Numerical Modeling of Solidification Process

Mochnacki, B.

doi:10.5772/24496

Cited by 15 publications

(19 citation statements)

References 14 publications

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“…The artificial internal heat source contains the coupling factor with (3), the solution of (22) requires the knowledge of the solution to equation (3). In a similar way the other equations creating the sensitivity ( ) t x U , model can be obtained.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Sensitivity of transient temperature field in the casting domain with respect to latent heat perturbations

Tuzikiewicz

2014

J. Appl. Math. Comput. Mech.

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Abstract. The mathematical model of thermal processes in the casting domain can be formulated using the fixed domain approach. The energy equation corresponding to this model contains the parameter called a substitute thermal capacity (STC), in which the alloy latent heat appears. The aim of considerations is the application of sensitivity analysis methods for estimation of temperature field changes due to the perturbations of alloy latent heat. In this the analytical form of STC results from the consideration concerning the lever arm model and the Scheil model. The equations determining the sensitivity function are found using the so-called direct approach. At the stage of numerical modeling the finite difference method is used. In the final part of the paper the example of computations is shown.

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Section: Sensitivity Analysismentioning

confidence: 99%

Sensitivity of transient temperature field in the casting domain with respect to latent heat perturbations

Tuzikiewicz

2014

J. Appl. Math. Comput. Mech.

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“…Because for T l < T S : S(T l ) = 1, this means dS(T l )/dT l = 0 and for T l > T L : S(T L ) = 0, this means dS(T l )/dT l = 0, the definition of substitute thermal capacity of lattice can be extended on the whole domain [7,8,9]. If one assumes that…”

Section: T X T T X T C T T T X X G T T X T T X Tmentioning

confidence: 99%

“…The problem is solved using finite difference method [8] under the assumption that Δt = 0.0001 ps and h x = 1 nm. Figure 2 shows the changes of electrons and lattice temperatures at the irradiated surface.…”

Section: Examples Of Computationsmentioning

confidence: 99%

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Numerical Modeling of Melting Process of Thin Metal Films Subjected to the Short Laser Pulse

Majchrzak¹,

Dziatkiewicz²

2012

Archives of Foundry Engineering

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Thin metal film subjected to a short-pulse laser heating is considered. The parabolic two-temperature model describing the temporal and spatial evolution of the lattice and electrons temperatures is discussed and the melting process of thin layer is taken into account. At the stage of numerical computations the finite difference method is used. In the final part of the paper the examples of computations are shown.

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“…At the stage of this source function construction the thermal processes proceeding in the micro scale are taken into account. A capacity of source function is proportional to the crystallization rate, more precisely, to time derivative of function f S (x, t) corresponding to the local and temporary volumetric fraction of solid state at the point considered [3][4][5][6] and the kinetics of nucleation and nuclei growth determines the local and temporary value of this function. It is assumed that the driving force of nucleation and nuclei growth is the undercooling below the solidification point T * .…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis of the crystallization model with respect to cooling conditions

Szopa

Tuzikiewicz

Siedlecki

2013

J. Appl. Math. Comput. Mech.

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Abstract. In the paper the pure metal crystallization process is considered. The cooling conditions of the metal domain are determined by the mould dimensions and thermophysical parameters of the mould material (volumetric specific heat and thermal conductivity). The mathematical model of heat transfer processes proceeding in the system metal -mould is created by the system of heat diffusion partial differential equations corresponding to the sub-domains considered supplemented by the adequate geometrical, physical and boundary-initial conditions. The sensitivity model determining the perturbations of thermal processes due to the perturbations of cooling processes can be constructed using the direct approach (differentiation with respect to parameters analyzed) or using the differential quotients. Both approaches will be discussed in the paper presented.

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Numerical Modeling of Solidification Process

Cited by 15 publications

References 14 publications

Sensitivity of transient temperature field in the casting domain with respect to latent heat perturbations

Sensitivity of transient temperature field in the casting domain with respect to latent heat perturbations

Numerical Modeling of Melting Process of Thin Metal Films Subjected to the Short Laser Pulse

Sensitivity analysis of the crystallization model with respect to cooling conditions

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