Abstarct: One of the most popular non-contact heating devices is an induction furnace. They are widely in use in most mextal industries to heat and melt mextals due to their excellent thermal efficiency, high production speed, and clean working medium. The available data on induction heating systems are normally obtained from manufacturing environments directly. These experimental methods or trial and error approaches are very time-consuming and non cost-effective. Therefore, numerical methods are highly recommended for induction heating problems. In this study, the basis of induction heating and its advantages over other heating methods have been discussed and then the heat transfer and magnetic fields in a vacuum induction melting furnace (VIM) have been numerically investigated. The induction furnace model employed in this study, has been simulated baxsed on a real industrial model. Induction heating was applied to a ferromagnetic and a non-magnetic material. The temperature behavior in the heated material from furnace startup until the melting temperature of the material has been investigated. Flow density variations and furnace temperature changes are also studied. The total heat sources of an induction furnace include magnetic loss (hysteresis loss) and resistance loss (Foucault). The total loss for both materials have been found. Results indicate that the desired heat generated in ferromagnetic material is greater than that of a non-magnetic material. This fact solely justifies the use of inductions furnaces for ferromagnetic materials. It was attempted to achieve a reasonable model for designing the furnace in small scale by using a parametric approach. The effect of crucible and coil geometry on the time the material reaches its melting point has been examined. Increasing the number of turns in the coil while keeping other parameters constant, will lead to a shorter time for the material to meet its melting point. In this thesis, the effects of the number of coil turns on the furnace have been also explored considering the flow density and inducted flow to be constant. In addition, the effect of the location of the coil around the crucible has been also studied and the results for two different types of materials have been reported. It is claimed that the least gap possible between the turns may lead to the shortest time possible for a material to reach to its melting point.