Inverse Radiant Boundary Design for Ensuring Desired Heat Treatment in Vacuum Batch Furnaces

Optimizing heat treatment processes is crucial for achieving optimal product quality within economically and environmentally effective ways. Non-uniformities in heat treatments can have detrimental effects on product quality, resulting in substantial losses in manufacturing efficiency. To optimize these heat treatment processes, this study employs nonlinear least square minimization with the Gauss-Newton algorithm to solve inverse boundary design problems. A vacuum batch furnace has been considered where the desired heat treatment is imposed at the specific locations referred to as design points within the workpiece. Two heater layouts were analyzed, and the required furnace heater temperatures have been successfully determined to achieve the desired heat treatment for both layouts. The findings highlight that ensuring uniform treatment at the design points requires nonuniform heater temperatures. Our analyses reveal that inverse solutions for heat treatment processes provide valuable tools for obtaining a range of desired treatments while highlighting the trade-offs between treatment effectiveness and practical implementation.