Implementation of the heat balance in the finite element solution to the temperature field of the plastically deformed material

•The paper shows mathematical model of heat transfer in plastic deformation process.•To determine the temperature of the deformed material transient FEM has been used.•Solution improvement by determination of the heat balance in the control volume.•The results of numerical calculations have been experimentally verified.•The surface temperature is higher in the case of algorithm with the heat balance.

The paper presents mathematical model of heat transfer employed to determine the temperature field of the material subjected to plastic deformation. To determine the temperature of the deformed material transient finite element model has been used. The numerical model is based on the Galerkin weighed residual method. Accuracy of the finite element method solution to the temperature field has been validated based on the heat balance of the system. The developed solution allows modeling subsequent operations of the metal forming process of the work piece drawing out. The work piece temperature field is computed for cooling in air, forging, heating and reheating operations. The results of numerical calculations have been experimentally validated by thermo vision measurements performed at metallurgical plant.