Reliable estimates in the anisotropic heat conduction problems

Abstract. The heat conduction problems for anisotropic bodies are studied taking into account the uncertainties in the material orientation. The best estimations of the upper and lower bounds of the considered energy dissipation functional are based on developing new approach c onsisting in solution of some optimization problems and finding the extremal internal material structures, whic h realize minimal and maximal dissipation. The motivation of this study comes from paper making pr ocesses, and more precisely, drying process, which consumes about 50% of the energy f ed into the paper machine. The understanding of the effect of uncertainties in the process arises from structural properties of paper will provide the possibility to optimize the drying system.