Perturbative analysis of planar phase change processes with time-dependent temperature at the boundary

Ch Charach; M. Huleihil; Y. Zarmi

doi:10.1063/1.341230

Perturbative analysis of planar phase change processes with time-dependent temperature at the boundary

Ch Charach, M. Huleihil, Y. Zarmi

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Abstract

The perturbation method developed recently for analysis of planar phase change processes is extended to the case of time-dependent temperature boundary conditions. Approximate solutions uniformly valid in time are derived. The role of time scales, that of the driving signal and the (time-dependent) response time of the emerging phase, in the dynamics of a weakly nonlinear melting process is clarified. The short and long time asymptotics are studied in detail. The analytical results are compared with the numerical solution for the problem of melting in a semi-infinite slab induced by a periodically varying boundary condition.

Original language	English
Pages (from-to)	4832-4837
Number of pages	6
Journal	Journal of Applied Physics
Volume	64
Issue number	10
DOIs	https://doi.org/10.1063/1.341230
State	Published - 1 Dec 1988

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Physics and Astronomy (all)

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10.1063/1.341230

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title = "Perturbative analysis of planar phase change processes with time-dependent temperature at the boundary",

abstract = "The perturbation method developed recently for analysis of planar phase change processes is extended to the case of time-dependent temperature boundary conditions. Approximate solutions uniformly valid in time are derived. The role of time scales, that of the driving signal and the (time-dependent) response time of the emerging phase, in the dynamics of a weakly nonlinear melting process is clarified. The short and long time asymptotics are studied in detail. The analytical results are compared with the numerical solution for the problem of melting in a semi-infinite slab induced by a periodically varying boundary condition.",

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N2 - The perturbation method developed recently for analysis of planar phase change processes is extended to the case of time-dependent temperature boundary conditions. Approximate solutions uniformly valid in time are derived. The role of time scales, that of the driving signal and the (time-dependent) response time of the emerging phase, in the dynamics of a weakly nonlinear melting process is clarified. The short and long time asymptotics are studied in detail. The analytical results are compared with the numerical solution for the problem of melting in a semi-infinite slab induced by a periodically varying boundary condition.

AB - The perturbation method developed recently for analysis of planar phase change processes is extended to the case of time-dependent temperature boundary conditions. Approximate solutions uniformly valid in time are derived. The role of time scales, that of the driving signal and the (time-dependent) response time of the emerging phase, in the dynamics of a weakly nonlinear melting process is clarified. The short and long time asymptotics are studied in detail. The analytical results are compared with the numerical solution for the problem of melting in a semi-infinite slab induced by a periodically varying boundary condition.

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Perturbative analysis of planar phase change processes with time-dependent temperature at the boundary

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