh numbers as high as 106 to demonstrate the method and to indicate the effect of natural convection on the solid—liquid interface morphology.

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“…To determine the temperature distribution in the solid and liquid domains Eqs". (17) to (19) Equations (2) (17) and (18) are more difficult to solve.…”

Section: Description Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A finite element method for the study of solidification processes in the presence of natural convection

Yoo

Rubinsky

1986

Numerical Meth Engineering

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“…Fortunately it was found that even very strong natural convection through the interface, has negligible effect on the interface position [23][24]. This fact lets to provide analytical solution to some simplified cases.…”

Section: Rectangular Finned Containermentioning

confidence: 96%

“…Thermo-physical parameters: ρ , c p,l , c p,s , k l , k s , L, l α , s α , all are constant. Its similarity solution could be obtained as [11]: (24) where X(t) is the solid-liquid interface, Table 1. Left wall is set to C°600 and its initial temperature is equal with C°700 .…”

Section: Code Verificationmentioning

confidence: 99%

Lattice Boltzmann application on the PCM solidification within a rectangular finned container

Talati

Taghilou

2015

Applied Thermal Engineering

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Numerical Modelling of Twin-Roll Casting by the Coupled Fluid Flow and Heat Transfer Model

Chang

Weng

1997

Int. J. Numer. Meth. Engng.

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SUMMARYThe twin-roll process is modelled by a coupled fluid flow and phase change model by means of a versatile finite element method. Here, a simple numerical scheme is proposed to solve the problem of determining the interface shape under the thermal equilibrium condition. The procedure is based on a finite element method using a transform technique. The simple numerical method provides an efficient and accurate way to find the interface position and shape with arbitrary boundary geometry. This method can easily be implemented on the existing finite element program, and provides a simple and efficient tool to simulate the solidification as well as the fluid flow problem of the twin-roll casting process.

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The solution of a two-dimensional freezing problem including convection effects in the liquid region

Cited by 75 publications

References 11 publications

A finite element method for the study of solidification processes in the presence of natural convection

A finite element method for the study of solidification processes in the presence of natural convection

Lattice Boltzmann application on the PCM solidification within a rectangular finned container

Numerical Modelling of Twin-Roll Casting by the Coupled Fluid Flow and Heat Transfer Model

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