Approximate Analytical Method to Stefan Problem for Spheres with Wide Temperature Range of Phase Transition

Ryoichi Chiba

doi:10.4028/www.scientific.net/AMM.627.145

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 627Approximate Analytical Method to Stefan Problem...

Approximate Analytical Method to Stefan Problem for Spheres with Wide Temperature Range of Phase Transition

Abstract:

The two-dimensional differential transform method is applied to solve the one-dimensional phase change problem for a solid sphere with time-dependent boundary temperature. The problem assumes that the phase change occurs over a range of temperatures and the initial temperature of the sphere is an arbitrary constant. An approximate analytical (series) solution is derived for the temperature profile in the melting or solidifying sphere. The solution is based on the apparent specific heat method. Numerical results illustrate the effects of the Stefan number, which is the ratio of sensible heat to latent heat, on the transient temperature profile in the sphere.

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Periodical:

Applied Mechanics and Materials (Volume 627)

Pages:

145-148

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.627.145

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Online since:

September 2014

Authors:

Ryoichi Chiba*

Keywords:

Analytical Solution, Apparent Specific Heat Method, Differential Transform Method, Nonlinear Heat Conduction, Phase Change, Sphere

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* - Corresponding Author

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