A novel, efficient and reliable method for thermal process design and optimization. Part I: theory

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The design and optimization of thermal processing of foods needs accurate dynamic models through which to systematically explore new operation policies. Unfortunately, the governing and constitutive equations of thermal processing models usually lead to complex sets of highly nonlinear partial differential equations (PDEs), which are difficult and costly to solve, especially in terms of computation time. We overcome such limitation by using a powerful model reduction technique based on proper orthogonal decomposition (POD) which yields simple, yet accurate, dynamic models still based on sound first principles. Model reduction is carried out by projecting the original set of PDEs on a low dimensional subspace which retains most of the relevant features of the original system. The resulting model consists of a small set of differential and algebraic equations (DAEs) suitable for real-time industrial applications (optimization and control). Further, this approach can be easily adapted to handle complex nonlinear convection-diffusion processes regardless of how irregular the domain geometry might be.