A hybrid inverse method for the thermal design of radiative heating systems

This work applies the inverse analysis for the thermal design of a three-dimensional radiative enclosure formed with diffuse-gray surfaces. The objective is to determine the powers and locations of the heaters to attain prescribed uniform temperature and radiative heat flux on the design surface. The solution is based on a hybrid solution that couples two different approaches to solve the inverse problem, optimization and regularization. The determination of the locations of the heaters is treated via optimization with the generalized extremal optimization (GEO), whereas the evaluation of the required heat inputs in the heaters, a problem that embodies the Fredholm equation of first kind, is achieved through the truncated singular value decomposition (TSVD) regularization of the ill-conditioned system of equations. The results illustrate that the hybrid solution is a more flexible and accurate approach than the explicit solution based on regularization, and less time consuming than the implicit solution based solely on optimization.