Model reduction in numerical heat transfer problems

Four recent model reduction schemes, namely, balanced truncation, singular perturbation balanced truncation, Hankel norm approximation, and H_∞ norm approximation are applied to a two-dimensional transient heat conduction problem. The approximations of these four model reduction methods for step response in temperature variation were compared with the finite difference model. It is found that a substantial model order reduction for heat transfer problem is possible. The results are encouraging and attractive especially for the purpose of simulation and control problems.