The nodal integral and finite difference methods are useful in the solution of one-dimensional Stefan problems describing the melting process. However, very few explicit analytical solutions are available in the literature for such problems, particularly with time-dependent boundary conditions. Benchmark cases are presented involving two test examples with the aim of producing very high accuracy when validated against the exact solutions. Test example 1 (time-independent boundary conditions) is followed by the more difficult test example 2 (time-dependent boundary conditions). As a result, the temperature distribution, position of the moving boundary and the velocity are evaluated and the results are validated.

Issue Section:
Technical Notes
Keywords:
finite difference methods, heat transfer, temperature distribution, melting, heat conduction, Finite difference, Heat Transfer, Melting, Moving Boundaries, Numerical Methods, Phase Change
Topics:
Boundary-value problems, Finite difference methods, Heat transfer, Melting, Temperature distribution, Errors, Temperature, Numerical analysis
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 by ASME
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