Optimization of transient heater settings to provide spatially uniform heating in manufacturing processes involving radiant heating

This article presents an optimization methodology for finding the heater settings that provide spatially uniform transient heating in manufacturing processes involving radiant heating. Equations governing the transient temperature and temperature sensitivity distributions over the product are first derived using an infinitesimal-area technique and then solved numerically to calculate the objective function and gradient vector. Minimization is done using a quasi-Newton algorithm that incorporates an active set method to enforce design constraints. This methodology is demonstrated by finding the optimal transient heater settings of a two-dimensional annealing furnace.