The hardness of heat treated steel and probability of occurrence of quenching cracks depend on the cooling time and temperature distribution. Therefore, the investigation of cooling process is a crucial issue in heat treatment to evaluate the obtained structure of the work-piece. In the present work, a vertical hollow circular cylinder is heated up to a specific temperature by a moving coil at a given velocity along it, and the heated parts then quenched by a moving water–air spray. After passing the spray, the cylinder is cooled by natural convection with the surrounding air. An analysis of coupled magnetic problem and transient conjugated thermal problem between the solid and the surrounding air is performed using finite-element method to obtain temperature field in each time step. This procedure includes moving boundary conditions, effect of radiation with ambient, temperature-dependent properties, and change in magnetic permeability of specified alloy at the Curie temperature. The obtained results show how both spray and natural cooling affect the temperature distribution and rate of cooling of the cylinder. Furthermore, the effect of geometry and velocity of coil on the rate of cooling and chance of quenching cracks are investigated.

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