### Abstract

A mathematical description of a complete package or packed bed dyeing machine is developed. The processes of convection, dispersion, absorption and desorption of dye to and from the packed bed of fibres are modelled, while account is also taken of the addition of dye to, and the possible removal of liquor from, the mixing tank. A numerical simulation of the mathematical model based on finite differences is developed and numerical results presented. Techniques for monitoring the accuracy of the results based on conservation properties of the system are discussed. Formulae for the expected theoretical steady states of the system are also given. The significance of this study lies in the fact that the dynamic behaviour of an actual machine may be studied as all sections of the equipment are accounted for in the mathematical model. This leads to the ability to design and control such machinery with great precision in a way which has never been achieved before. © 1985.

Original language | English |
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Pages (from-to) | 33-39 |

Number of pages | 7 |

Journal | Applied Mathematical Modelling |

Volume | 9 |

Issue number | 1 |

Publication status | Published - Feb 1985 |

### Keywords

- finite differences
- mathematical model
- package dyeing machine

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## Cite this

*Applied Mathematical Modelling*,

*9*(1), 33-39.