ABSTRACT
In this work, the stability properties as well as possible applications of a partial differential equation (PDE) with state-dependent parameters are investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (potential) Burgers’ equation. We show that for certain forms of coefficient functions, the PDE converges to a stationary solution given by (fixed) boundary conditions that make physical sense. These boundary conditions are either symmetric or asymmetric of Dirichlet type. Furthermore, we present an observer design based on the PDE model for estimation of inner-domain temperatures in block-frozen fish and for monitoring freezing time. We illustrate the results with numerical simulations.
Acknowledgements
The authors wish to thank the anonymous referees for their highly appreciated comments, which helped in improving the comprehensibility and readability of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. The standard EN 60584 defines three accuracy classes, where the first allows deviations of ±1.5K