An explicit solution for an instantaneous two-phase Stefan problem with nonlinear thermal coefficients

Briozzo, Adriana C.

doi:10.1093/imamat/67.3.249

Cited by 20 publications

(22 citation statements)

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“…Explicit solutions are given in (Briozzo et al, 2007(Briozzo et al, & 2010Briozzo & Tarzia, 2002;Natale & Tarzia, 2006;Rogers & Broadbridge, 1988;Tirskii, 1959;Tritscher & Broadbridge, 1994) where nonlinear thermal coefficients are considered and in (Natale & Tarzia, 2000;Rogers, 1986) for Storm's materials.…”

Section: The Stefan Solution For the Planar Phase-change Surface Movimentioning

confidence: 99%

Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

Tarzia¹

2011

Advanced Topics in Mass Transfer

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Section: The Stefan Solution For the Planar Phase-change Surface Movimentioning

confidence: 99%

Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

Tarzia¹

2011

Advanced Topics in Mass Transfer

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“…In most situations, the Stefan problem can only be solved numerically; however, finding analytical solutions for the problem has always been of great interest to the researchers. It is encouraging to see that many analytical solutions, which take into account complicated conditions such as nonlinear thermal properties, variable latent heat, and different types of boundaries, have been developed [17][18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

One-dimensional non-Darcy flow in a semi-infinite porous media: a multiphase implicit Stefan problem with phases divided by hydraulic gradients

Zhou

Shi

2017

Acta Mech. Sin.

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One-dimensional non-Darcy flow in a semiinfinite porous media is investigated. We indicate that the non-Darcy relation which is usually determined from experimental results can always be described by a piecewise linear function, and the problem can be equivalently transformed to a multiphase implicit Stefan problem. The novel feature of this Stefan problem is that the phases of the porous media are divided by hydraulic gradients, not the excess pore water pressures. Using the similarity transformation technique, an exact solution for the situation that the external load increases in proportion to the square root of time is developed. The study on the existence and uniqueness of the solution leads to the requirement of a group of inequalities. A similar Stefan problem considering constant surface seepage velocity is also investigated, and the solution, which we indicate to be uniquely existent under all conditions, is established. Meanwhile, the relation between our Stefan problem and the traditional multiphase Stefan problem is demonstrated. In the end, computational examples of the solution are presented and discussed. The solution provides a useful benchmark for verifying the accuracy of general approximate algorithms of Stefan problems, and it is also attractive in the context of inverse problem analysis.

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“…Over the past decades, many complicated conditions for the problem such as nonlinear thermal properties, different types of boundaries have been considered, and corresponding exact solutions have been developed [1][2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Exact solution for Stefan problem with general power-type latent heat using Kummer function

Zhou

Li-jiang

2015

International Journal of Heat and Mass Transfer

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An explicit solution for an instantaneous two-phase Stefan problem with nonlinear thermal coefficients

Cited by 20 publications

References 0 publications

Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

Explicit and Approximated Solutions for Heat and Mass Transfer Problems with a Moving Interface

One-dimensional non-Darcy flow in a semi-infinite porous media: a multiphase implicit Stefan problem with phases divided by hydraulic gradients

Exact solution for Stefan problem with general power-type latent heat using Kummer function

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