Abstract
Stefan problem is a problem involving phase transition from solid to liquid or vice versa where boundary between solid and liquid regions moves as function of time. This paper presents numerical solution of one-dimensional two-phase Stefan problem by using finite element method. The governing equations involved in Stefan problem consist of heat conduction equation for solid and liquid regions, and also transition equation in interface position (moving boundary). The equations are difficult to solve by ordinary numerical method because of the presence of moving boundary. As consequence, the equations is reformulated into the form of internal energy (enthalpy). By the enthalpy formulation, solution of the heat conduction equations is no longer concerning the phase state of material. The advantage of the enthalpy formulation is that, finite element method can be easily implemented to solve Stefan problem. Numerical simulation of interface position, temperature profile, and temperature history has good agreement with the exact solution. The approximation of interface position using finite element method was found that it is more accurate than the approximation by using Godunov method. The simulation results also reveal that the finite element method for solving Stefan problem have smaller mean absolute error than the Godunov method.
Highlights
S TEFAN problem is a problem related to phase change, from solid to liquid or from liquid to solid, where the boundary between the solid and liquid regions moves as functionReceived on Jan 2019
This paper focuses on numerical solution of onedimensional two-phase Stefan problem using finite element method
Numerical results of finite element simulation will be compared with exact solution and numerical solution by using Godunov method which has been discussed in [13]
Summary
S TEFAN problem is a problem related to phase change, from solid to liquid (melting) or from liquid to solid (solidification), where the boundary between the solid and liquid regions moves as function. The governing equations involved in the Stefan problem are heat conduction equations for the solid and liquid regions, and an equation connecting solid and liquid regions which is called a moving boundary. The essence of solving Stefan problem is to find solutions of heat conduction equations for solid and liquid regions and the moving boundary. Solving the heat conduction equation is not really difficult, but when the boundary is moving, the solution of the heat conduction equations becomes complicated. The presence of moving boundary is main characteristic of the Stefan problem and is part of the solution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
