A FINITE-ELEMENT METHOD FOR STEADY-STATE CONDUCTION ADVECTION PHASE-CHANGE PROBLEMS

A new finite element technique is developed to solve steady-state cond uction-advection problems with a phase change. The energy balance equa tion at the solid/liquid interface is employed to calculate the veloci ty of the solid/liquid interface in the Lagrangian frame. The position of the solid/liquid interface in the Eulerian frame is determined bas ed on the composition of the velocity of the solid/liquid interface in the Lagrangian frame and the steady-state velocity of a rigid body. T he interface position and the finite element mesh are continuously upd ated during an incremental process. No artificial diffusion is needed with this new finite element approach. An analytical solution for soli dification of a pure material with a radiative boundary condition is a lso developed in this paper. Numerical experimentation is conducted an d the corresponding results are compared with analytical solutions. Th e numerical results agree well with analytical solutions.