Modeling, approximation, and time optimal temperature control for binder removal from ceramics

Abstract

<p style='text-indent:20px;'>The process of binder removal from green ceramic components-a reaction-gas transport problem in porous media-has been analyzed with a number of mathematical techniques: 1) non-dimensionalization of the governing decomposition-reaction ordinary differential equation (ODE) and of the reaction gas-permeability partial differential equation (PDE); 2) development of a pseudo steady state approximation (PSSA) for the PDE, including error analysis via <inline-formula><tex-math id="M1">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula> norm and singular perturbation methods; 3) derivation and analysis of a discrete model approximation; and 4) development of a time optimal control strategy to minimize processing time with temperature and pressure constraints. Theoretical analyses indicate the conditions under which the PSSA and discrete models are viable approximations. Numerical results indicate that under a range of conditions corresponding to practical binder burnout conditions, utilization of the optimal temperature protocol leads to shorter cycle times as compared to typical industrial practice.</p>