Approximate solutions to the Stefan problem with internal heat generation

Crepeau, John; Siahpush, Ali

doi:10.1007/s00231-007-0298-8

Cited by 20 publications

(12 citation statements)

References 13 publications

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“…This matches the steady-state value calculated previously using approximate methods [13]. It also gives the minimum value of Q (>2) for which melting occurs in this geometry.…”

Section: Steady-statesupporting

confidence: 89%

“…The transient portion of the temperature distribution in the liquid phase, Eqs. (13) and (14) can be solved using standard separation of variables techniques [24]. The resulting temperature profile is given as,…”

Section: Problem Descriptionmentioning

confidence: 99%

“…Crepeau and Siahpush [13] found approximate solutions to the Stefan problem with internal heat generation using quasi-static methods, valid for Stefan numbers less than one. Crepeau et al [14,15] then compared those solutions to results from the computational analysis of Spotten [16] and showed good agreement for Stefan numbers less than one.…”

Section: Introductionmentioning

confidence: 99%

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Analytical solutions to the Stefan problem with internal heat generation

McCord

Crepeau

Siahpush

et al. 2016

Applied Thermal Engineering

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“…This matches the steady-state value calculated previously using approximate methods [13]. It also gives the minimum value of Q (>2) for which melting occurs in this geometry.…”

Section: Steady-statesupporting

confidence: 89%

Section: Problem Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical solutions to the Stefan problem with internal heat generation

McCord

Crepeau

Siahpush

et al. 2016

Applied Thermal Engineering

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“…We assume initially that the material is completely liquid and that freezing occurs from the outer portion of the cylinder and moves to the centerline. Previously, Crepeau and Siahpush [15] It is clear from Eq. (21) that when the internal heat generation multiplied by r 0 /2 is equal to the heat flux out of the system, Equation (26) is compared with Eq.…”

Section: Freezing With Constant Surface Heat Flux Boundary Conditionsmentioning

confidence: 88%

Scale/Analytical Analyses of Freezing and Convective Melting With Internal Heat Generation

Siahpush

Crepeau

Sabharwall

2013

Volume 2: Heat Transfer Enhancement for Practical Applications; Heat and Mass Transfer in Fire and Combustion; Heat Transfer In

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Using a scale/analytical analysis approach, we model phase change (melting) for pure materials which generate constant internal heat generation for small Stefan numbers (approximately one). The analysis considers conduction in the solid phase and natural convection, driven by internal heat generation, in the liquid regime. The model is applied for a constant surface temperature boundary condition where the melting temperature is greater than the surface temperature in a cylindrical geometry. The analysis also consider constant heat flux (in a cylindrical geometry).We show the time scales in which conduction and convection heat transfer dominate.

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“…Many different approximations and simplifications have been proposed in this case (see [5] and citations therein). For instance, in [6], under the hypothesis that the Stefan number is lower than one, a quasi-static approximation was discussed and compared in [7] with CFD calculations with and without convection; a good agreement was reported. In [5], closures for the complete set of integral energy equations (liquid, solid and interface) are obtained based on Hermite approximations for integrals that define the average temperatures and boundary heat fluxes.…”

Section: Introductionmentioning

confidence: 99%

On the treatment of plane fusion front in lumped parameter thermal models with convection

Tellier

Skrzypek

Saas

2017

Applied Thermal Engineering

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Within the framework of lumped parameter models for integral codes, this paper focus on the modelling of a two-phase Stefan fusion problem with natural convection in the liquid phase. In particular, this specific Stefan problem is of interest when studying corium pool behavior in the framework of light water reactor severe accident analysis. The objective of this research is to analyze the applicability of different approximations related to the modelling of the solid phase in terms of boundary heat flux closure relations. Three different approximations are considered: a quadratic profile based model, a model where a parameter controls the power partitioning at the interface and the steady state conduction assumption. These models are compared with an accurate fronttracking solution of this plane fusion front problem. This "reference" is obtained by combining the same integral conservation equations as the approximate models with a mesh-based solution of the 1D heat equation. Numerical results are discussed for a typical configuration of interest for corium pool analysis. Different fusion transients (constructed from nondimensionalization considerations in terms of Biot and Stefan numbers) are used in order to highlight the potential and limitations of the different approximations.

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Approximate solutions to the Stefan problem with internal heat generation

Cited by 20 publications

References 13 publications

Analytical solutions to the Stefan problem with internal heat generation

Analytical solutions to the Stefan problem with internal heat generation

Scale/Analytical Analyses of Freezing and Convective Melting With Internal Heat Generation

On the treatment of plane fusion front in lumped parameter thermal models with convection

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