Application of inverse analysis to determine the geometric configuration of filament heaters for uniform heating

In typical designs of ovens, it is often desired to determine the position and geometrical configurations of heaters to attain uniform heating of the materials subjected to thermal processes. In this study, uniform temperature and heat flux are prescribed in one of the surfaces of a radiative system, while the shape and position of filament heaters are left to be found. This is equivalent to the inverse problem of the conventional trial-and-error approach. The oven is modeled as a three-dimensional enclosure formed with diffuse-gray walls, and filled with transparent medium. The inverse problem is solved as an optimization problem. The solution is obtained by the generalized extreme optimization (GEO) algorithm, a stochastic global optimization method. The proposed methodology can lead to filament heaters capable of satisfying the two conditions on the design surface with maximum deviation of about 2% and average deviation less than 0.5%.