A continuous- or intermittent-melt induction furnace useful for heating and/or melting semi-conductor or other materials includes an induction coil, a susceptor switchable between open and closed electric circuit modes, and a crucible. The susceptor is inductively or resistively heated in the closed circuit mode and transfers heat to material in the melting cavity to make it susceptible to inductive heating. The susceptor is then switched to the open circuit mode and the susceptible material is directly inductively heated to melt remaining solid material. A cone-shaped flow guide in the melting cavity improves molten material flow to improve the ability to draw small-particle material into the melt and increase crucible life due to improved heat uniformity. A trap passage communicating with the melting cavity and an exit opening in the crucible allows the flow of material through the exit opening to be controlled by pressure differentials on either side of the trap passage.