Energy conservation in the one-phase supercooled Stefan problem

T. G. Myers; S. L. Mitchell; F. Font

doi:10.1016/j.icheatmasstransfer.2012.09.005

Energy conservation in the one-phase supercooled Stefan problem

T. G. Myers, S. L. Mitchell, F. Font

Department of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

A one-phase reduction of the one-dimensional two-phase supercooled Stefan problem is developed. The standard reduction, employed by countless authors, does not conserve energy and a recent energy conserving form is valid in the limit of small ratio of solid to liquid conductivity. The present model assumes this ratio to be large and conserves energy for physically realistic parameter values. Results for three one-phase formulations are compared to the two-phase model for parameter values appropriate to supercooled salol (similar values apply to copper and gold) and water. The present model shows excellent agreement with the full two-phase model.

Original language	English
Pages (from-to)	1522-1525
Number of pages	4
Journal	International Communications in Heat and Mass Transfer
Volume	39
Issue number	10
DOIs	https://doi.org/10.1016/j.icheatmasstransfer.2012.09.005
Publication status	Published - Dec 2012

Keywords

Energy conservation
Kinetic undercooling
Phase change
Stefan problem
Supercooling

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10.1016/j.icheatmasstransfer.2012.09.005

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abstract = "A one-phase reduction of the one-dimensional two-phase supercooled Stefan problem is developed. The standard reduction, employed by countless authors, does not conserve energy and a recent energy conserving form is valid in the limit of small ratio of solid to liquid conductivity. The present model assumes this ratio to be large and conserves energy for physically realistic parameter values. Results for three one-phase formulations are compared to the two-phase model for parameter values appropriate to supercooled salol (similar values apply to copper and gold) and water. The present model shows excellent agreement with the full two-phase model.",

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AU - Myers, T. G.

AU - Mitchell, S. L.

AU - Font, F.

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N2 - A one-phase reduction of the one-dimensional two-phase supercooled Stefan problem is developed. The standard reduction, employed by countless authors, does not conserve energy and a recent energy conserving form is valid in the limit of small ratio of solid to liquid conductivity. The present model assumes this ratio to be large and conserves energy for physically realistic parameter values. Results for three one-phase formulations are compared to the two-phase model for parameter values appropriate to supercooled salol (similar values apply to copper and gold) and water. The present model shows excellent agreement with the full two-phase model.

AB - A one-phase reduction of the one-dimensional two-phase supercooled Stefan problem is developed. The standard reduction, employed by countless authors, does not conserve energy and a recent energy conserving form is valid in the limit of small ratio of solid to liquid conductivity. The present model assumes this ratio to be large and conserves energy for physically realistic parameter values. Results for three one-phase formulations are compared to the two-phase model for parameter values appropriate to supercooled salol (similar values apply to copper and gold) and water. The present model shows excellent agreement with the full two-phase model.

KW - Energy conservation

KW - Kinetic undercooling

KW - Phase change

KW - Stefan problem

KW - Supercooling

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VL - 39

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EP - 1525

JO - International Communications in Heat and Mass Transfer

JF - International Communications in Heat and Mass Transfer

IS - 10

ER -

Energy conservation in the one-phase supercooled Stefan problem

Abstract

Keywords

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