# Solution of One-Dimensional Stefan Problem with Orthogonal Collocation

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A Stefan problem is a boundary value problem for a partial differential equation in which a phase boundary can move with time. An orthogonal collocation method is used in this Demonstration to solve the one-dimensional Stefan problem with periodic boundary condition.

Contributed by: Jorge Gamaliel Frade Chávez (March 2011)

Open content licensed under CC BY-NC-SA

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Consider the one-dimensional Stefan problem with periodic Dirichlet boundary condition. The diferential equation for this nonlinear problem, expressed in dimensionless form, is given by

where

1) ;

2) ,

3)

This problem has applications in heat and mass transfer, for example, the melting of ice, recrystallization of metals, evaporation of droplets, etc.

Reference: S. Savovic and J. Caldwell, "Finite Difference Solution of One Dimensional Stefan Problem with Periodic Boundary Conditions," *International Journal of Heat and Mass Transfer*, 46(15), 2003 pp. 2911–2916.

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