A heat equation for freezing processes with phase change: stability analysis and applications

Christoph Josef Backi, Jan Dimon Bendtsen, John-Josef Leth, Jan Tommy Gravdahl

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

3 Citationer (Scopus)

Resumé

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.
OriginalsprogEngelsk
TidsskriftInternational Journal of Control
Vol/bind89
Udgave nummer4
Sider (fra-til)833-849
ISSN0020-7179
DOI
StatusUdgivet - 2016

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Freezing
Partial differential equations
Boundary conditions
Fish
Hot Temperature
Monitoring
Computer simulation
Temperature

Citer dette

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A heat equation for freezing processes with phase change : stability analysis and applications. / Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John-Josef; Gravdahl, Jan Tommy.

I: International Journal of Control, Bind 89, Nr. 4, 2016, s. 833-849.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - A heat equation for freezing processes with phase change

T2 - stability analysis and applications

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AU - Bendtsen, Jan Dimon

AU - Leth, John-Josef

AU - Gravdahl, Jan Tommy

PY - 2016

Y1 - 2016

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AB - 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.

KW - Distributed parameter systems

KW - Stability Analysis

KW - Observer Design

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