Optimization of industrial processes involving radiant heating, through non-linear programming

Radiant enclosures are often used in manufacturing processes; examples include the rapid thermal processing of semiconductor wafers, automotive paint curing, and baking food products. In these processes, infrared radiant heaters are used to impose a specified temperature history on the product. In order to ensure the homogeneity of the final product and to avoid deformation due to thermal stresses, a uniform temperature must also be maintained over the entire product throughout the process. This paper presents an optimization methodology that determines the optimal transient heater settings by minimizing an objective function defined as the sum of the variance of the temperature from the desired temperature evaluated at discrete locations on the product surface, integrated throughout the duration of the process. The radiation heat transfer analysis is first carried out using an infinitesimal-area technique. The objective function is then minimized using a quasi-Newton method incorporating an active set method in order to enforce design constraints derived from the heater characteristics. This design methodology is demonstrated by solving two industrially-relevant design problems.