Solution of One-Dimensional Stefan Problem with Orthogonal Collocation

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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


Snapshots


Details

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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send