Discretisation of the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements

Abstract

-The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.

Kinetic approach to modeling the freezing porous media: Application to the food freezing

“…In expressions ( [16,20,22], and we use for solving the appropriate approximation functions -Eq. (2.10) and Eq.…”

“…The study of these properties and states is inseparable and, in addition, important part of the thermal and physical analysis in theoretical and experimental aspects. It is also known that the cryogenic actions effect on the media texture formation and vary its thermal and physical properties [16,20,[39][40].…”

“…One of important subjects of the problem is the determination of the time required for transition of the system to the equilibrium state. This relaxation time (and equilibrium unfrozen water content) can be obtained from the experimental investigations (see for example [20][21][22]). …”

“…The models presented in the literature on the food freezing are based on the quasi-steady state statement or on the basis of heat transfer process [20,[30][31][32]. As an example we discuss briefly the analytical Plank's solution [31,32] for estimation of freezing time, which is based on the Stefan problem in the classical form.…”

Heat transfer analyses using computational fluid dynamics in the air blast freezing of guava pulp in large containers

“…One of the most recommended equations (Cleland, 1990;Delgado and Sun, 2001;Resende et al, 2007) for predicting the freezing time of one-dimensional foodstuffs (t f,slab ) is the method of Pham (1986).…”