Entrance Flows of Electrically Conducting Fluids between Two Parallel Plates : Transient and Steady Flows

In the present paper, using a new finite-element method for incompressible electrically conducting fluid, transient and steady entrance flows are simulated. The GSMAC method is employed as the main algorithm of calculation to satisfy the conservation laws of both mass and magnetic flux. Entrance flows between two parallel plates under a uniform magnetic field are calculated to verify this method. Meanwhile, the entrance length can approximately be expressed as an explicit function of the Hartmann number, using the Oseen approximation and the momentum integral method. Numerical and theoretical results obtained here agree well with other numerical results or exact solutions.