### Abstract

In this paper a survey is given concerning to the stochastic modelling approaches in transport processes with a special emphasis on application possibilities for simultaneous heat and mass transfer in drying. First, the mostly used classical modelling methods for drying are discussed which lead to a linear parabolic type of PDE systems supposing constant (stateindependent) conductivity coefficients. Powerful discretisation methods are shown for their solution. Basic principles of variational calculus are discussed then with an attention on direct methods. As a simple application a first-order approximation example is formed, and the solution of the system equation is presented. It is also shown, that the thermodynamical state-dependence of the conductivity coefficients has a crucial influence on the flow pattern of the coupled heat and mass transfer, which is particularly obvious in the cases, when the so-called percolative phase transitions take place. It effects a discrete change of the conductivity coefficients and their probabilities as well. An illustration is shown for percolative phase transition. Describing statistical properties of percolative system the dynamic scaling theory was applied. Characterising the system decay a correlation length was introduced as a parameter. Finally, a simple case of two fields is described together with relevant transfer functions.

Original language | English |
---|---|

Pages (from-to) | 541-559 |

Number of pages | 19 |

Journal | Drying Technology |

Volume | 18 |

Issue number | 3 |

Publication status | Published - 2000 |

### Fingerprint

### Keywords

- Direct variational method
- Drying
- Dynamical scaling theory
- Modelling
- Percolation theory
- Phase transition
- Transport phenomena

### ASJC Scopus subject areas

- Chemical Engineering (miscellaneous)

### Cite this

*Drying Technology*,

*18*(3), 541-559.

**Mathematical and physical foundations of drying theories.** / Farkas, I.; Mészâros, Cs; Bâlint, Á.

Research output: Contribution to journal › Article

*Drying Technology*, vol. 18, no. 3, pp. 541-559.

}

TY - JOUR

T1 - Mathematical and physical foundations of drying theories

AU - Farkas, I.

AU - Mészâros, Cs

AU - Bâlint, Á

PY - 2000

Y1 - 2000

N2 - In this paper a survey is given concerning to the stochastic modelling approaches in transport processes with a special emphasis on application possibilities for simultaneous heat and mass transfer in drying. First, the mostly used classical modelling methods for drying are discussed which lead to a linear parabolic type of PDE systems supposing constant (stateindependent) conductivity coefficients. Powerful discretisation methods are shown for their solution. Basic principles of variational calculus are discussed then with an attention on direct methods. As a simple application a first-order approximation example is formed, and the solution of the system equation is presented. It is also shown, that the thermodynamical state-dependence of the conductivity coefficients has a crucial influence on the flow pattern of the coupled heat and mass transfer, which is particularly obvious in the cases, when the so-called percolative phase transitions take place. It effects a discrete change of the conductivity coefficients and their probabilities as well. An illustration is shown for percolative phase transition. Describing statistical properties of percolative system the dynamic scaling theory was applied. Characterising the system decay a correlation length was introduced as a parameter. Finally, a simple case of two fields is described together with relevant transfer functions.

AB - In this paper a survey is given concerning to the stochastic modelling approaches in transport processes with a special emphasis on application possibilities for simultaneous heat and mass transfer in drying. First, the mostly used classical modelling methods for drying are discussed which lead to a linear parabolic type of PDE systems supposing constant (stateindependent) conductivity coefficients. Powerful discretisation methods are shown for their solution. Basic principles of variational calculus are discussed then with an attention on direct methods. As a simple application a first-order approximation example is formed, and the solution of the system equation is presented. It is also shown, that the thermodynamical state-dependence of the conductivity coefficients has a crucial influence on the flow pattern of the coupled heat and mass transfer, which is particularly obvious in the cases, when the so-called percolative phase transitions take place. It effects a discrete change of the conductivity coefficients and their probabilities as well. An illustration is shown for percolative phase transition. Describing statistical properties of percolative system the dynamic scaling theory was applied. Characterising the system decay a correlation length was introduced as a parameter. Finally, a simple case of two fields is described together with relevant transfer functions.

KW - Direct variational method

KW - Drying

KW - Dynamical scaling theory

KW - Modelling

KW - Percolation theory

KW - Phase transition

KW - Transport phenomena

UR - http://www.scopus.com/inward/record.url?scp=0342699494&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0342699494&partnerID=8YFLogxK

M3 - Article

VL - 18

SP - 541

EP - 559

JO - Drying Technology

JF - Drying Technology

SN - 0737-3937

IS - 3

ER -